Game-theoretic implications for uncovering the effects of virtual tipping in complex user networks

Abstract

Consumer-generated media (CGM), including social live streaming service (SLSS), often incorporate gamification elements to engage users. Online virtual tips and gifts, such as “bits” in Twitch, exemplify this approach by fostering interactive dynamics between live streamers and their audience. However, issues remain in understanding the impact of (virtual) tips on user behavior and how platform commissions, which are partly collected from the tips provided by other users, influence the platform’s overall revenue and user behavioral strategies. This study considers a CGM/SLSS platform, such as Twitch, as a variation of the public goods game and proposes a game-theoretical model integrated with a platform-mediated tipping system with a certain commission rate. In experiments, the proposed model was applied to artificial and actual SLSS networks, demonstrating that the influence of a tipping system on user behavior is significant, impacting the motivation for live streaming and the effort to improve its quality. Depending on individual preferences for psychological or monetary reward, the commission rate is determined by the platform depending on the users’ network positions, such as the degree of connectivity, which corresponds to the number of followers/followees in SLSS networks. Our findings offer valuable insights into the design and management of SLSS platforms and further suggest that there may be an appropriate commission rate to maximize platform revenue.

Introduction

Social live streaming services (SLSS), including YouTube Live, Twitch, YouNow, and Taobao, are used by a wide variety of people worldwide. The real-time streaming provided by SLSS serves as daily entertainment for people and is also a means of revenue for profit-seeking professional gamers (Kaytoue et al. 2012). Further uses of SLSS include e-commerce (Sun et al. 2019; Wongkitrungrueng and Assarut 2020), online education (Lu et al. 2018), and facility promotion through live streaming (Lau 2020).

SLSS and social networking services (SNS) are instances of consumer-generated media (CGM), a type of media that can be sustained by voluntary user participation, such as posting, streaming, and commenting. Unlike traditional media such as newspapers, magazines, and TVs, which only unilaterally publish articles/videos produced by professional writers and production companies, participatory behaviors in CGM require users to create articles/videos, which imposes costs on individual users (Woodcock and Johnson 2019). Therefore, user behavior appears somewhat irrational; however, there are certain incentives in return because CGMs help construct social relationships (Hilvert-Bruce et al. 2018), share information within a community (Kapoor et al. 2018), and provide psychological satisfaction to users, such as the desire for self-expression and a sense of belonging (Nadkarni and Hofmann 2012). Such psychological incentives are also induced by user content and responses. To enhance the incentives, major SNS functions have comments, reposts, meta-comment, and “like!” buttons to promote participatory behavior (Toriumi et al. 2012; Hirahara et al. 2014). Furthermore, monetary rewards are being increasingly offered by the SNS from platforms in addition to psychological rewards from other users, such as providing advertising revenue to contributors according to certain criteria. Monetary rewards have been found to encourage user participation by granting money to contributors at the appropriate time (Usui et al. 2022, 2024).

Similarly, the SLSS employ a variety of mechanisms to provide incentives. For example, an activities community formed by the commenting behavior of video/streaming viewers promotes the desire to watch the streaming (Bründl et al. 2017) and provides a virtual third place for community formation (Hamilton et al. 2014). Various gamification elements (Scheibe and Zimmer 2019) exist as mechanisms to realize these elements. Comments, stamps, and a display of the number of viewers in real time are examples of gamification that satisfy the streamer’s desire for self-expression, motivate viewers to comment, and satisfy their desire to assert themselves (Scheibe 2018; Scheibe et al. 2016).

In addition to providing these gamified incentives, the SLSS possess distinctive elements, such as direct money transfers, virtual gifts, and virtual tips from viewers rather than from the platform or a commercial company. This includes Super Chat on YouTube Live and Twitch bits, which allow viewers to highlight their comments and transfer money (or equivalent rewards) directly to the streamer after a certain commission rate that is deducted by the media platform to express appreciation for the stream content. Therefore, streamers can garner benefits, and viewers who offer virtual gifts and tips can receive direct reactions from streamers and other associated psychological rewards. Indeed, the purchase of virtual gifts or tips is a behavior to obtain a desired streamer’s performance or appreciation (Xu et al. 2022), as well as attract the attention of the crowd and express one’s own opinion on the stream content (Lee et al. 2019). Furthermore, the expectation of a direct response from the streamer is one reason for offering virtual tips (Hou et al. 2020), which is also considered the motivation for viewing streams (Scheibe 2018). Although motivations and prevalence of virtual gifts and tips in SLSS have been studied, their impact on user behavior and the benefits to the media platforms have not been sufficiently discussed theoretically.

Therefore, we propose a game-theoretical model with virtual tipping behavior between users by extending the SNS-norms game (SNS-NG) (Hirahara et al. 2014), which is the basic SNS/CGM model for user behavior, assuming the posted items (including articles and streams) to be public goods. The impact of such tips on user strategies and the platform revenue specified by the commission rate are then experimentally investigated assuming that in a realistic situation, user behavioral strategies are not uniform but diverse, depending on the topological structure of local connections for each user and the strategies of its neighboring agents. To investigate diverse behavioral strategies, we analyzed the users’ emerging strategies that co-evolve with the multiple world genetic algorithm (MWGA) (Miura et al. 2019), showing how the commission rates of virtual tips affect behavior, which impacts platform revenue. We believe that the implications of our experimental results will enable media-independent discussions and help design the implementation of monetary rewards that can be circulated among users on SLSS and SNS after deducting commissions.

Related work

Many studies have discussed CGM, including SNS and SLSS. For example, Sjöblom and Hamari (Sjöblom and Hamari 2017) examined Twitch streaming data, determining that the motivation for watching live game playing revolves around social integrative factors, allowing users to be deeply involved in the community, gather information, experience emotions, and find distraction. Lim et al. (2020) introduced a structural equation model and revealed that the reasons for recurrent viewing on SLSS can be psychological immersion in conversations and the aspiration to become part of a community.

A few studies have focused on the effects of virtual tips and gifts on user attitudes and behaviors in CGM. For example, Xu et al. (2022) indicated that the motivation for providing virtual tips is mostly anchored in individuals’ appreciation of the enjoyment of the streamer’s performance and the knowledge gained from its content. Zhou et al. (2019) used text-mining techniques to show that (virtual) tips and gifts are influenced by the number of words in comments, especially words describing excitement. Lin et al. (2021) found that when streamers are happy, viewers are also happy, and the tipping activity is increased. Furthermore, Li and Peng (2021) found that the attractiveness and credibility of streamers stimulate user emotions and facilitate virtual tipping. Lee et al. (2019) argued that virtual tipping captures viewers’ attention and communicates the desired topics of the tip providers to both streamers and their communities. As a negative aspect, Lee et al. (2019) pointed out that users may be negatively affected by the inconvenience, inaccessibility, and unaffordability related to tipping. However, it should be noted that these studies are based on empirical and statistical studies conducted on specific platforms and may not necessarily represent theoretical arguments applicable to all platforms.

