Coordination Game Research Articles

Abstract The paper presents an economic theory of morality and, based on it, a classification of social sciences and economic subdisciplines. Following the introduction, sections 2 to 4 seek to internalise morality into economics, both from a decision-theoretic and a game-theoretic point of view. In sections 5 and 6 moral principles are reconstructed as institutions, and it is shown why and how moral principles turn mixed-motive games into coordination games (along a hierarchy of moral stages and the respective games). This reveals the immense importance of morality not only in real life but also with respect to theoretical and empirical work in economics. Further, it may be asked whether there remains a proper realm for morality (or ethics) above and beyond the economic frame of reference. This issue is addressed in section 7, where the structural differences and the systematic relations between economic and neighbouring disciplines are discussed. Section 8 concludes and discusses important ramifications.

This paper revisits the well-known volunteer’s dilemma on the production of a public good when a single participant is sufficient for the task. We propose a cost-sharing model with a volunteering cost that decreases exponentially in the number of volunteers. We show that, at the unique mixed-strategy equilibrium, the probability of production may increase in the number of players for sufficiently low volunteering costs. This provides an alternative account of the fit of the model with some political-military conflict situations: A larger group does erode the individual incentive to volunteer but in an offsetting way that favors the production of the public good. A second result is that the mixed-strategy Nash equilibrium may be more socially efficient than the pure-strategy Nash equilibrium for some parameter values, which is a major reversal with respect to the standard dilemma and many other coordination games.

The article considers game-theoretic modeling of researchers’ mobility between cities of own country. Two simple game-theoretic models are constructed. The first model characterizes the decision-making process of a researcher regarding the location of his activity by assessing the probability of success of such activity in conditions of individual or group participation, and is an antagonistic (matrix) game. The second model takes into account the interaction of researchers in a group, expressed through comparison of changes in individual and joint knowledge. Different professional and quantitative composition of researchers in cities generates multiple equilibria, characteristic of coordination and anti-coordination games. The problem of choosing the best Nash equilibrium is proposed to be solved using an additional parameter: the degree of possibility of continuing a scientific topic that was conducted in the city of departure. It is revealed that differences in the degree of such possibilities between cities can form the priority of researchers’ movement.

Pilgrimage has received long-standing scholarly attention, but most theoretical work focuses on how these rituals can be maintained, rather than the bigger puzzle of how they emerge. Using empirical inspiration from a new pilgrimage in Peru, we address this gap by outlining a theoretical framework more capable of accounting for how these phenomena get off the ground. We contend that the framework of an assurance game (a type of coordination game) captures the challenge of a collective ritual like pilgrimage emerging. By combining this assurance game with a model of Bayesian learning under uncertainty we illustrate how pilgrimage can be institutionalized on occasion. We further argue that our approach sheds light on the relationship between rituals and uncertainty, without having to make strong assumptions about individuals’ psychological needs.

Dense, microbial communities are shaped by local interactions between cells. Both the nature of interactions, spanning antagonistic to cooperative, and the strength of interactions vary between and across microbial species and strains. These local interactions can influence the emergence and maintenance of microbial diversity. However, it remains challenging to link features of local interactions with spatially mediated coexistence dynamics given the significant variation in the microscopic mechanisms involved in cell-to-cell feedback. Here, we explore how microbial interactions over a broad range of ecological contexts spanning antagonism to cooperation can enable coexistence as spatially explicit domains emerge. To do so, we introduce and analyze a family of stochastic coordination games, where individuals do better when playing (i.e., interacting) with individuals of the same type than when playing with individuals of a different type. Using this game-theoretic framework, we show that the population dynamics for coordination games is governed by a double-well shaped interaction potential. We find that in a spatial setting this double-well potential induces phase separation, facilitating coexistence. Moreover, we show that for microbes engaged in symmetric coordination games, phase separation takes on a universal scaling that follows ‘Model A’ coarsening, consistent with prior experimental observations for Vibrio cholerae mutual killers. Finally, we derive a PDE equivalent of the spatial stochastic game, confirming both the double-well nature of spatial coordination games and the universality of phase separation. Altogether, this work extends prior findings on the link between microbial interactions and population structure and suggests generic mechanisms embedded in local interactions that can enable coexistence.

