Individual Payoffs Research Articles

Donations triggered by inequality tolerance affect the evolution of cooperation in spatial public goods game.

Generosity through donation plays a crucial role in reducing inequality and influencing human behavior. However, previous research on donation has overlooked individuals' acceptance of the extent of inequality, which acts as a trigger for donation. To address this gap, this paper systematically explores the impact of donation based on inequality tolerance on the evolution of cooperation in spatial public goods game. Specifically, donation occurs only when an individual's payoff advantage exceeds her inequality tolerance. The results show that donation patterns are crucial for the emergence and stability of cooperation. In the enduring period, the defector-to-cooperator donation pattern helps to form cooperative clusters. In the expanding period, cooperator-to-cooperator, defector-to-defector, and defector-to-cooperator donation patterns create a stable three-layer structure through self-organization, providing a payoff advantage to boundary cooperators. As donation ratio increases, the three-layer structure provides a greater payoff advantage to boundary cooperators, leading to an increase in cooperation. As inequality tolerance increases, changes in donation patterns weaken the three-layer structure, causing cooperation to decrease or disappear through discontinuous phase transitions. Subsequently, all critical points of discontinuous phase transitions are identified by specific spatial configurations. In addition, the influence of donation patterns on the evolution of cooperation is robust, even in heterogeneous small-world networks. This paper offers valuable insights into the dynamics of cooperation evolution and the role of donation in shaping behavior.

Evolutionary dynamics in spatial public goods games with environmental feedbacks.

Collective actions aimed at achieving goals such as resource sustainability and environmental protection often face conflicting interests between individuals and groups. These social dilemmas can be modeled using public goods games and collective risk dilemmas. However, in reality, multiple generations share a common pool of resources, leading to high costs for today's overexploitation that impacts future generations' welfare. This delayed effect creates a multigenerational conflict. To address this, we develop a coupled social-ecological coevolutionary model by establishing a relationship between individual payoffs and regional environmental quality. Our goal is to study how cooperative behaviors spread in a public goods game with environmental feedback and to identify the factors influencing this spread. We achieve this by examining the mechanisms behind certain phases and phase transitions, monitoring the spatial distribution of strategies, and assessing the environmental quality of all regions. Our findings reveal some counterintuitive results. For instance, despite cooperators' ability to enhance the environment, the overall level of cooperation in the system sometimes decreases. This is linked to cooperative clusters being invaded by defectors within the clusters' cracks. Additionally, the destructive power of defection and the cost of cooperation have more complex effects on the system.

Decentralized Matching with Transfers: Experimental and Noncooperative Analyses

We experimentally examine the Becker-Shapley-Shubik two-sided matching model. In the experiment, the aggregate outcomes of matching and surplus are affected by whether equal split is in the core and whether efficient matching is assortative; the canonical cooperative theory predicts no effect. In markets with an equal number of participants on both sides, individual payoffs cannot be explained by existing refinements of the core, but are consistent with our noncooperative model’s predictions. In markets with unequal numbers of participants, noncompetitive outcomes, are not captured by the canonical cooperative model, but are included in the set of predictions in our noncooperative model. (JEL C71, C72, C78)

Evolutionary mechanisms that promote cooperation may not promote social welfare.

Understanding the emergence of prosocial behaviours among self-interested individuals is an important problem in many scientific disciplines. Various mechanisms have been proposed to explain the evolution of such behaviours, primarily seeking the conditions under which a given mechanism can induce highest levels of cooperation. As these mechanisms usually involve costs that alter individual pay-offs, it is, however, possible that aiming for highest levels of cooperation might be detrimental for social welfare-the latter broadly defined as the total population pay-off, taking into account all costs involved for inducing increased prosocial behaviours. Herein, by comparing stochastic evolutionary models of two well-established mechanisms of prosocial behaviour-namely, peer and institutional incentives-we demonstrate that the objectives of maximizing cooperation and of maximizing social welfare are often misaligned. First, while peer punishment is often more effective than peer reward in promoting cooperation-especially with a higher impact-to-cost ratio-the opposite is true for social welfare. In fact, welfare typically decreases (increases) with this ratio for punishment (reward). Second, for institutional incentives, while maintaining similar levels of cooperation, rewards result in positive social welfare across a much broader range of parameters. Furthermore, both types of incentives often achieve optimal social welfare when their impact is moderate rather than maximal, indicating that careful planning is essential for costly institutional mechanisms to optimize social outcomes. These findings are consistent across varying mutation rates, selection intensities and game configurations. Overall, we argue for the need of adopting social welfare as the main optimization objective when designing and implementing evolutionary mechanisms for social and collective goods.