Furthermore, many model-based studies have explored the characteristics of CGM. For instance, Chalakudi et al. (2023) used an evolutionary game to elucidate how user sentiments and emotions influence changes in streaming and related environments. Other studies examined the effects of psychological rewards on CGM using evolutionary theoretical games. For example, Toriumi, Yamamoto, and Okada (Toriumi et al. 2012) found that CGMs exhibit characteristics similar to public goods (Axelrod 1986) and introduced the concept of meta-reward game inspired by Axelrod’s meta-norm game. They found that meta-comments, that is, comments returned in response to an article/video can play an important role in motivating voluntary participation. The meta-reward game was later modified as SNS-NG (Hirahara et al. 2014) to better align with the nature of SNS. Meta-comments in SNS are usually posted by users who have already posted their first article/video. Usui et al. (2022) extended this to explore the impact of monetary incentives provided by SNS platforms and identify general dominant behaviors. However, this model does not consider the tips exchanged between users, such as the virtual tips seen in SLSS, despite constituting monetary rewards. It is also assumed that the dominant strategies of all users are uniform without considering users’ local connectivities and strategies of their neighbors, which we do consider.

Among studies considering monetary rewards, Axelrod (2023); Usui et al. (2024) adopted a game-theoretical model to explore the impact of monetary rewards. However, they assumed that monetary rewards are provided by a platformer to increase activities (Usui et al. 2024) or that the experiments are limited to artificial networks (Axelrod 2023). Therefore, we conducted extensive experiments on real-world networks collected from Facebook and Twitch, comparing the results between artificial and realistic networks. We further investigated the effects of commission rates on user behavior and the dependence among commission rate, platformer’s revenue, and activities of users who provide virtual tips as well as post articles as contributors in live streams.

Fig. 1

Flow of SNS-norms game with monetary rewards and quality

Background

SNS-norms game with monetary rewards and quality

The SNS-norm game with monetary rewards and quality (SNS-NG/MQ) (Usui et al. 2022) is an extension of SNS-NG and an abstract model that represents user behavior on CGM/SNS with uniform monetary rewards from the media platform. In this game, a user is modeled as an agent $a_i \in A$, where $A=\{a_1, \dots , a_N\}$ denotes the set of N agents. Connectivities between agents are represented by graph $G=(A,E)$; therefore, each agent corresponds to a node in $A$ and connections between agents are represented by $(a_i,a_j) \in E$, indicating the follower/followee or friend relationship between agents $a_i$ and $a_j$. We also define the set of neighboring agents of $a_i$ as $N_{a_i}=\{a_j \in A \mid (a_i,a_j) \in E \}$. The number of neighboring agents (i.e., number of edges) of $a_i$, denoted by $\textit{deg}(a_i)=|N_{a_i}|$, is called the degree of $a_i$.

An agent in SNS-NG/MQ has probabilistic parameters $B_i$, $Q_i$, $L_i$, and $M_i$ ($0 \le B_i,Q_i,L_i,M_i \le 1$), determining its own potential behavioral strategy. The posting rate $B_i$ represents the $a_i$’s potential willingness to post an item on CGM, and $Q_i$ denotes the quality of an item, that is, the extent to which $a_i$ is inclined to improve the quality of the posting content. Parameter $L_i$ is the comment/meta-comment rate, representing the willingness to comment on an item posted by the agent (viewer) in $N_{a_i}$ or commenting in response to a comment from the viewer. These values constituting $a_i$’s strategy are learned using algorithms such as the genetic algorithm (GA) to maximize the total reward in the game. The monetary preference $M_i$ expresses the extent of preference for monetary rewards over psychological ones. Because this seems to be an intrinsic preference, $M_i$ is assumed to be invariant for each agent during the game.

The game flow of SNS-NG/MQ with the associated probabilities and costs is shown in Fig. 1, illustrating one round for a certain agent $a_i \in A$. Note that the rounds for all agents occur simultaneously. First, in Stage 1, agent $a_i$ posts an item with probability $P^0_i$, which is determined based on $B_i$ and $Q_i$. The higher $B_i$ and the lower $Q_i$, the higher is $P^0_i$ because we believe that a higher-quality item is harder to polish for publication. When contributor $a_i$ posts an item, $a_i$ pays cost $c^0_i$. Subsequently, the neighboring agent $a_j \in N_{a_i}$ reads/views $a_i$’s item with a probability of $P^1_{j,i}$, where $P^1_{j,i}$ increases if the quality $Q_i$ is higher. After reading or viewing an item, $a_j$ receives a psychological reward of $r^0_i$ for the information obtained from the item. The values of $c^0_i$ and $r^0_i$ also depend on the parameter value for the quality of item $Q_i$.

In Stage 2, agent $\forall a_j\in N_{a_i}$ who has viewed $a_i$’s item, posts a comment about it with probability $P^2_{j,i}$ along with the payment of $a_j$’s cost $c^1$. Then, $a_i$ who is the contributor of the first item and also the recipient of the comment from $a_j$ earns a reward $r^1$. Similarly, in Stage 3, $a_j$ can receive a meta-comment from $a_i$ with probability $P^3_{i,j}$, along with the payment of $a_i$’s cost $c^2$, at which time $a_j$ earns reward $r^2$. Here, $P^2_{j,i}$ (and $P^3_{i}$) is higher if the comment rate $L_j$ (and $L_i$) is higher, and both are higher if the quality of the original item $Q_i$ of contributor $a_i$ is higher. The probability formulae for these actions are described in Sect. “SNS-norms Game with Tip and Quality”. Please see Usui et al. (2022) for more details, including the cost and reward formulas.

All rewards and costs that have appeared thus far are psychological rewards and costs, and in SNS-NG/MQ, contributor $a_i$ may also receive a monetary reward $\pi (> 0)$ from the platform at the end of either one of the Stages 1, 2, or 3. The series of rounds for all the agents is called the game round. During a few of the game rounds, each agent calculates its utility, which is the weighted sum of the psychological and monetary rewards minus the total cost. Thus, utility can be interpreted as suggesting the level of adaptation with respect to $a_i$ with local connections in a CGM. All the agents attempt to find a better strategy to maximize their utility.

Multiple-world GA

The SNS-NG and SNS-NG/MQ were originally proposed for learning using GA. However, the emergent behavioral strategies of individual agents tend to be uniform, as they are likely to use the genes of the agent with the highest utility. We believe that agents’ appropriate strategies differ depending on their local situation, such as the number of connections (i.e., friends and/or followers) and neighbors’ strategies determine utility maximization. Miura et al. (2019) proposed MWGA, in which agents in an SNS-NG co-evolve diverse strategies (Miura et al. 2021). Subsequently, Usui et al. (2024) applied MWGA to SNS-NG/MQ. In this section, we present an overview of MWGA.

The multiple world GA is a co-evolutionary algorithm that extends GA to a complex network to learn parameter values. In MWGA, the network of agents is replicated so that all agents can be trained adopting various strategies of neighbors in multiple worlds in parallel, in an attempt to find better strategies through co-evolution with neighboring agents’ strategies. First, G is replicated in $W>0$ graphs (the positive integer W is called the multiple world number). Let $G^l=(A^l,E^l)$ ($1 \le l \le W$) be the l-th graph, from now on referred to as the l-th world, and the set of agents in $G^l$ is denoted by $A^l=\{a^l_1, \dots , a^l_N\}$. Because agents $a^l_i$ and $a^{l'}_i$ are created by copying $a_i$, they are called siblings, and the set of all siblings of $a_i$ is denoted by ${\mathcal {S}}_i=\{a_i^1, \cdots , a_i^W\}$.

