Public Goods Game Research Articles

Evolution of cooperation driven by sampling punishment

Punishment is a key incentive to maintain cooperation. But it is costly, hence its effectiveness is under permanent debate. To overcome this difficulty, we here introduce a sampling punishment method and explore its consequences on public goods game and collective-risk social dilemma. In our model, just a small portion of participants are sampled and defectors are punished only if their portion exceeds a certain threshold. We show that the cooperation level can be effectively improved under low punishment threshold and small sample size when the punishment intensity is considerable. To identify the optimal conditions of sampling punishment, we monitor the punishment probability and related cost. We find that the adoption of a low punishment threshold and a small sample size under a considerable punishment intensity is the best, which always leads to a high cooperation level with a low related cost. Our observations are both valid in these two games.

Being green first: Simultaneous vs. sequential abatement decisions

We investigate the effect of the timing of green technology investment in a polluting duopoly facing environmental regulation. We consider a three-stage game where (i) firms sequentially choose their investment in the first stage, (ii) the regulator sets the optimal emission fee in the second stage, and (iii) the polluting good is produced in the third stage. When free-riding incentives are strong the leader enjoys a first-mover advantage, investing less in abatement than the follower, as in sequential public good games. We also show that sequential investment decisions achieve higher abatement than simultaneous decisions, and identify in which settings such a difference is the largest.

Evolution of cooperation with nonlinear environment feedback in repeated public goods game

The mutual feedback between the environment and the strategy is a significant mechanism in the evolution of cooperation. A feedback-evolving repeated public goods game model with nonlinear effects is explored. The players' behaviors in the current round may influence the environment, leading the environment feedback on the behavior by the modulation of payoffs in the form of positive or negative. Under the former case, the groups realize the synergy effect of payoffs in the next round. Vice versa, the discount effect will be instead. The introduction of nonlinear effects enables heterogeneous feedback of the environment on different groups without introducing too many environmental states. The results show the enhancing role of the nonlinear effects on the evolution of cooperation compared to linear switching of enforcement factors. Compared to static game environments, the dynamic feedback scenario can realize better performance in the evolution of cooperation. The effect is more pronounced as the synergy factor increases or the discount factor decreases. The results are verified when the game environment changes between two or three states and under different environment transition structures. In addition, under the scenarios of probabilistic transition, the results are explored by taking into account the cases of state-independent and state-dependent, where both the homogeneity and heterogeneity transition probability are considered in the state-independent case, respectively. The probabilistic transition results further emphasized the transition probability's significant role in the evolution of cooperation when cooperation behaviors are more likely incentivized to interact in the valuable environment.

The effect of commitment in the public goods game with endogenous institution formation

AbstractThis study focuses on the endogenous formation of institutions for the provision of public goods. Institutions that impose a contribution on their members can increase social welfare. However, without powerful executive authority, not all players become institutional members, and those who choose not to join the institution do not contribute to public goods. Endogenous institution formation—for example, international treaties to prevent global warming—may be a solution. This study examines the effect of commitment on endogenous institution formation for solving the public goods problem. We compared two rules in which participants either committed to join or did not join an institution. Under both rules, players who proposed to form an institution could withdraw from it during the formation process. Under the breakaway rule, the institution can be formed even if some proposers withdraw, whereas under the unanimity rule, the institution is never formed if at least one proposer withdraws. Thus, the unanimity rule required the commitment of proposers for institution formation. Our experimental result showed that the unanimity rule increased the contribution to public goods, whereas the breakaway rule did not. Our findings suggest that the commitment to become a member of an institution is essential for endogenous institution formation.

Willingness intensity and co-evolution of decision rationality depending on aspiration enhance cooperation in the spatial public goods game.