Comparison between young children's and college students' cooperative success in an online Stag Hunt: Do prior training, sex, relationship, and nature of communication matter?

Reporting is widespread in human society, yet its theoretical mechanisms for cooperation in a monitored society remain unclear. Here, we introduce a reporting mechanism into the public goods game to investigate its impact on the emergence of cooperative behavior in a monitored environment. We analyze well-mixed populations and structured populations. Through theoretical analysis and numerical calculations, we find that when the fine is low, the introduction of the reporting mechanism effectively transforms the public goods game into a coordination game, thereby enhancing the feasibility of cooperation. Moreover, when the fine is high, cooperation emerges as a globally stable evolutionary strategy. Our results further indicate that reporting intensity exerts a nonlinear effect on public cooperation: moderate reporting intensity favors the evolution of cooperation, whereas excessive frequency or generosity in reporting may weaken its efficacy. Additionally, Monte Carlo simulation results on structured populations are consistent with those obtained in well-mixed populations. Notably, we observe a discontinuous phase transition in cooperation levels upon variation of reporting parameters, which can precipitate an outbreak of cooperation. These findings reveal reporting as a double-edged sword, emphasizing the need to balance its reporting parameters for optimal cooperation.

Massively multiplayer online games (MMOGs) are becoming more and more significant places for people to work together online. Researchers still do not know much about how individual traits affect how teams work together in games. Studies on players and game playability are still in the early stages. This study performed a quantitative analysis of data from 1,038 Chinese online players to investigate the interrelations between emotional intelligence (EI), transformational leadership (TL), team effectiveness (TE), and playability (PB). Drawing on the Input–Process–Output (IPO) model, social identity theory, and user experience theory, the research focused on how individual characteristics shape team outcomes and player experiences. The findings of this study indicate that both EI and TL have a positive impact on TE, which acts as a key mediating variable influencing the impact of both on PB. The findings also show that EI has a stronger link to PB than TL does. Notably, EI demonstrates a stronger association with PB than TL, highlighting its crucial role in enhancing team coordination and overall game enjoyment. This research augments current theories on virtual team collaboration and offers pragmatic guidance for game developers to improve player engagement and team coordination in online settings.

Abstract Efficient coordination is a major source of efficiency gains. We study in an experimental coordination game with 727 children and teenagers, aged 9 to 18 years, the strategies played in pre-adulthood. In our one-shot, experimental coordination game, we vary the incentives for reaching the more efficient equilibrium and the number of subjects within a group. Looking at strategy choices dependent on age, we do not find robust age effects in the aggregate. Yet, we see that smaller group sizes and larger incentives increase the likelihood of choosing the efficient strategy. The larger strategic uncertainty in larger groups is obviously harmful for overall efficiency. Regarding incentives, we find that increasing the profits in the efficient equilibrium seems to work better than providing a cushion in case of miscoordination. Beliefs play an important role as well, as subjects are more likely to play the efficient strategy when they expect others to do so as well. Our results are robust to controlling for individual risk-, time-, and social preferences.

Promoting cooperation remains a major challenge in natural science. While most studies focus on single strategy update rules, individuals in real-life often use multiple strategies in response to dynamic environments. This paper introduces a mixed update rule combining imitation and reinforcement learning (RL). In imitation learning (IL), individuals adopt strategies from higher-payoff opponents, while RL relies on personal experience. Simulations of the Prisoner's Dilemma Game (PDG), Coexistence Game (CG), and Coordination Game (CoG), both in well-mixed populations and square lattice networks, show that: (i) cooperation and defection coexist in the PDG, resolving the dilemma of universal defection; (ii) cooperation exceeds the mixed Nash equilibrium in the CG; and (iii) cooperators dominate in the CoG. The mixed update rule outperforms single strategy approaches in those games, highlighting its effectiveness in fostering cooperation.