Initially, randomly generated genes expressing $B_i$, $Q_i$ and $L_i$ are assigned to all the agents in $A^l$ ($1\le l\le W$). Thus, the agents in ${\mathcal {S}}_i$ have different genes and thus different strategies although they are positioned at the same place in the replicated worlds. This also means that the behaviors of neighboring agents follow different strategies in their respective worlds. We express the strategy of the parameters $a_i^l \in A^l$ as $B^l_i$, $Q^l_i$, and $L^l_i$. Each parameter is represented by 3 bits; thus, each agent has a 9-bit gene. The parameters $B_i^l$ and $L_i^l$ are interpreted as $0/7,1/7,\cdots ,7/7$, and $Q_i$ is interpreted as $1/8=Q_{\textit{min}},2/8,\cdots ,8/8$, where $Q_{\textit{min}}$ is the minimum quality value.

The MWGA process consists of parent selection, crossover, and mutation, as in conventional GA, and is mostly the same as in GA, except for parent selection. In MWGA, $a^l_i$ ($1\le l\le W-1$) selects two agents as parents: one is itself, and the other is selected from siblings ${\mathcal {S}}_i^{-l}$ ($={\mathcal {S}}_i\setminus \{a^l_i\}$) probabilistically using roulette wheel selection based on fitness values, which are defined as the utilities of individual agents in ${\mathcal {S}}_i$. Therefore, the sibling agent with the highest utility in a different world is likely to be selected as a parent. Meanwhile, in the Wth world, $a^W_i$ is replaced by the agent with the highest utility in ${\mathcal {S}}_i$ to execute the best interaction (see Sect. “Co-evolution of Behavioral Strategies”. For further details, please refer to Miura et al. (2019).

Proposed model

Overview

In this study, another extension of SNS-NG, an SNS-norms game with tip and quality (SNS-NG/TQ) is proposed in the context of SLSS, as an abstraction of live-streaming social media. This extension aims to capture the dynamics of virtual tipping in SLSS to further clarify the influence on an agent’s behavioral strategy, including the level of assertiveness in live streaming and attitudes towards stream quality. Therefore, an item post refers to live streaming that can last from a few seconds to minutes. Similar to conventional SNS, comments are text messages posted by agents while viewing live streams. Meta-comments are text message responses from streamers to viewer comments.

In our game model, we reshaped the monetary reward mechanism, shifting from a unilateral to an interactive provision among agents. We assume that these monetary provisions are transferred to another agent at a specific commission rate $\lambda$ ($0\le \lambda \le 1.0$) for secure collection and transfer by the platform. We also introduced a new parameter called the tipping interest to define each agent’s inclination towards tipping.

The concept of virtual tips is considered, as exemplified by platforms such as “bits” in Twitch and YouTube live’s “SuperChat,” where viewers can offer virtual tips independently with/without a text message (comment). Three distinct types of responses use comments and tips, as follows:

tip-only::

virtual tip without message.

comment-only::

comment (or chat) as in a conventional SNS.

tip-with-comment::

virtual tip with a message.

To simplify tipping in our model, the number of tips is fixed as $\rho \ge 0$. Therefore, the platform collects $\lambda \cdot \rho$ as a commission for each tip.

SNS-norms game with tip and quality

The proposed game, SNS-NG/TQ, is played on a graph $G=(A,E)$, similar to SNS-NG/MQ in Sect. “SNS-norms game with monetary rewards and quality”. We assume that an item posted by agent $a_i\in A$ is envisioned to be a live stream by $a_i$, and $N_{a_i}$ is the set of registrant agents of $a_i$. Behavioral strategy of agent $a_i \in A$ is similarly characterized by parameters: the streaming rate $B_i$ (i.e., the willingness of live streaming, which corresponds to the posting rate in SNS-NG/MQ), comment (and meta-comment) rate $L_i$ ($0\le B_i, L_i\le 1$), and item quality $Q_i$ (i.e., quality of live streaming). As in SNS-NG/MQ, $0\le B_i, L_i\le 1$, and $0< Q_{\textit{min}}\le Q_i\le 1$, where $Q_{\textit{min}}$ is a positive value indicating the lower limit of the quality parameter. Consequently, these parameters indirectly influence the agent’s utility via interactions with neighboring agents who also have their own behavioral strategies specified by these parameters.

The parameter tipping rate $T_i$ ($0<T_i, T_{\textit{int,i}}<1$) is introduced to characterize the virtual tipping behavior in SNS-NG/TQ based on the tipping interest $T_{\textit{int,i}}$ of $a_i$, where tipping rate is defined as

$$\begin{aligned} T_i = (1-\lambda ) \cdot T_{\textit{int,i}} \end{aligned}$$

(1)

for $\forall a_i\in A$. Here, $T_{\textit{int,i}}$ is assumed to be an individual’s inherent inclination toward tipping without being affected by the commission rate $\lambda$ determined by the platform, whereas $T_i$ reflects the influence of the commission rate. Thus, agents may hesitate to tip if the commission rate is high.

Using a method similar to that of SNS-NG/MQ, parameter $M_i$ is introduced to represent the extent of agent $a_i$’s preference for monetary rather than psychological rewards. Note that $0\le M_i\le 1$ is unique and invariant for each agent. Based on the value of $M_i$, agents are divided into two classes:

$$\begin{aligned} A_\alpha&=\{a_i \in A \mid M_i < 0.5 \}, \text { and}\end{aligned}$$

(2)

$$\begin{aligned} A_\beta&=\{a_i \in A \mid M_i \ge 0.5 \} \end{aligned}$$

(3)

An important difference between SNS-NG/TQ and SNS-NG/MQ with respect to parameter $M_i$ is the monetary reward mechanism, that is, in SNS-NG/MQ, the platform provides the monetary reward, whereas in SNS-NG/TQ, the reward for tipping is provided by other agents. As a result, the tipping behavior imposes a monetary cost on individual agents, and the behaviors of $A_\alpha$ and $A_\beta$ agents are affected differently by parameter $M_i$. For instance, agents in $A_\alpha$ are likely to tip more if they receive greater psychological rewards, whereas agents in $A_\beta$ may be unwilling to pay even if psychological rewards are available.

Fig. 2

Flow of SNS-norms game with tip and quality

Game steps

Agent $a_i\in A$ participates in SNS-NG/TQ by interacting with neighboring agents on $G=(A,E)$. The flow of actions by $a_i$ with neighboring agents is shown in Fig. 2. During or following the viewing of live streaming by $a_i$, the neighboring agent $a_j\in N_{a_i}$ decides whether to provide a virtual tip $\rho$ to $a_i$ or to post a comment on live stream. This decision sequence aligns with the actual SLSS. If no tips are provided, the subsequent game process is the same as in SNS-NG/MQ.

The parameters $B_i$, $L_i$, $Q_i$, and $T_i$ determine the behavioral strategy of agent $a_i$. In Stage 1, agent $a_i$ participates in a live stream with streaming probability $P^0_i$, where

$$\begin{aligned} P_i^{0}=B_i \cdot \frac{Q_{\textit{min}}}{Q_i}. \end{aligned}$$

(4)

Equation (4) implies that if $Q_i$ is higher, agent $a_i$ is less likely to stream live as it would require more effort to improve the quality of the live content. It is important to note that the actions of all agents in a game round progress simultaneously. If $a_i$ is live streaming, a cost $c^0_i=C^0 \cdot Q_i$ is incurred by $a_i$. If $a_i$ chooses not to live stream, $a_i$’s round ends.

Subsequently, the neighboring agent $a_j\in N_{a_i}$ has the opportunity to view the live streaming of agent $a_i$ with probability $P^1_{j,i} = Q_i/s_j$, where $s_j$ represents the number of live streams by its neighboring agents in $N_{a_j}$ in the same game round. If $s_j=0$, we set $P^1_{j,i} = 0$. Therefore, $P^1_{j,i}$ is high if the quality of stream $Q_i$ by $a_i$ is also high, whereby $a_j$ earns psychological reward $r^0_i=R^0 \cdot Q_i$ as the benefit of viewing the stream.