A complete classification of evolutionary games with environmental feedback.

A tragedy of the commons, in which rational behavior of individuals to maximize their own payoffs depletes common resources, is one of the most important research topics in game theory. To better understand the social dilemma problem, recent studies have developed a theoretical framework of feedback-evolving game where individual behavior affects an environmental (renewable) resource and the environmental resource changes individual payoffs. While previous studies assumed that the frequency of defectors increases (prisoner's dilemma [PD] game) when the environmental resource is abundant to investigate an oscillating tragedy of the commons, it is also possible for other types of game to produce the social dilemma. In this paper, we extend the feedback-evolving game by considering not only PD game, but also the other three game structures when the environmental resource is replete for a reasonably complete classification. The three games are Chicken game where defectors and cooperators coexist through minority advantage, Stag-Hunt (SH) game with minority disadvantage, and Trivial game where the frequency of cooperators increases. In addition, we utilize a dilemma phase plane to visually track (transient) dynamics of game structure changes. We found that an emergent initial condition dependence (i.e. bistability) is pervasive in the feedback-evolving game when the three games are involved. We also showed that persistent oscillation dynamics arise even with Chicken or SH games in replete environments. Our generalized analysis will be an important step to further extend the theoretical framework of feedback-evolving game to various game situations with environmental feedback.

Moore interval subtraction and interval solutions for TU-games

Standard solutions for cooperative transferable utility (TU-) games assign to every player in a TU-game a real number representing the player’s payoff. In this paper, we introduce interval solutions for TU-games which assign to every player in a game a payoff interval. Even when the worths of coalitions are known, it might be that the individual payoff of a player is not known. According to an interval solution, every player knows at least a lower- and upper bound for its individual payoff. Therefore, interval solutions are useful when there is uncertainty about the payoff allocation even when the worths that can be earned by coalitions are known. Specifically, we consider two interval generalizations of the famous Shapley value that are based on marginal contributions in terms of intervals. To determine these marginal interval contributions, we apply the subtraction operator of Moore. We provide axiomatizations for the class of totally positive TU-games. We also show how these axiomatizations can be used to extend any linear TU-game solution to an interval solution. Finally, we illustrate these interval solutions by applying them to sequencing games.

Market Power and Price Informativeness

Abstract We study the distributional effects of asset ownership on price informativeness in a general equilibrium model. The model features investors (oligopolists) with different degrees of price impact and abilities to learn about individual asset payoffs from private and price signals, and a competitive fringe that only learns from asset prices. We show that price informativeness is non-monotonic in the oligopolists’ aggregate size, decreasing in the sector’s concentration and in the size of the passive sector. We further show that the size effect can be decomposed into a learning channel capturing investors’ quality of private signals and an information pass-through channel measuring the sensitivity of investors’ trades to private signals, with the latter one being the primary source of variation in price informativeness relative to the size distribution.

On the Positive Effects of Overconfident Self-Perception in Teams

In this paper, we study the individual payoff effects of over confident self-perception in teams. In particular, we demonstrate that the welfare of an overconfident agent who works in a team with a rational agent or in a team with an overconfident agent can be higher than the welfare of the members of a team of two rational agents. This result holds irrespective of the assumption about the agents’ awareness of their colleague’s bias. Moreover, we show that an overconfident agent is always better off when he is unaware of a potential bias of his colleague. Thus, our results provide a potential rationale for the widespread dissemination of overconfidence.

Borrowing Absolute and Relative Gains to Science Diplomacy Conceptualization

Science diplomacy is an emerging concept in International Relations. But the existing traditional conceptualization of science diplomacy (science in diplomacy, diplomacy for science, and science for diplomacy) has optimistic scope and objective while ignoring the conflictual nature of international relations. This article argues borrowing relative and absolute gains can address the conceptual problem of science diplomacy. The borrowing presents a classification of science diplomacy into two types, prospective (using diplomacy to attain the maximum individual payoffs in science) and restrictive (using diplomacy to hinder others from advancing capabilities in science). By demonstrating it with Japan's science diplomacy in the inaugural meeting of Science and Technology in Society (STS) Forum and the first meeting of the East Asia Science and Innovation Area (e-ASIA) Joint Research Forum, this article found that the classification of science diplomacy as prospective and restrictive helps study the cooperative and competitive aspects of state actors' science diplomacy.

