A game perspective on collaborative learning among students in higher education

Abstract Understanding how students decide whether to participate during collaborative learning activities and what factors are their main concerns is important for efficient use of such activities in or out of the classroom. Based on evolutionary game theory, this study proposed a game model for collaborative learning that aimed to analyze the dynamic process by which bounded rational students adapt their strategies in collaborative learning. Based on the analysis of evolutional stable strategy in the model, the results identified perceived academic value, social gains, and social loss as motivators resulting in collaboration, while the cost of effort and time acted as the major barrier to collaborative learning. In addition, this study focused on the joint influence of these factors on students’ collaborative learning behavior. It further provided several implications for developing theory-building of collaborative learning and educational policymaking.


Introduction
People working together, establishing social organizations to complete tasks they could not accomplish individually, has been a common theme throughout human history (Kozlowski & Ilgen, 2006). In fact, teamwork skills are important for organizations' success. According to a survey by the Association of American Colleges and Universities, 71% of employers wanted higher education to stress the importance of developing teamwork skills and the ability to collaborate with diverse people (Office of student affairs, 2010); in fact, in the late 1990s and the early 2000s, calls for adoption of collaborative Learning (CL) in higher education became prevalent (Lammers & Murphy, 2002).
CL is a teaching method in which students are brought together to work on common goals (Johnson, 2006;Prince, 2004). This method simulates a real work environment, facilitating students to share learning experiences and update knowledge structures through cognitive conflict with peers (Almajed et al., 2016). Furthermore, CL has been shown to positively influence students' social skills

PUBLIC INTEREST STATEMENT
Collaborative learning is a teaching method in which students are brought together to work on common goals. This method facilitates student both academic and non-academic outcomes. Students' willingness and behavior in collaborative learning is expected to trigger effective learning mechanisms. This paper outlines the behavior strategy of student in collaborative learning activities in higher education context. It provides the reader with an opportunity to understand the reason why student choose to participate in collaborative learning, and provide suggestion to policy makers, educators how to involve student in this active learning activity. and higher-order thinking skills, such as interpersonal, communication, critical thinking, and problemsolving skills and self-reflective thinking (Sultan et al., 2020;Vizgirdaite & Fridrikaite, 2012).
Students' willingness and behavior in CL is expected to trigger effective learning mechanisms. Numerous studies have identified facilitative and impeditive factors that influence the CL process at the primary and secondary levels of education (Ginsburg-Block et al., 2006;Smith et al., 2014). Compared to K-12 students, college students are more autonomous in their learning (Boud, 1988); that is, students have more responsibility for learning, their ability to learn without the constant presence or intervention of a teacher is stronger than in elementary or secondary education levels. In terms of teaching strategy, instructors are encouraged to provide more autonomy rather than control (Black & Deci, 2000). Furthermore, with cognitive development and past experience, college students are more cognitively sophisticated and rational in their thinking than young children (Toplak et al., 2014); thus, college students are more cognitively advanced than adolescents, and as such, they would be more rational and capable of formulating strategies based on their own benefit. Because of these reasons, college students are more likely to be unwilling to collaborate with others, as they are more worried that other students may outperform them or that the lack of in-depth peer relationships may lead to free riding (Yuen & Majid, 2007). However, a common feature of the existing studies is that they are built on the assumption that students are more willing to collaborate with their peers; as a result, this stream of research fails to address the question of why students choose to collaborate when making decisions. Therefore, drawing students into CL is especially noteworthy and challenging in higher education.
There has been research adopting game theory to describe students' CL strategies, answering the question of why college students are willing to collaborate with peers (Burguillo, 2010;Chiong & Jovanovic, 2012;Huang et al., 2011). For example, Saito et al. (2020) developed a game model to describe the decisions of teachers and students in CL. However, obvious gaps remain between models and real-world practices for the following reasons.
First, previous game theoretical studies have generally led to simplification of the situations, such as environmental factors or players' characteristics. In particular, the conventional CL game model generally neglects the effect of benefit and cost factors on students' decision-making (Razmerita & Kirchner, 2015;Zhang & Jiang, 1997). Second, the conventional CL model assumes that college students are rational and able to obtain all decision-making information and use optimal strategies (Axelrod & Hamilton, 1981). However, this assumption of fully rational students almost never holds in the real world, as students' capabilities of obtaining information and computation of strategy are based on information they have sought (Fudenberg & Levine, 1998;Wolpert, 2004). Therefore, the CL model must be modified to accommodate the bounded rationality of real-world students. Third, the major game theoretical models of CL lack a dynamic view of students who observe others' behavior, reflect on their own, and adapt their strategies after learning about the environment (Chiong & Jovanovic, 2012).
Building on previous research, the present study aimed to address this gap by exploring what factors affect students' CL strategy making, and the influence mechanism of these factors using a game model. This study developed an evolutionary game model for CL by quantitatively analyzing students' CL strategies in different scenarios. By analyzing equilibrium solutions for students' CL behavior in various conditions, this study examined the separate and joint effects of these factors on students' behavioral decisions. Finally, this study provided several implications for developing theory-building of CL and educational policymaking.