As indicated by Stages 2A and 2B in Fig. 2, agent $a_j$ upon viewing the live streams by $a_i$, determines whether to provide a virtual tip $\rho$ to $a_i$ with probability $P^2_{j,i} = T_j\cdot Q_i$ (recall that $T_j= (1-\lambda ) \cdot T_{\textit{int,j}}$). Thus, the probability $P^2_{j,i}$ is affected by the commission rate $\lambda$ and quality of live streaming. If $a_j$ determines to provide tip $\rho$, then both agents $a_i$ and $a_j$ proceed to Stage 2A; otherwise, they move to Stage 2B. In Stage 2A, agent $a_j$ provides $\rho$ to $a_i$ who receives the virtual tip $\rho \cdot (1-\lambda )$ as a monetary reward after subtracting the commission charged by the platform. Agent $a_j$ also determines whether to comment on the tip-with-comment live with probability $P^3_{j,i} = L_j \cdot Q_i$. Otherwise, $a_j$ provides only one tip (tip-only) and proceeds to Stage 3A’. If $a_j$ posts a comment, it incurs a cost $c^1=C^1$ and $a_i$ gains a psychological reward $r^1=R^1$ for every tip-with-comment and comment-only request from neighboring agents. They then proceed to Stage 3A.

In Stage 2B, $a_j$ comments live using $a_i$ (comment-only) with probability $P^3_{j,i}$. If $a_j$ comments on it, $a_j$ incurs cost $c^1=C^1$, and $a_i$ receives a psychological reward $r^1=R^1$ for every tip-comment or comment-only that is received. Then, Stage 3B ensues. If $a_j$ decides not to comment, the round ends.

In Stages 3A, 3A’, and 3B, irrespective of the type of response (tip-only, comment-only, or comment-with-tip), $a_i$ streams the live comment first and the response received from $a_j\in N_{a_i}$ determines whether to post a meta-comment to $a_j$ as a response with probability $P^4_i = L_i \cdot Q_i$. In case of a response, $a_i$ incurs a cost $c^{2,t}$, $c^{2,c}$, or $c^{2,tc}$, depending on tip-only, comment-only, or comment-with-tip, respectively. In addition, $a_j$ obtains a psychological reward $r^{2,t}$, $r^{2,c}$, or $r^{2,tc}$ for receiving the meta-comment from the first contributor $a_i$. These rewards and costs are defined according to the commission rate $\lambda$.

$$\begin{aligned} \begin{aligned} r^{2,t}&=(1-\lambda )\cdot R^t,&c^{2,t}&=(1-\lambda )\cdot C^t,\\ r^{2,c}&=R^c,&c^{2,c}&=C^c, \\ r^{2,tc}&=(1-\lambda ) \cdot R^t+R^c, \text { and}&c^{2,tc}&=(1-\lambda ) \cdot C^t+C^c, \end{aligned} \end{aligned}$$

(5)

In Eq. (5), $R^t$ and $C^t$ represent the psychological reward and base cost, respectively, for tip-only, whereas $R^c$ and $C^c$ represent psychological reward and base cost for comment-only, respectively. These costs and rewards from the meta-comments associated with tipping decrease as the value of $\lambda$ increases, indicating that a higher commission deduction from tipping by the platform would reduce the impact of providing tipping.

In an extreme case in which $\lambda =1$, the platform collects all the tips and provides nothing to the agents; therefore, tipping is meaningless to agents, and there is no incentive to provide virtual tips. This means that the agents never advance to Stage 2A, making SNS-NG/TQ equivalent to SNS-NG/MQ without a monetary reward. This special case of SNS-NG/TQ is called the SNS-norms game with quality (SNS-NG/Q).

At the end of one game round, $\forall a_i\in A$ utility $U_i$ is accounted for, as follows:

$$\begin{aligned} U_i=M_i\times (K^{+}_i - K^{-}_i) + (1-M_i)\times R_i - C_i. \end{aligned}$$

(6)

Here, $K^{+}_i$ is the total monetary reward received in tip; $K^{-}_i$ is the monetary cost of providing tips; and $R_i$ is the total psychological reward during the game round. $C_i$ is the cost incurred by $a_i$ for other activities, including live streaming, as well as posting comments and meta-comments. The fitness value of $a_i$ in evolving the parameters of the behavioral strategies in MWGA is defined as $a_i$’s utility, $U_i$.

Co-evolution of behavioral strategies

Parameters $B_i$, $L_i$, $Q_i$, and $T_{\textit{int,i}}$ determine the behavioral strategy of agent $a_i$, which is individually adjusted to maximize utility. As discussed in Sect. “Multiple-world GA”, the agent’s strategy must be diverse and appropriately learned depending on the local topological structure of network G and the strategies of its neighboring agents. Therefore, we employed MWGA to evolve diverse strategies. Similar to the use of MWGA for SNS-NG/MQ, $G=(A,E)$ was duplicated to create W worlds, denoting the lth world by $G^l=(A^l, E^l)$, as in Sect. “Multiple-world GA”.

Each behavioral parameter, $B_i$, $L_i$, $Q_i$ or $T_{\textit{int,i}}$, is represented using three bits; thus, $a_i$ has a 12-bit gene for its strategy by concatenating all parameters. Expressions of $B_i$, $L_i$, and $T_{\textit{int,i}}$ correspond to 0/7, 1/7, $\dots$, 7/7, respectively and those of $Q_i$ correspond to the values 1/8 ($=Q_{\textit{min}}$), 2/8, $\dots$, 8/8, respectively. All the agents $a_i^l\in \cup _{l=1}^WA^l$ are initially assigned different strategies by providing random values for $B_i$, $L_i$, $Q_i$, and $T_{\textit{int,i}}$. Thus, the sibling agents in ${\mathcal {S}}_i$ have different strategies in different worlds, and interact with their neighboring agents, who also have different strategies depending on their worlds. Thus, each sibling agent of $a_i$ will have different experiences through the game interactions. The length of one generation of MWGA is defined as $N_\textit{gen}$ ($\ge 1$) game rounds, and the length of one episode is g ($\ge 1$) generations. The fitness value of agent $a_i^l$ is defined as the total utility gained in a generation.

Parent selection

Parent selection is performed in the same manner as described in Sect. “Multiple-world GA”. In other words, for each agent $a_i^l\in A^l$ ($1\le l\le W-1$), the two parents comprise the agent itself and another agent selected from ${\mathcal {S}}_i^{-l}$ using the roulette wheel selection based on the fitness values, in which the sibling agent $a_i^k\in {\mathcal {S}}_i^{-l}$ (including $a_i^W$) is selected with probability $\Pi _i^{k}$:

$$\begin{aligned} \Pi ^k_i=\dfrac{(u^k_i-u_{i,\textit{min}})^2+\varepsilon /(W-1)}{\sum _{a^\kappa _i\in {\mathcal {S}}^{-l}_i} (u^\kappa _i-u_{i,\textit{min}})^2+\varepsilon }, \end{aligned}$$

(7)

where $U_i^k$ is the fitness value of $a_i^l$, that is, the utility during the current game round, and $u_{i,\textit{min}}=\min _{a^\kappa _i\in {\mathcal {S}}_i^{-l}}u^\kappa _i$. Parameter $\varepsilon$ ($\ll 1$) is a positive value, whereby to avoid division by zero, we set $\varepsilon = 0.00001$ in the experiments.