STAS: Spatial-Temporal Return Decomposition for Solving Sparse Rewards Problems in Multi-agent Reinforcement Learning

Centralized Training with Decentralized Execution (CTDE) has been proven to be an effective paradigm in cooperative multi-agent reinforcement learning (MARL). One of the major challenges is credit assignment, which aims to credit agents by their contributions. They lack the functionality to model complicated relations of the delayed global reward in the temporal dimension and suffer from inefficiencies. To tackle this, we introduce Spatial-Temporal Attention with Shapley (STAS), a novel method that learns credit assignment in both temporal and spatial dimensions. It first decomposes the global return back to each time step, then utilizes the Shapley Value to redistribute the individual payoff from the decomposed global reward. To mitigate the computational complexity of the Shapley Value, we introduce an approximation of marginal contribution and utilize Monte Carlo sampling to estimate it. We evaluate our method on an Alice & Bob example and MPE environments across different scenarios. Our results demonstrate that our method effectively assigns spatial-temporal credit, outperforming all state-of-the-art baselines.

Coalition Stability in International Environmental Matching Agreements

This study presents empirically calibrated simulations of three different variants of environmental matching agreements aimed at reducing global greenhouse gas emissions. We determine whether matching agreements can produce larger stable coalitions and increase abatement contributions and payoffs as compared to standard agreements. The matching agreements we analyze feature uniform matching rates by which coalition members match the unconditional contributions of (i) the other coalition members, (ii) all other players, or (iii) only non-members, while non-members do not commit to any matching and maximize their individual payoffs. The simulation considers twelve asymmetric world regions with linear abatement benefits and quadratic costs, calibrated based on the STACO 3 model, and uses emissions data from the shared socioeconomic pathways database. We find that the first variant of the matching game fails to produce any stable coalitions and thus performs worse than the standard agreement that produces a stable two-player coalition. The second variant produces a stable grand coalition and significantly increases the abatement and payoff levels beyond the non-cooperative Nash baseline. Partial coalitions are unstable in this game. The third variant produces a two-player coalition similar to the standard coalition formation game, but with different members and higher abatement and payoff levels due to the matching mechanism.

Abundant resources can trigger reduced consumption: Unveiling the paradox of excessive scrounging

In ecological contexts, it is conventionally expected that increased food availability would boost consumption, particularly when animals prioritize maximizing their food intake. This paper challenges this conventional wisdom by conducting an in-depth game-theoretic analysis of a basic foraging model, in which animals must choose between intensive food searching as producers or moderate searching while relying on group members as scroungers. Our study reveals that, under certain circumstances, increasing food availability can amplify the inclination to scrounge to such an extent that it leads to a reduction in animals' food consumption compared to scenarios with limited food availability. We further illustrate a similar phenomenon in a model capturing free-riding dynamics among workers in a company. We demonstrate that, under certain reward mechanisms, enhancing workers' production capacities can inadvertently trigger a surge in free-riding behavior, leading to both diminished group productivity and reduced individual payoffs. Our findings provide intriguing insights into the complex relationships between individual and group performances, as well as the intricate mechanisms underlying the emergence of free-riding behavior in competitive environments.

Enhancing cooperative evolution in spatial public goods game by particle swarm optimization based on exploration and q-learning