Student CL and influencing factors
CL is an effective method in which students work together in groups to improve their performance by discussing problems and suggesting potential solutions (Almajed et al., 2016;Johnson & Johnson, 1989). Social constructivism, a socially-oriented learning theory, contends that interpersonal interactions include sharing knowledge, presenting thoughts, and being involved in cognitive conflicts, which tends to promote the internalization of external knowledge and enhance students' learning performance (Vygotsky et al., 1962). CL has advantages over other learning methods, including sharing learning experiences and information, obtaining social support from peers, developing opportunities for cognitive conflict with team members, and gaining social abilities, information-seeking skills, and presentation skills (Osman et al., 2011).
Recently, researchers have defined factors that affect students' willingness to collaborate with peers. Previous studies on CL tended to focus on contextual factors, including evaluation mechanisms, fairness, trust, mutual goals, teacher's personality, previous experience, teacher's engagement, scaffolding teaching, and feedback (Almajed et al., 2016;Razmerita & Kirchner, 2015;Sriratanaviriyakul & El-Den, 2017;Vizgirdaite & Fridrikaite, 2012). For example, Osman et al. (2011) found that comfortable class environment and the role of teachers influenced the effectiveness of CL. Fellenz (2006) suggested that ensuring fair and accurate assessment methods are efficient ways to maximize student CL. Driver (2001) stressed that exposing students to creative classroom environments, such as encouraging diversity of thinking and stimulating risk taking, can foster students' CL behavior.
Moreover, Thomas (1979) argued that students' learning strategies were influenced by their level of transparency, meaning the degree to which people make information and knowledge transparent to others, and receptivity, indicating the degree of willingness or readiness to receive others' information and knowledge. In addition, Thomas (1979) found that high levels of both factors tended to facilitate the learning strategy of collaboration, whereas only high levels of receptivity led to competition strategies. Compared with the one-way lecturing teaching method, previous studies found that CL was absent from hierarchical management, indicating that learners were responsible for their own learning processes, and could select their own strategies and methods to reach their goals (Barkley et al., 2007). In the CL process, teachers do not possess the main responsibility of transferring knowledge to students; rather, they played the role of CL facilitators (Chiong & Jovanovic, 2012;Vizgirdaite & Fridrikaite, 2012). Therefore, it was also found that students' personal factors, such as personality, previous experience, and self-efficacy are key factors that influence their willingness to collaborate (Razmerita & Kirchner, 2015). For example, Cheng (2016) examined the relationship between past experience and CL behavior, and found that students who had experience of CL were more willing to participate in the next instance. Hilliard et al. (2020) found that students may be unwilling to collaborate with following instances with peers if they felt anxiety or disappointed in their previous CL. Garg et al. (2021) found a significant influence of self-efficacy on students' willingness in CL.