Abstract We investigate experimentally the role of costly information acquisition as a selection mechanism in coordination games with incomplete information. We find that subjects’ behavior, conditional on their precision choice, varies along two dimensions. Higher precision choices lead to more coordination attempts (and successful coordination) and more predictable strategies than low precision choices. These differences in behavior are absent when information precision is exogenous, suggesting that information choices act as a selection device. We find that individual precision choices are stable and unaffected by others’ past precision choices from the beginning of the experiment, suggesting that that selection is not driven by strategic anticipation but rather by unobserved heterogeneity in subjects’ preferences. We show that these effects have significant payoff consequences.

We try to rationalize the fact that the impact of higher education spread on aggregate productivity tends to disappear as a higher share people completes college. For that purpose, we model this situation by means of a coordination (Stag Hunt) game, where a youngster reaps the benefit of higher education only if there is a critical mass of students. During the initial stage, the net reward of higher education is high, so that the Nash equilibrium with general enrolment is selected. As higher education becomes widespread, its relative benefit tends to decline because the relative wage of skilled labour falls with the rise in its supply and universities face diseconomies of scale as they expand over lower density territories. The decrease in the reward is multiplied by the fact that the strategy of avoiding higher education becomes “risk-dominant”, which more likely leads to a coordination breakdown, where the tertiary schooling rate might rise despite the output per worker decreases.

When two people are motivated solely to coordinate their actions, but one is better informed than the other about how best to achieve this, confidence signalling can facilitate mutually rewarding choices, and the use of this so-called confidence heuristic has been confirmed in experiments using coordination games. To investigate whether confidence signalling can also be used deceptively, we investigated behaviour in strategic games in which the better-informed player can benefit selfishly by misrepresenting confidence signals deliberately. We manipulated the relative quality of information provided to members of 55 dyads who discussed, under incomplete and asymmetric information, a series of problems in which they had to decide which of two shapes was closest in size to a target shape. Monetary incentives were structured according to the Deadlock game. We found that players with superior information felt greater confidence and attempted on a substantial minority of trials to deceive the other player, mainly by withholding the correct answer at the start of the discussion. We conclude that confidence signalling, even without lying, is sometimes used to deceive.

We study the exploration-exploitation trade-off for large multiplayer coordination games where players strategise via Q-Learning, a common learning framework in multi-agent reinforcement learning. Q-Learning is known to have two shortcomings, namely non-convergence and potential equilibrium selection problems, when there are multiple fixed points, called Quantal Response Equilibria (QRE). Furthermore, whilst QRE have full support for finite games, it is not clear how Q-Learning behaves as the game becomes large. In this paper, we characterise the critical exploration rate that guarantees convergence to a unique fixed point, addressing the two shortcomings above. Using a generating-functional method, we show that this rate increases with the number of players and the alignment of their payoffs. For many-player coordination games with perfectly aligned payoffs, this exploration rate is roughly twice that of p-player zero-sum games. As for large games, we provide a structural result for QRE, which suggests that as the game size increases, Q-Learning converges to a QRE near the boundary of the simplex of the action space, a phenomenon we term asymptotic extinction, where a constant fraction of the actions are played with zero probability at a rate o(1/N) for an N -action game.

Adventure camp activities have become increasingly popular with children and teens, allowing them to develop their gross motor skills through outdoor experiences and motor challenges. These experiences not only promote the development of motor skills among the school population but also have a positive impact on cognitive and emotional development. Studies show that engaging in such activities increases coordination, balance and muscle strength, essential for well-developed motor skills. The presented research aimed to identify the influences of adventure activities that propose games of coordination, balance and sustained effort. The sample included 228 students aged between 11 and 14 years who were given initial and final tests on standardized tests: Star Excursion Test, Denisiuk Test and the Ruffier Test. The research period was 21 days and included three series of 7 days each. Within it, the Development through Education and Adventure experimental program was implemented and included suspended obstacle course games, slackline, adventure trails, balance games, imposed and freecycling trails, climbing and hiking. In research tests, descriptive statistical analyses reveal significant results within each group for p<0.05 and r<0.08. The operational methodological approach of the research, through the proposed activity program, optimizes the level of coordination capacity, general motor skills and effort capacity. Theme and content addressed to contribute to the identification of the motor benefits of this type of recreational activities in the school environment and contribute to the broad context of research on behaviour and their effects.