The Fermi rule states that rational or irrational sentiment affects individual decision-making. Existing studies have assumed that individuals' irrational sentiments and behavior willingness have fixed values and do not change with time. In reality, people's rationality sentiment and behavior willingness may be influenced by some factors. Therefore, we propose a spatial public goods game mechanism, in which individuals' rational sentiment is co-evolution synchronously depending on the difference between aspiration and payoff. Moreover, the intensity of their subjective willingness to change the status quo depends on the gap between aspiration and payoff. We likewise compare the combined promotion effect of the stochastic "Win-Stay-Lose-Shift" (WSLS) and random imitation (IM) rules. Simulation experiments indicate that high enhancement factors are not conducive to cooperation under the IM rules. When aspiration is small, WSLS is more conducive to promoting cooperation than IM, while increasing aspiration, and the opposite phenomenon will appear. The heterogeneous strategic update rule is beneficial to the evolution of cooperation. Lastly, we find that this mechanism performs better than the traditional case in enhancing cooperation.

Preferences for honesty can support cooperation

AbstractMany collective action problems are inherently linked to honesty. By deciding to behave honestly, people contribute to solving the collective action problem. We use a laboratory experiment from two sites (n = 331 and n = 319) to test whether honest preferences can drive cooperation and whether these preferences can be differentially activated by framing. Subjects participate in an asymmetric information variant of the public goods game in one of two treatments that vary only in their wording: The Contribution Frame uses a standard public good game framing, while in the Honesty Frame, words aimed to trigger honesty are used. We measure subjects' honesty in three ways using the (i) sender–receiver task, (ii) the die‐roll task, and (iii) self‐reported honesty levels and account for other‐regarding preferences and social norms to disentangle key alternative motives. We find that all three measures of honesty preferences robustly predict contributions, as do other‐regarding preferences and empirical expectations but not normative expectations. Additionally, honesty preferences predict contributions in the Honesty Frame but not in the Contribution Frame, although the difference between these is not consistently significant. Finally, we find no differences in average cooperation across the treatments.

Rice Farming and the Origins of Cooperative Behaviour

Abstract This paper provides novel evidence for links between historic farming practices and current norms of cooperative behaviour. We hypothesise that the cooperation required in wetland rice farming gives rise to strong cultural norms of cooperativeness. We compare participants from prefecture cities that predominately practice wetland rice cultivation to those from non-rice regions. A public goods game with and without punishment is the main measure for cooperative behaviour. Results indicate a strong and robust positive effect of wetland rice farming on cooperative behaviour and pro-social punishment. Complementary, consistent evidence from a natural field experiment and a survey further enriches our data.

Social exclusion with antisocial punishment in spatial public goods game

In the spatial public goods game (SPGG), social exclusion is an effective strategy to quickly promote group cooperation. However, the second-order free riding occurs among cooperators who do not bear additional exclusion costs in the process of exclusion. To ensure that the exclusion strategy works while solving the second-order free-riding problem, we introduce an antisocial punishment strategy. The model employs four counterbalancing strategies: pure cooperators invest into the public pool; the defectors are the first-order free-riders of the cooperators; the excluders restrict the defectors from riding the cooperators with a certain probability, and the excluded defectors cannot share the benefits of the common pool; and the antisocial punishers punish the cooperators. Through the Monte Carlo simulations, we found that the cooperative excluders protected the cooperators from invasion by defectors and defective punishers, and more importantly, the second-order free-riding problem of the system was eliminated by the defective punishers.

Leave behind or migrate? Evidence from a field experiment in China concerning the impact of being left behind/migrating status on children's behaviour and preferences

With the great economic and social development achieved in China in the past 40 years of reform and opening up has come the extensive flow of China's very large rural labour force between urban and rural areas and among regions, as well as populations of left-behind children and migrant children who cannot be ignored. In this paper, four populations—non-left-behind children in rural areas, left-behind children in rural areas, migrant children in urban areas, and local children in urban areas—were recruited in a large-scale field experiment that included the dictator game, ultimatum game, trust game, public goods game, coin-tossing task, intertemporal choice task, a calculation contest task, and a gambling task. Both being left behind and migrating had a negative effect on the children's prosocial behaviour (including fairness, trust, trustworthiness, cooperation, and honesty) and economic decision-making (including time and competition preferences). Moreover, the effect on migrant children was relatively greater, but this effect dissipated progressively as time since migration increased. Additionally, shorter migration distances were associated with a decreased effect of migration on migrant children, and having access to one parent had a positive effect on left-behind children.