Meanwhile, agent $a_i^W\in A^W$ in the next generation is set as the sibling agent in ${\mathcal {S}}_i$ that has the highest utility.

$$\begin{aligned} a_i^w = \mathop {\mathrm{arg~max}}\limits _{a_i^l\in {\mathcal {S}}_i} U_i^l \end{aligned}$$

(8)

No crossover or mutation is applied. Consequently, the Wth world may comprise agents with the highest utility from all worlds.

Crossover

We adopted the uniform crossover, that is, $1\le l\le W-1$ in the l-th world, randomly selecting the n-th bit of the gene of the child from the n-th bit of the genes of the selected parents.

Mutation

To prevent the risk of falling into a local optimum, each bit of the 12-bit gene of each agent of $A^l$ is inverted with mutation probability $Pr_m$ ($0\le Pr_m\le 1$) for $1\le \forall l \le W-1$.

Final outcome

The results in each generation of MWGA are determined by the outcomes of the Wth world.

Experiments and discussion

Experimental setting

We explored the emerging behaviors of individual agents within SNS-NG/TQ on artificial complex networks, the Facebook (ego), and Twitch (musae EN) networks (Leskovec and Krevl 2014; Rozemberczki et al. 2019) under the commission rate $\lambda = 0.5$, to understand the distribution of user strategies. The characteristics of these networks are outlined in Table 1. Moreover, to confirm the effect of the presence or absence of virtual tips on agent behaviors, experiments were conducted in SNS-NG/Q with no tips, by setting $\lambda =1.0$. We also conducted an experiment with a stepwise increase in the commission rate $\lambda$ from 0 to 1.0 in increments of 0.05 to investigate its effect on media dynamics and users’ emerging behaviors, such as their commitment to the quality of live streaming and platform revenue from commissions, depending on their preferences for psychological/monetary rewards and on follower/followee counts.

Artificial complex networks have been generated using the connecting nearest-neighbor model (CoNN model) (Vázquez 2003), which is based on the principle that friends of friends are more likely to form direct friendships. Therefore, the edges between them are referred to as potential edges. Network generation begins with a small complete graph. Then, every time step, a node (agent) is added to the network with probability $1-u$ and one potential edge becomes a normal edge with probability u, where u is called a transition probability. A CoNN network possesses the properties of high cluster coefficients, small-world characteristics, and scale-freeness, which are typical of real-world social networks. The transition probability was set to $u = 0.9$ for CoNN networks in our experiments because network characteristics related to the degree of connectivity and clustering coefficient seem to have values between those of the real Facebook and Twitch (Table 1) networks.

The other parameters and their values are listed in Tables 2 and 3. The balance of cost and reward parameters is based on previous studies (Usui et al. 2022; Okada et al. 2015), that is, it ensures that users’ cooperative behavior is mainly encouraged for psychological rewards in the absence of monetary rewards with $\lambda =1.0$, which allows us to more clearly discuss the impact of monetary rewards. The experimental results for the two real networks below are the mean values of the 1000th generation of 50 independent trial runs. The mean values of all the parameters are denoted as B, L, Q and T, omitting the subscripts. The same episode length was set for CoNN, but its results were the average of 1000 trial runs.

Table 1 Parameters of the networks

Table 2 Parameter values in experiments

Table 3 Values of reference for rewards and costs in experiments

Fig. 3

Distribution of behavioral parameters over degrees in a CoNN network

Distribution of agent strategies

Figures 3, 4, and 5 show the scatter plots of the agents’ strategy parameter values as a function of the degree of agents in the CoNN, Facebook, and Twitch networks in SNS-NG/TQ, respectively for $\lambda =0.5$. In these graphs, the blue and orange dots represent agents in $A_\alpha$ (preferring psychological rewards) and $A_\beta$ (preferring monetary rewards), respectively. In Fig. 3, the data from one experimental trial are displayed. Notably, the trend of this graph is similar to the others.

CoNN network

In the CoNN network of Fig. 3a the agents with a low degree ranging from 0.1 to 100 are distributed over various streaming rates $B_i$ ranging from 0.0 to 0.94. In particular, agents with $B_i < 0.3$ prefer monetary rewards. Notably, all agents with degrees greater than 100 are distributed at $B_i=0.9$ or higher, regardless of whether they are in $A_\alpha$ or $A_\beta$. As high-degree agents have more connections, their live streaming is more likely to be watched by others. Thus, they are likely to receive more psychological and monetary rewards and have a higher streaming rate $B_i$, taking advantage of the opportunities in favorable surrounding conditions. However, agents with a low degree cannot take the certainty of the reward; moreover, some neighboring agents may be free riders with little or no contribution to the media. Therefore, they engage in fewer streaming activities. The distribution of $Q_i$ shown in Fig. 3b exhibits a tendency similar to that of $B_i$, but there is no difference between the $Q_i$ of agents on $A_\alpha$ and $A_\beta$, meaning that the attitudes toward streaming quality remain largely unchanged. This seems to be because quality always contributes to increasing psychological and monetary rewards in proportion to the number of neighboring agents.

As shown Fig. 3c, the distribution of $L_i$ is split depending on $A_\alpha$ and $A_\beta$. The values of $L_i$ for agents with lower degrees ($0<\textit{deg}{a_i} \le 100$) in $A_\alpha$ are primarily between 0.5 and 0.9 whereas those in $A_\beta$ are between 0.25 and 0.5. Thus, agents preferring psychological rewards have a higher value of $L_i$, meaning that they post more comments and meta-comments. This is because comments only provide psychological rewards, and these agents adjust their strategies to exchange more comments. In contrast, the value of $L_i$ tends to decrease as the degree increases, meaning that agents with higher degrees are unlikely to provide comments and meta-comments. Because they also have more chances to view streaming by neighboring agents, to avoid the higher cost of posting many comments, they adjust their strategies to reduce the number of comments.

In Fig. 3d, as in the case of $L_i$, the distribution of $T_i$ values is clearly separated according to whether the agents belong to $A_\alpha$ or $A_\beta$, as in the case of $L_i$, that is, the agents in $A_\alpha$ are more likely to provide virtual tips. As these agents prefer psychological rewards, they provide tips to obtain rewards. By contrast, agents in $A_\beta$ are reluctant to offer virtual tips because tipping reduces the monetary rewards obtained. Another observation in Fig. 3d is that unlike other parameters, the distribution of $T_i$ is within a narrow range and $T_i$ values are less affected by the agents’ degrees. Agents with higher degrees are more likely to receive both psychological and monetary rewards and possess an advantage in adopting strategies that lead to higher $B_i$ and $Q_i$, streaming more high-quality content. Conversely, because tipping is a direct interaction between two agents, an agent offers a virtual tip $\rho$ to one streamer and receives only one meta-comment, at most, as a psychological reward. Therefore, tipping within a stream is relatively ineffective for agents with high degrees regardless of whether they belong to $A_\alpha$ or $A_\beta$.

Fig. 4

Distribution of behavioral parameters as a function of degree in Facebook network

Fig. 5

Distribution of behavioral parameters over degrees in Twitch network

Facebook and twitch networks

The distribution of the behavioral strategy parameters for Facebook (Fig. 4) and Twitch networks (Fig. 5) display characteristics similar to those of CoNN networks, except that their values are somewhat widely distributed. In more detail:

• 1. The values of $B_i$ range between 0.1 and 0.95 in CoNN networks, whereas they range between 0 and 0.98 in real-world networks.