Benefit and cost of CL
According to SET, students choose to collaborate with others when this provides more benefits than learning individually. Numerous studies have investigated the benefits that motivate students' willingness to collaborate. It has been suggested that students are willing to actively participate in CL, as it helps learners express their thoughts, improve their understanding of topics, challenge others' ideas, and develop non-technical skills (Almajed et al., 2016;Chiong & Jovanovic, 2012;Ong et al., 2011). Yuen and Majid (2007) investigated the patterns of collaboration among undergraduates and suggested that social benefits are an essential factor for CL among students. In addition, learning together has also been recognized as an effective way to establish and maintain social relationships with peers, place trust in others, and improve individual impressions (Talanker).
Further, the costs of additional time and effort required for collaborative groupwork lead to students' reluctance to participate (Ramayah et al., 2013). Almajed et al. (2016) argued that the main reason for students' reluctance to collaborate with peers is the extra time required to derive and disseminate information. Kankanhalli et al. (2005) noted the effort required to codify knowledge as the cost of knowledge sharing . Similarly, Shih et al. (2006) suggested that useful information requires intensive preparatory work before communication, requiring students to make it available and understandable to others through words, drawings, models, and other methods.
Thus, this paper proposes the following hypotheses: H1: Benefit factors (academic value and social gains) will motivate students to choose to collaborate with peers.
H2: Cost factors (time and effort) will deter students from choosing to collaborate with peers.

Use of game theory in CL
Game theory was originally developed to describe the social interaction between intelligent and rational decision-makers by using mathematical models (Ho et al., 2011;Romp, 1997). Game theory can predict players' future movements by describing their strategies. Numerous studies have used game models to analyze and forecast students' behavior in CL (Huang et al., 2011;Saito et al., 2020;Shih et al., 2006;Talanker). Game models of CL include at least two students and two types of strategies: non-collaboration, in which knowledge is not shared among students, and collaboration, in which students are willing to share knowledge with peers with a common goal.
The models of static game, including prisoner's dilemma and snowdrift, as well as evolutionary games have been adopted in prior research to investigate students' decision-making strategies in CL. Shih et al. (2006) proposed a theoretical model based on the prisoner's dilemma game theory to analyze the behaviors of collaboration and competition among students and found that students' purpose was to receive a high mark on their performance, while taking time and energy to disseminate information in a team tended to be useless for marks when the evaluation was given to individuals rather than team performance. Therefore, it is more likely to be a social dilemma when the given marks are based on evaluations of students' individual performance. However, Chiong and Jovanovic (2012) suggested that the model of snowdrift game was more appropriate, allowing players to obtain more benefits from their collaboration compared to the prisoner's dilemma game. Therefore, for students in the snowdrift game, collaboration is a better option than non-collaboration, as, although there is a partner refusing to collaborate, it is better to learn in a group.
These classic static game models have the advantage of simplifying students' CL decisions, revealing that collaboration can be achieved only when an individual's perceived relative benefit is satisfied, after which the collective benefit can be achieved. However, these models are oversimplified and do not fully represent real-life situations, such as assuming that players are rational and able to obtain all decision-making information and use the optimal strategy (Binmore, 2007). Furthermore, these are one-shot games, where players cannot adjust their strategies when they notice the consequence of others' decisions. In recent years, evolutionary game theory (EGT) has been used extensively as a tool for exploring the emergence and maintenance of collaboration. As a new dimension of game theory approaches, evolutionary games have dropped the unrealistic assumption of rationality, allowing players to adapt their strategies by learning from their own and others' behaviors (Peter et al., 1978). Liu et al. (2015) used EGT to analyze CL in supply chain management and identified the factors that affected members' decisions regarding CL and knowledge sharing. Li and Kang (2019) developed a knowledge-sharing model based on EGT and determined the main barriers to knowledge sharing. Chiong and Jovanovic (2012) adopted the idea of EGT and demonstrated that students could learn from games and adapted a better strategy by remixing the group based on their level of collaboration in the initial group. EGT is more in line with realistic situations than the conventional ones, assuming that players are bounded rational agents and able to learn from the game and environment over time until an evolutionarily stable strategy (ESS) is reached in the game .

Model assumptions and variables
In general, game theory has three components: players, strategies, and payoffs.

Assumption 1 (players)
To simplify the model, this study assumed two students (students 1 and 2) in a CL activity, both of which were bounded rational agents.

Assumption 2 (strategies)
In the game model, two players collaborate with each other when they share common interests and goals, at the same time, they compete due to differences in interests and objectives.
Within the CL context, both students have two options in selecting their strategy: collaborate or not. Students' collaborative willingness is associated with two problems: the competition among students to outperform other students in CL and a lack of trust. Competition or distrust may result in the free riding phenomenon, in which students are unwilling to collaborate with peers while expecting to benefit from their contributions.