Complex evolutionary interactions in multiple populations.

In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.

Survival of altruistic preferences in a large population public goods game

A large population of agents play a public goods game. Agents’ subjective payoff differs according to their level of altruism. More altruistic agents generate greater positive externality in Nash equilibrium. The strength of institutions determines the extent to which agents can materially benefit from the positive externalities they generate. Therefore, stronger institutions confer evolutionary advantage on more altruistic preferences, enabling such preferences to survive and proliferate.

Deterrence through punishment can resolve collective risk dilemmas in carbon emission games.

Collective risk social dilemmas are at the heart of the most pressing global challenges we are facing today, including climate change mitigation and the overuse of natural resources. Previous research has framed this problem as a public goods game (PGG), where a dilemma arises between short-term interests and long-term sustainability. In the PGG, subjects are placed in groups and asked to choose between cooperation and defection, while keeping in mind their personal interests as well as the commons. Here, we explore how and to what extent the costly punishment of defectors is successful in enforcing cooperation by means of human experiments. We show that an apparent irrational underestimation of the risk of being punished plays an important role, and that for sufficiently high punishment fines, this vanishes and the threat of deterrence suffices to preserve the commons. Interestingly, however, we find that high fines not only avert freeriders, but they also demotivate some of the most generous altruists. As a consequence, the tragedy of the commons is predominantly averted due to cooperators that contribute only their "fair share" to the common pool. We also find that larger groups require larger fines for the deterrence of punishment to have the desired prosocial effect.

Cumulative advantage is a double-edge sword for cooperation

The Matthew effect emphasizes the influence of early advantage on shaping long-term development by amplifying it over time, and its implications for public cooperation are yet to be fully understood. In this letter, we propose and study a spatial public goods game driven by cumulative advantage, where players who achieve high payoffs in a given round receive greater allocations in the next. The simulation results show that the Matthew effect leads to an irreversible polarization of individual wealth on the network. Such polarization makes moderate cooperation levels more prevalent, which helps to explain the widespread coexistence of prosocial and antisocial behavior. Meanwhile, heterogeneous networks may restrict the polarization of wealth, but also inhibit the evolution of cooperation, requiring a reconsideration of the commonly held view that heterogeneous networks enhance cooperation.

Social incentives foster cooperation through guilt aversion: An effect that diminishes with primary psychopathic traits.

The association between primary psychopathic traits and non-cooperative behaviors is well-identified. There is a lack of studies on how to motivate cooperative behaviors in individuals with primary psychopathic traits. This study investigated the effects of monetary incentives and social incentives on promoting cooperation in healthy adults with varying primary psychopathic traits. Participants played a one-shot public goods game (PGG) with other anonymous players in three different contexts: a social incentives context where participants' decisions would be judged by others, a monetary incentives context where participants' decisions would result in winning or losing money depending on their contributions, and a control condition where no additional incentives were implemented. We found that, compared to the control condition, both monetary and social incentives significantly improved participants' contributions to the public project-an indicator of cooperative behavior. However, the association between higher primary psychopathic traits and less cooperation was only observed in the context of social incentives. Computational modeling further revealed that this effect can be explained by the diminishing guilt aversion when participants deliberately violated their inferred expectations of themselves from others' perspectives. This study found that social incentives can encourage cooperative behaviors in non-clinical psychopathy, and identified the mental processes navigating this effect.