In evolutionary game theory, the emergence and maintenance of cooperative behavior in a population often face challenges posed by the temptation of free-riding behavior, which offers high individual payoff. Recently, apart from a range of mechanisms that promote the formation of cooperation, individual learning abilities under limited information have emerged as a key factor in adjusting agents' strategies. This paper introduces q-learning and particle swarm optimization into the realm of evolutionary dynamics. The primary focus is on investigating the impact of Exploration-based Particle Swarm Optimization (EPSO) and Q-learning-based Particle Swarm Optimization (QPSO) on the evolution of cooperation in a continuous version of the spatial public goods game (SPGG) with punishment. EPSO defines a rule for updating agents' strategies based on individual and limited population information. It also integrates an exploration mechanism to increase the diversity and directionality of the strategies. Additionally, QPSO serves to adaptively optimize the parameters of EPSO, addressing the issue of parameter control limiting the EPSO's performance. Leveraging experiential learning and iterative adjustment, QPSO progressively refines system parameters, thus rationally assimilating knowledge and updating individual strategies to attain optimal payoff. Through extensive simulation studies, it has been observed that employing QPSO's adaptively optimized parameters in EPSO significantly promotes the cooperative evolution in the SPGG with punishment. Furthermore, individual learning coefficients, when too low or too high, both facilitate the occurrence of cooperation. Simultaneously, higher inertia weight coefficients strengthen the system's cooperation level, while lower punishment intensity coefficients and higher gain intensity coefficients effectively promote the cooperation emergence and exert a significant influence on the overall cooperation level of the system. This research provides a new perspective for designing real-world schemes that encourage cooperation and offers insights into the intricate dynamics of cooperation in complex systems.

Is peace a human phenomenon?

Peace is a hallmark of human societies. However, certain ant species engage in long-term intergroup resource sharing, which is remarkably similar to peace among human groups. We discuss how individual and group payoff distributions are affected by kinship, dispersal, and age structure; the challenges of diagnosing peace; and the benefits of comparing convergent complex behaviours in disparate taxa.

Optimal Evolution Strategy for Continuous Strategy Games on Complex Networks via Reinforcement Learning.

This article presents an optimal evolution strategy for continuous strategy games on complex networks via reinforcement learning (RL). In the past, evolutionary game theory usually assumed that agents use the same selection intensity when interacting, ignoring the differences in their learning abilities and learning willingness. Individuals are reluctant to change their strategies too much. Therefore, we design an adaptive strategy updating framework with various selection intensities for continuous strategy games on complex networks based on imitation dynamics, allowing agents to achieve the optimal state and a higher cooperation level with the minimal strategy changes. The optimal updating strategy is acquired using a coupled Hamilton-Jacobi-Bellman (HJB) equation by minimizing the performance function. This function aims to maximize individual payoffs while minimizing strategy changes. Furthermore, a value iteration (VI) RL algorithm is proposed to approximate the HJB solutions and learn the optimal strategy updating rules. The RL algorithm employs actor and critic neural networks to approximate strategy changes and performance functions, along with the gradient descent weight update approach. Meanwhile, the stability and convergence of the proposed methods have been proved by the designed Lyapunov function. Simulations validate the convergence and effectiveness of the proposed methods in different games and complex networks.

Distributed GNE Seeking Strategy for Second-Integrator Multiplayer Systems Over Directed Topologies.

This article studies the generalized Nash equilibrium (GNE) seeking problem of second-integrator multiplayer systems. In particular, each player is endowed with an individual payoff function with respect to collective decision variables, and simultaneously, a coupling inequality constraint and a set constraint are imposed to each player. The players communicate with their local neighbors over a directed topology. To begin with, a distributed-observer-based seeking strategy is synthesized by leveraging a proper composite variable. It is first demonstrated using nonsmooth analysis that the established distributed observer enables each player to accurately estimate the decision variables of others in terms of a strongly connected topology condition. Upon this basis, all the decision variables are then shown to converge to the expected GNE asymptotically borrowing from convex theory. In addition, three extension results are also given under the built GNE seeking framework. First, under the postulation that the velocity information is unavailable, a velocity-free distributed GNE seeking strategy is synthesized for second-integrator systems by implementing a proper auxiliary dynamics. Second, we consider nonlinear Euler-Lagrange systems with unknown inertia parameters and synthesize an improved distributed GNE seeking strategy resorting to an adaptation technique. Third, we focus on integrator chain systems and synthesize a modified distributed GNE seeking strategy using a new composite variable based on a proper coordinate transformation. For three extension cases, we all show in detail the achievement of the GNE seeking objective. Finally, a practical example is simulated to confirm the built GNE seeking results.

Explaining mobilization for revolts by private interests and kinship relations.