Assumption 3 (payoffs)
Before establishing the payoffs in the game model, variables must be defined.
V Δμ i ð Þ: perceived academic value. This refers to the academic benefits perceived by students in collaboration. As students are assumed to be bounded rational agents in the game, students have different levels of receptivity, and the academic benefit of CL depends on the extent to which they perceive it rather than the objective academic benefit. Therefore, the present study employed the prospect theory proposed by Tversky and Tversky (1979) to define the perceived value of CL from others . According to the prospect theory, decision-makers make choices based on a reference point, the location of which can be affected by the expectations of the decision-maker. This theory argues that people perceive outcomes as gains or losses, which are defined relative to the reference point. The function expression of the perceived value is defined as: where V is defined as the prospective value of the strategy and consists of the value function V Δμ i ð Þ and weight function ω p i ð Þ, with p i representing the occurrence probability of a cooperative learning event i. The weight function ω p i ð Þ has the following characteristic: when the value of p i is relatively small, then ω p i ð Þ>p i ; when it is relatively large, then ω p i ð Þ<p i , which assumes that people tend to overestimate the probability of low-probability events and underestimate the probability of high-probability events. Δμ i refers to student's subjective value perception of the difference between actual academic gains and reference point in event i. V Δμ i ð Þ is the value function of Δμ i , refers to the students' perceived value of the actual benefit in a CL event i. When Δμ i � 0, the value is positive, while for Δμ i <0, the value is negative. α(0 < α < 1) is defined as the degree of marginal decline in students' perceived value function; the greater the value, the greater the degree of decline. λ(λ � 1) is defined as the loss avoidance coefficient; the greater the value, the higher the participant's sensitivity to loss. V Δμ i ð Þ indicates that students have the characteristics of loss avoidance and gain preference, which is consistent with the decision-making scenario involving bounded rational players in uncertain conditions. a 1 ; a 2 : knowledge base. This is defined as the students' knowledge base and the maximum amount of knowledge that can be shared in CL. It is related to the willingness to collaborate and the extent to which knowledge is shared and hidden as well as the extent to which received knowledge is understood (Thomas, 1979). δ 1 ; δ 2 : knowledge sharing coefficient. This indicates each student's willingness to collaborate and the extent to which knowledge is shared.
Þ is defined as the academic value perceived in CL by a student who does not share knowledge, while the other one shares knowledge. V 0 δ i � a i ð Þ refers to the received knowledge value perceived by the student when both students choose to collaborate during learning. The perceived value could consist of one or more, including having the experience of working in a real work environment, deepening the understanding of the course content, updating the knowledge structure, creating, developing information seeking and retrieval skills, practicing social skills, and obtaining peer support within a CL team (Almajed et al., 2016).
k; k 0 :social gains and losses. A student who chooses to collaborate in learning signals their credibility to others and obtains benefits (k), such as increasing trustworthiness, improving others' impressions of the student, and promoting social relationships with peers. In contrast, if students choose individual learning in a group work, they may lose their reliability, destroy others' impressions of themselves, and worsen social relationships with others (k 0 ). C 1 ; C 2 : cost of time and effort. CL requires time and effort for students to seek and transmit relevant information and communicate with each other. To simplify the model, it is assumed that C 1 ¼ C 2 ¼ C.
The following four scenarios were proposed for the total benefits generated from a game involving two students: (1) Both student 1 and student 2 choose collaboration.
The revenue of student 1 is defined as: The revenue of student 2 is defined as: V 0 δ 1 � a 1 ð Þ þ k À C (2) Student 1 chooses collaboration, while student 2 chooses no collaboration.
The revenue of student 1 is defined as: k À C The revenue of student 2 is defined as: V δ 1 � a 1 ð Þ À k 0 (3) Student 2 chooses collaboration, while student 1 chooses no collaboration, and the revenues of two students are similar to scenario (2).
The revenue of student 1 is defined as: V δ 2 � a 2 ð Þ À k 0 The revenue of student 2 is defined as: k À C (4) Both student 1 and student 2 choose no collaboration.
The revenue of student 1 is defined as: À k 0 The revenue of student 2 is defined as: À k 0 Moreover, it is further assumed that the initial probability of student 1 choosing collaboration is x (0 < x < 1); thus, the initial probability of choosing no collaboration is (1-x). Similarly, student 2 chooses collaboration with a probability of y (0 < y < 1), with a (1-y) probability of choosing no collaboration. Table 1 shows the payoff function matrix for the total revenue gained from collaboration between two students.