• 2. No major difference are observed in the values of $Q_i$ in all networks.

• 3. The values of $L_i$ are widely distributed in real-world networks, especially in the Facebook network, indicating a broader diversity of strategies for posting comments and meta-comments.

• 4. The values of tipping rate $T_i$ also seem to be unaffected by agents’ degree except for the Twitch network, in which the values of $T_i$ for agents in $A_\beta$ tend to increase as their degrees increase. This tendency is also present in CoNN networks, albeit more pronounced. However, these values for agents in $A_\alpha$ are still larger.

Finally, we note that the agents’ strategies were not the same and that these diverse strategies are obtained by MWGA. In fact, with conventional GA, agents are likely to exhibit similar behavioral strategies, regardless of their degrees (Usui et al. 2024).

Fig. 6

Behavioral strategies of agents (CoNN)

Fig. 7

Real streaming rate $P^0$ of agents in the game (CoNN)

Strategies under various commission rate

Next, we investigate how agents’ behaviors co-evolving with MWGA are affected by the commission rate $\lambda$. First, agents are classified into four groups from $A_\alpha$ and $A_\beta$ based on their degrees:

$$\begin{aligned} \begin{aligned} A_{\alpha ,l}&=\{a\in A_\alpha \mid \textit{deg}(a)< 50\},\\ A_{\beta ,l}&=\{a\in A_\beta \mid \textit{deg}(a) < 50\},\\ A_{\alpha ,h}&=A_{\alpha }\setminus A_{\alpha ,l}, \text { and } A_{\beta ,h}=A_{\beta }\setminus A_{\beta ,l}. \end{aligned} \end{aligned}$$

(9)

Fig. 6 illustrates the transitions of the mean values of the four parameters B, L, Q, and T of the agents in CoNN networks as the commission rate varies from $\lambda =0.0$ to 1.0. Recall that $T=(1-\lambda ) \cdot T_{\textit{int}}$. We omit the graphs for Facebook and Twitch networks because their trends are almost identical to those of CoNN networks. The results are shown in Appendix A. The transition of strategy evolution until convergence in this experiment is discussed in Appendix B.

Initially, Fig. 6a shows that the streaming rate B of the agents varies across various $\lambda$ values, according to the agent’s degree and monetary preference. While the average value of the streaming rate B for the agents in $A_{\alpha }$ remain stable, it decreases in $A_\beta$, especially in $A_{\beta ,l}$, as $\lambda$ increases. This decrease is attributed to all agents receiving fewer tips (monetary rewards) as the commission rate increases, which reduces the incentive for the agents in $A_{\beta ,h}$ and $A_{\beta ,l}$ because these agents prioritize monetary rewards over psychological rewards. According to the increase in the commission rate, their monetary rewards decrease, reducing the incentives for live streaming. In particular, because agents in $A_{\beta ,l}$ have fewer opportunities to receive monetary rewards through virtual tips because of their low degrees, their incentives are considerably lower, leading to a marked decline in their streaming rates.

Meanwhile, the agents in $A_\alpha$ are likely to prefer psychological rewards, which are unaffected by the commission rate $\lambda$, thus retaining their streaming behavior. Another finding is that, irrespective of $\lambda$, agents with higher degrees ($A_{\alpha ,h}$) consistently exhibit higher values of B than those with lower degrees ($A_{\beta ,h}$) because the agents in $A_\alpha$ who act as live/video streamers have a higher probability of obtaining psychological rewards through comments, regardless of tip availability.

Second, Fig. 6b shows that the commission rate $\lambda$ has less impact on the value of Q except for the agents in $A_{\beta ,l}$. Similar to the streaming rate B, agents in $A_{\alpha }$ are less inclined to tip, and their attitudes toward the quality of content are unlikely to be influenced. Conversely, the agents in $A_{\beta ,l}$ seek greater monetary and psychological rewards with a smaller number of neighboring agents, which lowers their incentives for streaming and improving content to mitigate streaming costs if the commission rate is high. These observations on B and Q indicate that agents preferring monetary rewards are more inclined to stream items, and when the SLSS introduces a tipping system with a low commission rate, the number and quality of their items are maintained at a high level. However, this does not significantly alter the behavior of agents in $A_\alpha$; the average value of Q is slightly increased with an increase in the commission rate.

Regarding the average streaming probability $P_i^0$, the strategy of an agent with respect to live streaming should be determined by a combination of B and Q. Thus, we defined the streaming probability using Eq. 4. Figure 7 plots the values of $P^0$ for the various commission rates obtained in this experiment. This indicates that the average streaming probabilities are almost invariant, except for a slight decrease in the probability of $A_{\beta ,l}$ as commission rate increases, whereas B and Q of $A_{\beta ,l}$ decrease considerably, as shown in Fig. 6. This means that the agents in $A_{\beta .l}$ are less willing to live stream, thus lowering quality, to mostly maintain the same number of streaming.

Figure 6c shows that comment rate L is generally less sensitive to the commission rate. As $\lambda$ increases, L decreases slightly for agents in $A_\beta$ who prefer monetary rewards and increases slightly for agents in $A_\alpha$ who prefer psychological rewards. Because B for agents in $A_\beta$ declines with increasing $\lambda$, whereas that for agents in $A_\alpha$ remains almost constant, agents in $A_\alpha$ have fewer chances to view live streaming. To obtain more psychological rewards, the agents in $A_\alpha$ increase their comment rates, albeit only slightly. Conversely, the agents in $A_\beta$ decrease L. Notably, the agents in $A_{\beta ,h}$ have higher values of $B_i$ (Fig. 6a). Thus, they prefer to encourage their neighbors to provide as many tips as possible through meta-comments. However, this incentive weakens as the commission rate increases.

In Fig. 6d, the agents in $A_\alpha$ have higher average tipping rate T values than those of agents in $A_\beta$ Similar to Fig. 3d, this is mainly because the agents in $A_\alpha$ prefer psychological rewards and are less anxious about the monetary loss incurred by tipping than those in $A_\beta$.

The experimental results show that virtual tips increase the quality of the live stream and overall activity. Conversely, when $\lambda =1.0$, SNS-NG/Q without tips, reduces the quality of streaming for agents that prefer monetary rewards. The same experiments were conducted with Facebook and Twitch networks, confirming the same results with similar trends. For more information, please refer to Appendix A.

Fig. 8

Average utility of agents

Fig. 9

Platform revenue from commissions

Utilities of agents

Next, the variation in the mean values of utility U were examined according to the value of the commission rate $\lambda$. In this experiment, we set the virtual tip reward $R^{2,t}$ for the meta-comments as 1.0, 5.0 and 9.0. The average utility values presented in Fig. 8 indicate that agents in $A_{\beta ,h}$ experience a pronounced decline in their utility U compared with other agents. As agents with higher degrees are likely to receive greater monetary rewards as tips from others, the utilities of such agents, especially those in $A_{\beta ,h}$, are significantly affected by the commission rate. Comparing the graphs in Fig. 8 for larger $R^{2,t}$, the utilities are also larger for all types of agents, especially for agents with higher degrees (although detailed data are not shown here). This is because $R^{2,t}$ is the psychological reward for receiving tips and is independent of the psychological reward for comments. In other words, these results show that when the psychological rewards from the information associated with the tips to the streamer are high, the overall utility increases, affecting the behaviors of higher-degree agents more strongly.