Mobilization for revolts poses a significant challenge for rational choice theory because revolts are vulnerable to free-riding, which disincentivizes rational actors from mobilizing. Strong, informal relations such as kinship ties have been identified as factors that can shift the rational calculations of individuals and lead to mobilization for revolts. In social networks that are polarized by the presence of mobilized individuals, such as rebels, and actors opposing the mobilization effort such as the elite, kinship relations have not only a bridging effect but also a diverging one. Building on Tullock's private interest theory, we develop a framework in which kinship relations determine the extent of individual's payoffs and costs of mobilization for revolts against an elite. We posit that distant kin of the elite expect high payoffs of mobilization for revolts and face the lowest costs of mobilization for revolts by virtue of their position in the network of kinship relations. Using a unique, hand-collected dataset that reconstructs a revolt in Basel, Switzerland, in 1691, we test our framework and contribute to a better relational understanding of the mechanisms that lead rational actors to mobilize for revolts. Our analyses show that mobilization for revolts is mainly driven by distant kinship relations to the ruling elite rather than close kinship relations to the rebels.

The cooperative evolution in the spatial prisoner's dilemma game with the local loyalty of two-strategy

The loyalty of individual strategies is an important factor affecting cooperative behavior in human society. Previous researches on the loyalty have mostly focused on the loyalty of individual to a single strategy, that is, the loyalty of individual to cooperative strategy. But from the perspective of defective strategy, individual holding defective strategy can also be seen as so-called loyalty to defective strategy.This paper presents a spatial prisoner's dilemma game model with the local loyalty of two-strategy, in which the loyalty to cooperative strategy and loyalty to defective strategy are considered simultaneously. To distinguish the loyalties of these two types of strategies, the loyalty value corresponding to defective strategy is represented as a negative number. A fitness of an individual is defined as weighted average of individual's payoff and power of average loyalty of local nearest neighbors. In strategy learning, if the loyalty of an individual and the loyalty of the target neighbor are different signs, a discount coefficient is added to the strategy transition probability function to reduce the probability.Numerical simulations show that considering individual loyalty to the two strategies can promote cooperative behavior in the system when the strength index of local loyalty in fitness function is positive, and there are optimal values for the weighting coefficient and the strength index of local loyalty, which can enable the system to reach full cooperators state. The discount coefficient to the fitness of neighbor can impact on the frequency of cooperators surviving and the proportion of surviving cooperators during phase transition.

Social comparison feedback in decision-making context: Environmental externality levels and psychological traits matter

Social comparison feedback has been widely applied to encourage energy and water conservation, with the ultimate aim to protect ecosystems and the environment. Yet, the effectiveness of social comparison feedback varies. In this study, with 360 UK participants from Prolific, we conducted an online experiment based on a modified dictator game with multi-round purchasing decisions involving trade-offs between individual monetary payoff and real-world carbon offsets donation. A 2 × 3 between-subjects design was implemented, varying in the externality levels associated with the purchase (high versus low), and the type of feedback (self-feedback, social comparison feedback, and tangible emissions feedback – i.e. social comparison enriched with information relating environmental impacts to daily activity and nature). Furthermore, we measured several psychological traits of participants. Our findings show that social comparison interventions are only effective under certain circumstances. Both interventions with social comparison are more effective in the low-externality context. Furthermore, the effect of tangible emissions feedback is moderated by individuals’ tendency to conform to specific social norms and compete with others. Compared to standard social comparison feedback, social comparison feedback enriched with tangible emissions information is overall more effective. We highlight the importance of tailoring social comparison interventions to local environmental and cultural contexts.

Evolutionary dynamics with the second-order reputation in the networked [formula omitted]-player trust game

Network science has become an emerging and promising discipline within academia, which has induced extensive concern from a diverse range of realms including economics, social and computer science, mathematics and statistical mechanics. In this work, we investigate the impact of network topology on an N-player trust game by considering the second-order reputation rule. The model consists of three types of participants: investors (trusters), trustworthy trustees, and untrustworthy trustees. Based on the underlying network topology, players will interact with their neighbors at each game round. At the end of each interaction, they will update their strategies concerning their individual payoff and reputation. Meanwhile, we use different social networks and temptations of defection to explore the effect of degree distribution and clustering coefficients on the cooperative behaviors. Besides, the steady state of systems can be arrived at through the detailed theoretical analyses, and then the evolutionary process is extensively simulated on some real-world networks. We find that the trust can be spread in different network topologies and the cooperation or trust can be maintained at the higher level even though the intensity of the dilemma is higher. In addition, under the same network structure, the higher the average degree distribution of the network, the higher the trust level; under the same average degree distribution, the higher the aggregation coefficient, the lower the trust level. Current results provide some new insights into the evolution of cooperation or trust within the structured populations.