Analysis of evolutionary stable strategy
The basic idea of ESS is that the more fit a strategy is at any moment, the more likely it is to be used in the future (Hofbauer & Sigmund, 2003). To solve the stable strategy, Taylor and Jonker (1978) introduced the replicator dynamic equation, which describes the selection process where more successful strategies spread . In the present model, students were assumed to have bounded rationality, which means they tend to switch to a strategy that is doing well when they experience repeated scenarios. Therefore, applying the replicator dynamic equation matched well with the present research in analyzing the student CL strategy.

For student 1:
When student 1 chooses collaboration, the expected revenue is defined using Equation (2): When student 1 chooses no collaboration, the expected revenue is defined using Equation (3): The average expected revenue for student 1 is: The replicator dynamic equation is applied for student 1 as follows: There are two conditions that must be satisfied to solve the stable strategy in Equation (5): Þ , a stable strategy can be reached only either x � ¼ 0 or x � ¼ 1.
Situation 1: when This analysis indicates that the strategy of student 1 in CL is based on student 2ʹs choice. In particular, student 2ʹs collaboration probability y and stable equilibrium y � have an important influence on student 1ʹs willingness and choice regarding CL. When y>y � , collaboration in CL is a stable strategy for student 1, while for y<y � , no collaboration is a stable strategy in CL. That is, the smaller the y � , the greater the probability that student 1 will collaborate in CL.

For student 2:
When student 2 chooses collaboration, the expected revenue is defined using Equation (7): When student 2 chooses no collaboration, the expected revenue is defined using Equation (8).
The average expected revenue for student 2 is: Then, the replicator dynamic equation is applied for student 2 as follows: Þ , a stable strategy can be reached only either y � ¼ 0 or y � ¼ 1.
Similar to the analysis of student 1, the strategy of student 2 in CL is based on student 1ʹs choice. In particular, student 1ʹs collaboration probability x and stable equilibrium x � have an important influence on student 2ʹs willingness and choice regarding CL. When x>x � , collaboration in CL is a stable strategy for student 2, while for x<x � , no collaboration is a stable strategy in CL. That is, the smaller the x � , the greater the probability that student 2 will collaborate in CL.

Analysis results
This analysis revealed that four evolutionary stable strategies can be reached in four different situations for two students. Figure 1 shows students' stable strategies in the CL.
Area A: x>x � ; y>y � , collaboration is the ESS for both student 1 and student 2.
Area B: x x � ; y h iy � , no collaboration is the ESS for student 1, while collaboration is the ESS for student 2.
Area C: x>x � ; y<y � , collaboration is the ESS for student 1, while no collaboration is the ESS for student 2.
Area D: x<x � ; y<y � , no collaboration is the ESS for both student 1 and student Considering the preconditions for situations 2 and 4, the formula must be satisfied before students choose collaboration: In this formula, V δ i �a i ð Þ À k 0 refers to revenue of student i when he selects free-ride in CL. V 0 δ i �a i ð Þ þ k À C ð Þ refers to the revenue of student i when he and the other student both choose to collaborate. This formula reveals that students would choose collaboration under the precondition that the former value is smaller than the latter.
In addition, the results demonstrated that the probability of collaboration x; y is influenced by equilibrium points x � ; y � , respectively (x � ¼ . Moreover, as demonstrated in Table 1, when À k 0 À k À C ð Þ<V 0 δ i � a i ð Þ À V δ i � a i ð Þ, the smaller the x � ; y � are, the greater the area A, which indicates a greater probability of collaboration between students. Each equilibrium point x � ; y � is influenced by perceived value, social gain and loss, and the cost of time and effort.