The coordination of multi-agent is one of the critical problems in Multi-agent Reinforcement Learning (MARL). The traditional methods of MARL focus on finding a stochastically acceptable solution called Nash Equilibrium (NE) for all agents from the Markov Game in which multiple equilibria exist. However, learning a fair equilibrium is crucial for the sustainability and stability of collaboration in the long-term coordination game, especially when the leadership competition exists. In this article, we propose the bi-level reinforcement learning method N-Bi-AC, whose solution is a Pareto improvement for traditional NE, to choose a fair Equilibrium. There are two parts in our method, the first is that we propose the Negotiator to determine the leader in stage game, and the other is to update the Q-value of agents in the game by using a bi-level actor-critic learning method based on the Joint Mixed Strategy Equilibrium Q-learning algorithm (JMSE Q-learning). The convergence proof is given, and the learning algorithm is compared with the state-of-the-art algorithms. We found that the proposed N-Bi-AC method successfully converged to a fair NE, which guarantees the fairness of agents in different matrix game environments.

Abstract We introduce group cohesion to study the economic relevance of social relationships in team production. We operationalize measurement of group cohesion, adapting the “oneness scale” from psychology. A series of experiments, including a preregistered replication, reveals strong, positive associations between group cohesion and performance assessed in weak-link coordination games, with high-cohesion groups being likely to achieve superior equilibria. In exploratory analysis, we identify beliefs rather than social preferences as the primary mechanism through which factors proxied by group cohesion influence group performance. Our evidence provides proof of concept for group cohesion as a useful tool for economic research and practice.

Abstract We study the manager-agent game, a novel coordination game played between a manager and two agents. Unlike commonly studied coordination games, the manager-agent game stresses asymmetric information (agents know the state of the world, but managers do not) and asymmetric payoffs (for all states of the world, agents have opposing preferences over outcomes). Efficient coordination requires coordinating agents’ actions and utilising their private information. We vary how agents’ actions are chosen (managerial control versus delegation), the mode of communication (none, structured communication or free-form chat) and the channels of communication (i.e., who can communicate with each other). Achieving coordination per se is not challenging, but, averaging across all states of the world, total surplus only surpasses the safe outcome when managerial control is combined with three-way free-form chat. Unlike weak-link games, advice from managers to agents does not increase total surplus. The combination of managerial control and free-form chat works because, under these conditions, agents rarely lie about their private information. Our results suggest that common findings from the experimental literature on lying are not robust to changes in the mode of communication.

This study uses the game theory framework to deeply explore the interaction of all parties in auto insurance product pricing, aiming to reveal its complex game relationship and propose effective optimization strategies. Researchers have found that competition and information asymmetry among insurance companies have a significant impact on pricing, but there is still a research gap in the formation mechanism and long-term effect evaluation behind it. Therefore, this study uses the game theory framework, including models such as the prisoner's dilemma, coordination game and signaling game, to deeply explore the interaction of all parties in auto insurance product pricing, aiming to reveal its complex game relationship and propose effective optimization strategies. The results show that through indirect cooperation (such as setting industry standards and sharing non-sensitive data), insurance companies can avoid vicious price wars and improve market transparency; standardized services and simplified terms simplify consumer decisions and enhance market trust; introducing third-party verification and adjusting premiums based on driving records ensure that pricing more accurately reflects the level of risk. The research conclusion points out that this study provides valuable theoretical and practical guidance for game strategies in auto insurance pricing, but there are still limitations in data acquisition, model assumptions, regional differences and long-term effect evaluation. Further exploration and improvement are needed in the future to meet complex market challenges.

In this paper, we study descriptive norms under the veil of ignorance in symmetric coordination and anti-coordination games. We consider a finite population formed by different types of individuals. Players observe the type of their opponent but play under the veil of ignorance, i.e., act as if they did not know their own type. The question that we address is whether in such a symmetric environment a discriminating norm may arise. We show that there exist symmetric Nash equilibria in which players discriminate by acting differently according to the type of opponent that they face in anti-coordination games, while no such equilibrium exists in coordination games. Whenever individuals display a discriminating behavior, it is equally adopted by all agents, including by the individuals of the discriminated group. However, discrimination has a limit: the maximum number of groups where the treatment differs is three.