Platform revenue

The results presented in Fig. 9 show the total revenue collected by the platform at various commission rates, $\lambda$. Recall that the unit of revenue $\rho$ is assumed to be constant. First, we examine Fig. 9b when the reward for receiving a meta-comment for providing a virtual tip is $R^{2,t}=5.0$. Figures 6a and 6b demonstrate that the agents in $A_{\beta ,l}$ initially reduce their B and Q, whereas the agents in $A_{\beta ,h}$ decrease their B more slowly with an increase in $\lambda$. As agents in $A_{\beta ,h}$ have more opportunities to receive virtual tips because of their higher degrees, the increase in commission rates do not significantly affect their average rewards. Thus, as shown in Fig. 9b up to $\lambda =0.4$, the platform revenue continues to increase with an increase in $\lambda$.

Subsequently, the decline in B of agents in $A_{\beta ,h}$ leads to a decrease in platform revenue, but further increases in $\lambda$ boost revenue, appearing as an unstable plane in Fig. 9a. Eventually, tipping gradually becomes less active as $\lambda$ increases in the range of $0.8 \le \lambda \le 1.0$. This interference between the decrease in B and increase in $\lambda$ causes instability in platform revenue near the peaks.

Figure 9a ($R^{2,t}=1.0$) and 9c ($R^{2,t}=9.0$) also show similar characteristics, but the (un)stability around the peaks differ. When $R^{2,t}=1.0$, double peaks are observed (Fig. 9a); however, the value of the center between the two peaks increases relative to the rest as $R^{2,t}$ increases, becoming a single peak (Fig. 9c). Moreover, as $R^{2,t}$ increases, this peak value increases, and the width of the somewhat flatter and less variable range near the peak also changes (Fig. 9). When $R^{2,t}=9.0$ (Fig. 9a), the peak appears sharp. This is because when the commission rate changes, the value of the psychological rewards from the money for virtual tips increases, and as mentioned earlier, the changes in B and Q with respect to the increase in the commission rate also increase. Thus, the unstable revenue peaks are eliminated, and the increase or decrease in rewards becomes significant with an increase in the commission rate, producing a single peak.

Conversely, when $R^{2,t}=1.0$ (Fig. 9a), that is, when the psychological reward for receiving a virtual tip is small, utility decreases and live streaming behavior among users subsides, and thus, platform revenue decreases. Simultaneously, the tipping behavior becomes less sensitive to the commission rate $\lambda$, and a flat and unstable range is observed when $\lambda$ is between 0.4 and 0.7. These results indicate that there may be an optimal commission rate from a platform perspective although it may not be unique, particularly when the agents (users) who offer the tips obtain higher psychological satisfaction from the meta-comment (i.e., replying to tips).

Strategies of professional agents under SLSS

Finally, we attempted to add another property to the agents (users) to realistically represent the SLSS, including heterogeneous users, novices, and professionals. We assume that professionals tend to be able to create and deliver higher quality content than novices because they create content, including advertisements and campaigns for companies and groups, in return for their financial support. To model such a situation, the $Q_i$ values of professionals ranged from 0.5 to 1.0 ($0.5\le Q_i\le 1.0$), whereas those of novices ranged from 0 to 0.5 ($0\le Q_i\le 0.5$). We denote the sets of professionals and novices as $A_\textit{pro}$ and $A_\textit{nov}$, respectively.

Because this property does not correlate with $M_i$ and the degrees of agents, we consider the following eight sets of agents: $A_{\alpha ,h,pro}$, $A_{\alpha ,l,pro}$, $A_{\alpha ,h,nov}$, $A_{\alpha ,l,nov}$, $A_{\beta ,h,pro}$, $A_{\beta ,l,pro}$, $A_{\beta ,h,nov}$, and $A_{\beta ,l,nov}$, where the subscripts represent their properties, such as $A_{\alpha ,h,pro}= A_{\alpha ,h}\cap A_\textit{pro}$. The value of $Q_i$ is encoded into a 3-bit gene with 16 divided values; that is, $Q_i$ for $a_i\in A_\textit{nov}$ is one of $1/16=Q_{\textit{min}},2/16,\cdots ,8/16$ and $Q_i$ for $a_i\in A_\textit{pro}$ is one of $9/16, 10/16,\cdots ,16/16$. The same CoNN network used in previous experiments was used. We set $|A_{\alpha ,pro}|= 200$, $|A_{\alpha ,nov}|= 300$, $|A_{\beta ,pro}|= 200$, and $|A_{\beta ,nov}|= 300$, where $A_{\alpha ,pro}=A_{\alpha }\cap A_\textit{pro}$, $A_{\alpha ,nov}=A_{\alpha }\cap A_\textit{nov}$, $A_{\beta ,pro}=A_{\beta }\cap A_\textit{pro}$ and $A_{\beta ,nov}=A_{\beta }\cap A_\textit{nov}$. The learning generation or generations are the same as those in Table 2 and their experiment, with a stepwise increase in the commission rate $\lambda$ from 0 to 1.0 in increments of 0.05. The results were averaged over 100 trials.

Figure 10 shows the strategy trend for each agent set with respect to an increase in $\lambda$. First, we focus on the streaming rate B. From Fig. 10a, we observe that the values of $B_i$ for all agents in $A_\alpha$ do not vary for all $\lambda$ values, which is similar to the results in Fig. 6). The agents in $A_\alpha$ have larger B values in the order $A_{\alpha ,h,pro}$, $A_{\alpha ,l,pro}$, $A_{\alpha ,h,nov}$, $A_{\alpha ,l,nov}$. Agents with higher degrees have higher B values, as in the previous result, and it is worth noting that $A_{\alpha ,l,pro}$ has a higher B than $A_{\alpha ,h,nov}$. A professional agent is guaranteed to have a higher value of Q, which is more attractive for other novice agents. This has a stronger effect on streaming activities than the degree of agents. Even in $A_\beta$, B is larger in the order $A_{\beta ,h,pro}$, $A_{\beta ,l,pro}$, $A_{\beta ,h,nov}$, and $A_{\beta ,l,nov}$ for any $\lambda$ value, except for $\lambda <0.15$. In other words, the dominance of professional agents over degrees varies with the commission rate of the agents who prefer monetary rewards. When $\lambda$ is small, the reward per unit of money is high. Thus, high-degree agents who are likely to post low-quality items have a greater chance of obtaining tips. Although Fig. 6a also shows that the agents in $A_{\beta ,l}$ significantly decreased their willingness to stream with increasing $\lambda$, Fig. 10a shows that the change was smaller for the agents in $A_{\beta ,l,nov}$. In the previous experiment, agents in $A_{\beta }$ attempted higher-quality streaming to obtain more tips, but agents in $A_{\beta ,l,nov}$ could not increase the quality and, thus, had fewer chances of obtaining tips.

Figure 10b shows the Q values over $\lambda$. As modeled, the Q values of $A_\textit{pro}$ and $A_\textit{nov}$ were separated by 0.5. If we look at this figure closely, high-degree agents produced high-quality streams, and $A_\alpha$ who prefer psychological rewards maintained high quality within the range, while agents who prefer monetary rewards $A_\beta$ showed a gradual decrease with increasing $\lambda$, which is the same trend as the results shown in Fig. 6b. As with the B values, the decrease in the Q values of the agents in $A_{\beta ,l,nov}$ was the smallest. The obvious difference in quality between professionals and novices, which is different from that of Sect. “Strategies under various commision rate”, does not coincide with the high/low degree and high/low quality.