Figure 1. Students' stable strategies in CL.
First, the perceived value influences students' CL behavior. This model assumes that students have bounded rationality and different levels of receptivity, as they have different knowledge bases. Thus, the amount of academic revenue refers to the benefit perceived in collaboration rather than objective value. The perceived academic value when both students choose collaboration is different from the value when one student collaborates while the other does not. The results demonstrated that the perceived academic value in disparate scenarios has different relationships with the equilibrium points x � ; y � . Specifically, the perceived academic value in the situation in which both students choose collaboration has a negative relationship with equilibrium point x � ; y � , indicating that the greater the perceived academic value, the smaller the x � ; y � and the greater the probability of collaboration. In contrast, the perceived value when one student collaborates while the other does not is positively related to the equilibrium points x � ; y � , indicating that the smaller the perceived value, the smaller the x � ; y � and the smaller the probability of no collaboration.
Second, social gains and loss is positively related to students' CL behavior. Based on this assumption, social gains can be a positive social relationship, improvement in the individual's reliability and trustworthiness, and making a better impression on others. The results revealed that this type of gain is negatively correlated with x � ; y � and positively correlated with the probability of collaboration. However, social losses caused by a lack of collaboration include damaged social relationships, decrease in the individual's reliability and trustworthiness, and worsened image. Social loss is positively correlated with x � ; y � and the probability of collaboration. In conclusion, the factor of social effect increases the revenue of collaboration and the cost of no collaboration, facilitating students' collaboration in learning.
Third, the cost of time and effort in CL has a negative effect on students' CL behavior. Extra time and effort are required in CL and have a positive correlation with x � ; y � , indicating that the smaller the costs, the greater the probability of collaboration. However, if the costs are too high, students are more likely to choose individual learning rather than CL.

Discussion and implications
Using the model based on the evolutionary game, this study assumed students to have bound rationality and analyzed their CL strategies in different scenarios. The results indicated that bounded rational students are influenced by factors related to benefit and cost when choosing strategies. The results of the evolutionary stable strategy showed that perceived academic value, social gain and loss, and cost of time and effort influenced students' CL willingness and behavior choice.
The result showed that higher perceived academic values, such as removing confusion, expanding the scope of knowledge, strengthening memory, facilitating students' creativity, and practicing skills, increase the likelihood of student collaboration. This conclusion is consistent with the prior research. As suggested by Shih et al. (2006), during the CL process, students can share opinions and propose and receive constructive suggestions from peers. Thus, it is the revenue that motivates their behavior toward collaborating with others.
This paper also demonstrated that social outcome was a vital factor in promoting students' collaboration in learning. Social benefits showed a significant positive effect on students' intention to engage in CL, which was in line with previous studies (Talanker, ;Yuen & Majid, 2007). For example,) Bravo et al. (2019) suggested that students are more likely to engage in CL when the cohesiveness among students is strong. In addition, the current model expanded on previous research by examining the effect of social loss on students' choices, indicating that students are more likely to avoid refusing collaboration when they realize that being a free rider or being non-collaborative would damage their trustworthiness, the impression they make on others, and social relationships with others.
Although CL significantly benefits students, it requires additional time and effort to prepare for sharing knowledge, exchange useful information communication and negotiation, and coordinate with others. The results of the ESS indicated that the cost of time and effort have a negative correlation with students' collaborative behavior strategies. As previous research has suggested, the main reason why students are reluctant to collaborate with peers is the extra time required to derive and disseminate information (Almajed et al., 2016;Chiong & Jovanovic, 2012). Moreover, the game model in this study considered the effort cost when students collaborated with peers. Shih et al. (2006) suggested that useful information requires intensive preparation before communication and students must make it available and understandable to others through words, drawings, models, and other methods.
Furthermore, this study also addressed the gap of existing research, and revealed the reason that some students choose individual learning rather than learning with peers. As Shih (2006) stressed, students decide on their choices based on their strategies for various payoffs. It was found that students would like to collaborate with others only when the value of collaboration revenue is larger than the free-rider one. Conversely, if a student thinks the free riding is more rewarding, then he would not be willing to share knowledge with peers. From this perspective, this finding suggested that students who did not participate in CL should be regarded as reasonable and rational.
Using evolutionary game model analysis, this study contributes several theoretical implications to the literature. First, in order to achieve a situation closer to reality, this study developed a CL game model using evolutionary game theory. This study assumed students as bounded rational agents who could find a better strategy after learning more about the environment. The results demonstrated that this model is more practical than the traditional game, such as the prisoner's dilemma. Second, the replicator dynamic equation method was adopted to analyze the evolutionary stable strategy. This method fits the assumption that students are bounded rational agents and simulate the process by which students tend to switch to a better choice until they find a stable strategy. Third, this study provided a better understanding of the influence of benefits and costs on students' decision to collaborate. The results demonstrated that perceived academic value, social gains and losses, and cost of time and effort are critical factors that affect students' willingness to collaborate. In addition, the results revealed the preconditions required for collaboration. Students would choose to collaborate only when the value of collaboration revenue is larger than the free-rider one. Furthermore, according to discussions regarding ESS, students are more likely to choose collaboration only when perceived academic value and social gain and loss are increased and the cost of time and effort is reduced.
This study discussed how benefits and costs influence college students' CL willingness, which provides several practical implications regarding CL. As suggested by the analysis of the evolutionary game model, CL among students would generate various benefits. To facilitate mutual CL, teachers should explain and stress the academic and social benefits of collaboration and encourage students to share reciprocally. For instance, grades as an external motivation, student participation, and performance in CL should be considered in the assessment. Furthermore, teachers should build a fair environment to assure students that the benefit of mutual collaboration is greater than that of free riding. Moreover, consistent with Yamagishi et al.'s (2005) findings, this study demonstrated that if students do not know each other well in CL, they lack trust, leading to unwillingness to collaborate or wishing to only receive information from others without giving anything (Yamagishi et al., 2005). Therefore, the importance of trust emerges from its cyclical nature: a trust relationship creates a new collaboration, which in turn generates social benefits. To ensure effective collaboration, building and maintaining trust relationships among students is vital. As such, at the beginning of CL, teachers could use mechanisms of reward and punishment, such as giving marks based on the level of CL, to encourage students to trust others' intentions to collaborate. When students realize that trust is rewarded with benefits in collaboration, trust increases. After a solid trust relationship among students has been established, CL is more likely to be effective, as students realize collaboration is beneficial to make a good impression on others, build trustworthiness, and improve social relationships with peers, which are all important for school life. In that case, students would be willing to collaborate, despite the extra time and effort required. Moreover, teachers could facilitate communication among students by offering convenient platforms, such as social media, including wikis, Twitter, blogs. Social media has been recognized as an effective way for students to derive and disseminate information, as it reduces the time and effort required to share and communicate (Razmerita & Kirchner, 2015).

Conclusion
CL has become an increasingly important teaching method to improve college students' learning outcomes. This study shed light on the crucial issue of college students' CL choices. Drawing factors from the perspective of gains and losses related to CL, this study constructed an evolutionary game model to analyze the dynamic process in which bounded rational students adapt CL strategies. Based on the replicator dynamic equation, this model identifies perceived academic value and social gains and losses as important factors resulting in collaboration, while the cost of time and effort acts as the major barrier to CL. Furthermore, this study revealed that students would like to collaborate with others only when the value of collaboration revenue is larger than the free-rider one.
This study had some limitations. To simplify the model, this study focused on benefits and costs; however, in reality, students' CL willingness and behavior are more complicated. Future research should consider the impact of personal factors, such as self-satisfaction and selfconfidence. In addition, this study was conducted from the perspective of a game among students and the results are based on the analysis of a theoretical model with a lack of statistical analyses to quantify the real effect of the factors. Therefore, future studies should examine the influence of these factors on students' CL behavior using statistical methods. Furthermore, this study assumed students possessed bounded rationality and considered the evolutionary game model to be adaptive. In order to better understand the game in students' CL, future studies should compare and contrast alternative models based on the literature regarding CL game models to identify a more adaptive model. Despite these limitations, it is hoped that this study will be helpful in improving the quality of CL teaching methods in college classes, the effectiveness of students' participation in collaboration, and the avoidance of the phenomenon of free riding. You are free to: Share -copy and redistribute the material in any medium or format. Adapt -remix, transform, and build upon the material for any purpose, even commercially. The licensor cannot revoke these freedoms as long as you follow the license terms.
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