Figure 10c and d show the average comment rate L and average tipping rate T, respectively. First, let us focus on $A_\alpha$; that is, $A_{\alpha ,h,nov},A_{\alpha ,l,nov},A_{\alpha ,h,pro},A_{\alpha ,l,pro}$. As opportunities to obtain psychological rewards increased with an increase in $\lambda$, the comment rate L also slightly increased. However, the underlying strategy is different. In particular, agents in $A_{\alpha ,h,nov}$ have high degrees, but their quality of streaming is always lower than that of professional agents; they increase L with the advantage of high degrees instead of increasing quality. This phenomenon differs from that observed for $A_{\alpha ,h}$ in Fig. 6c, where all higher-order agents in $A_{\alpha ,h}$ conducted high-quality streaming to obtain a psychological reward.

The results for $A_\beta$ were consistent with those shown in Fig. 6c, regardless of whether they were professional or novice agents. However, the meta-comment to induce the viewing and tipping behavior of the surrounding agents gradually disappears as $\lambda$ increases. In contrast, the results for the tipping rate T in Fig. 10d closely resembles Fig. 6d. That is, compared to the streaming rate B, the degree agents had a small effect on tipping, but the increase in $\lambda$ suppresses this effect.

Fig. 10

Behavioral strategies of professional and novice agents (CoNN)

Discussion

Our experimental results indicate that the tipping system enhances the activities of some types of agents, especially agents in $A_{\beta ,h}$, that is, higher degrees of preference for monetary rewards. Furthermore, our results indicate that there is a certain spectrum for the optimal commission rate of tips in maximizing platform revenue, and that the rate depends on the ratio between the user’s preferences for monetary and psychological rewards. These insights, which stem from our theoretical model, are relevant to any platform that employs a virtual tipping system. Although the experiments only validated one type of virtual tip, they suggest a guideline for how real platforms should determine commission rates by properly calibrating the cost and reward parameters. Real-world media are unique, each with a different cost and reward balance, and the model can be adapted to streaming-based media for a more accurate discussion. The results of this study can be used to design rewards and gamification to maximize users’ ongoing participation behavior and revenue in media environments using monetary reward systems. For example, the creation of an environment in which users can smoothly receive rewards from other users may have an important impact on maximizing media rewards because the stability of peak and near-peak values changes depending on the promotion or suppression of psychological reward exchanges in meta-comments. The study also provides the following insights, not only for platforms but also for actual media users. Namely, clarification of the tipping system has the potential to increase user engagement behavior and the overall value of the platform. In particular, it can provide an opportunity for professional creators to gain a better understanding of revenue opportunities and to reconsider the behavior they have engaged in to satisfy their own financial and psychological needs. However, the experimental results have not been cross-referenced with empirical data from real media platforms; therefore, a comprehensive discussion of the validity of this model is needed.

In an experiment in a heterogeneous agent environment with professional and novice users, we also tested the impact of streaming quality on strategy changes among the respective users. The results showed that the overall behavioral tendencies of the agents did not change, but novice users, unlike professional users, found that the quality of streaming had a smaller impact on their behavior, especially when they were streamed by agents of lower degrees. Real-life agents have many other (heterogeneous) characteristics, some of which are not fully apparent in their real-life behavior. For example, age (Fietkiewicz et al. 2018) and social status (Hou et al. 2020) are thought to influence media viewing and consumption behavior, but their direct relevance remains debatable. As this study is concerned with the game-theoretic properties of tipping scenarios, it is beyond the scope of this paper to refer to user characteristics, but our model has the potential to represent these diverse properties.

Conclusion

In this study, the effect of virtual tipping and platform-mediated collection of commissions on user behavior was investigated on platforms such as SLSS/CGM using a game-theoretic approach. First, we introduce the game SNS-NG/TQ, which encompasses virtual tipping mediated by the platform and fixed commission rate charges, as well as the quality of live streaming. This game was played on complex artificial networks and actual networks generated based on Facebook and Twitch data. Subsequently, the distribution of user-emerging strategies was investigated using the co-evolutionary algorithm MWGA on the proposed SNS-NG/TQ game. Subsequently, user strategies were analyzed by categorizing agents according to their preferences for monetary/psychological rewards and their degrees, that is, the number of friends or followers/followees. These experimental results were compared with those obtained from SNS-NG/Q, which does not have a virtual tipping system. Our investigation revealed that the tipping system enhances the engagement of certain agents, leading to improved utility, especially for those with higher degrees of preference for monetary rewards.

Although this study investigated the impact of a simple tipping system on user behavior, an actual SLSS has various gamification elements that cannot be ignored. For example, our study did not consider recommendation systems. In general, the SLSS may recommend new streams to watch based on previously watched streams and the personalities of the genre distributors. Our study also did not consider changes in viewing probability. Viewing probabilities should change depending on past behavior during the game scenario, especially in relation to tipping behavior, and their impact should be investigated. In addition, this study considers tipping as an instantaneous exchange of monetary rewards and does not consider rewards that have long-term effects. For example, a subscription model involves payments returned as information or added value over a certain period. Such subscription models are widely used in SLSS, and will be a topic for future research.

Appendices

Appendix A: strategies of agents on facebook and twitch networks

A graph of the results obtained when increasing $\lambda$ on the Facebook and Twitch networks is shown in Figs. 11 and 12. These graphs indicate that the tendencies shown here are almost identical to those on CoNN networks. Because the CoNN model is proposed based on the generative process of some actual networks, a CoNN network has three well-known properties, small-worldness, a high-clustering coefficient and scale-freeness, which are often observed in realistic networks. The Facebook and Twitch networks used in this study also have these properties.

Fig. 11

Behavioral strategies of agents (Facebook network)

Fig. 12

Behavioral strategies of agents (Twitch network)

Appendix B: stability of convergence strategies

Figure 13 shows the convergence of co-evolutionary processes of the average values of the strategy parameters, B, Q, L and T when $\lambda =0.5$ over 1000 generations in the CoNN networks. It also includes the standard deviations over 1000 trials. As the trend of the final convergence values has already been discussed in Sect. “CoNN network” and, we discuss only the variability and stability here. Figure 13 indicates that all values of B, Q, and T of all were almost determined in the first 100 generations, and the average value of L also converged by 200 generations. Table 4, which lists the standard deviations at the last generation, indicates that all standard deviations are very small, meaning that the agents’ strategies are stable. We do not show here but the convergence process and standard deviation were almost similar for other $\lambda$ values.

The co-evolution process by MWGA was used to identify the optimal strategy with a mutation probability of 0.01 for each bit, as shown in Table 2 and described in Sect. “Mutation”. As an agent has 12 bits of genes, the probability of no mutation in all 1000 agents is $0.99^{1000\times 12}$, which is extremely small. Extensive searching over many generations by a large number of agents is expected to be the strategy found with many mutations in each experimental run. Therefore, Figure 13 shows that the equilibrium solutions converging in all settings are robust against exhaustive strategies with mutations. We expected that the strategies obtained through such diverse interactions between the agents would be evolutionarily stable.

As previously mentioned, the reward setup in this study is based on the assumptions of a previous study (Okada et al. 2015), which showed the stability of the solution in their environment. However, a detailed examination of the similarities of this game structure for various reward schemes is necessary to generalize the model. An exhaustive study considering the balance between costs and rewards in the media, daring to include unrealistic reward setpoints, could further generalize the conclusions of this study; however, this is outside the scope of this study and is therefore a topic for future research.

Fig. 13

Transition of behavioral strategies in co-evolutionary process (CoNN, $\lambda =0.5$)

Table 4 Standard deviations in the final generation (CoNN, $\lambda$=0.5)