Like parent, like offspring: Intergenerational association of parental scarcity mindset with offspring's cooperative behaviors

A sense of resource availability creates a scarcity mindset, leading people to behave in a more competitive way instead of in a collaborative way. This study aims to examine the relationship between scarcity mindset and cooperative behaviors among parents and offspring, and to explore whether parents' scarcity mindset is related to their offspring's scarcity mindset and cooperative behaviors. We collected 239 parent-offspring pairs from several universities in northwest China. They completed the scarcity mindset scale and a one-shot public good game (PGG). A path model analysis was conducted to examine the relationship between scarcity mindset and cooperative behaviors for offspring and their parents, respectively. The relationship between parental scarcity mindset and offspring's cooperative behaviors was also examined. The results showed that there was a high correlation of scarcity mindset between parents and their offspring. Scarcity mindset was negatively related to cooperative behaviors among both parents and offspring. In addition, both parents' cooperative behaviors and offspring's scarcity mindset mediated the relationship between the parental scarcity mindset and offspring's cooperative behaviors. Our results supported the idea that scarcity mindset triggers competitive rather than cooperative orientation. The present findings reveal an intergenerational relationship between scarcity mindset and cooperative behaviors by highlighting the impacts of parental scarcity mindset on that of their offspring's and its additional effects on offspring's cooperative behaviors.

Social preferences in the public goods game-An Agent-Based simulation with EconSim.

Using a reinforcement-learning algorithm, we model an agent-based simulation of a public goods game with endogenous punishment institutions. We propose an outcome-based model of social preferences that determines the agent's utility, contribution, and voting behavior during the learning procedure. Comparing our simulation to experimental evidence, we find that the model can replicate human behavior and we can explain the underlying motives of this behavior. We argue that our approach can be generalized to more complex simulations of human behavior.

Evolutionary games with environmental feedbacks under an external incentive mechanism

Compared with the mandatory personal carbon trading, mechanisms that encourage individuals to voluntarily participate in carbon emission reduction are more easily accepted, such as the CGSP (Carbon Generalized System of Preferences) project in Guangdong Province, China. Carbon emission reduction, as a joint effort of multiple generations, involves interest conflicts between individuals and groups in one single generation, as well as multigenerational conflicts. By establishing the interaction between local environmental quality and individual returns, we build a public goods game with environmental feedback to simulate ecological and social coevolution. In this game with the CGSP mechanism, cooperators who reduce carbon emissions receive carbon credits, with which they can exchange for welfare funds to invest in environmental protection (denoted as AC) or for goods to improve their personal payoffs (BC). Individuals who do not contribute anything to improve the environment are called defectors (D). To study the impact of CGSP as an external incentive mechanism on cooperation, we explore the stationary states of three systems. In addition, we study the mechanisms behind some phases and phase transitions by monitoring the spatial distribution of strategies and the environmental quality of each region. The results show that a higher subsidy is not always better, whether cooperators exchange carbon credits for goods or welfare funds. Furthermore, ACs can effectively improve the spatial competitiveness of BC clusters, but BCs as ‘second-order free-riders’ can inhibit the spread of ACs. Indirect territorial competition between two types of cooperators can solve such a ‘second-order social dilemma’.

Conditional switching between social excluders and loners promotes cooperation in spatial public goods game

We incorporate a conditional strategy that can switch between social excluders and loners in the spatial public goods game. Based on the number of defectors in the group compared to a controlled tolerance parameter, individuals can adopt an excluder strategy to become excluders and expel the defectors, or adopt a loner strategy to become self-sufficient loners and refuse to participate in the game. By multi-agent-based simulation, we fully discuss the effect of conditional switching between these two different strategies on the cooperation level from the perspectives of tolerance parameter, exclusion cost, and exclusion probability respectively. Results show that the introduction of this conditional strategy can fully facilitate the evolution of cooperation, and the lower the tolerance parameter of the number of defectors in the group, the more conducive to the emergence of cooperation. However, when the tolerance parameter is high enough, the conditional strategy might not work under the effect of the exclusion cost and exclusion probability. Moreover, under the same tolerance parameter, the advantages of smaller exclusion costs or the strengths of a larger exclusion probability in promoting cooperation are more pronounced. These results allow us to better understand the role of conditional strategy that switches between social excluders and loners in the evolution of cooperation.

Effects of the limited incentive pool on cooperation evolution in public goods game

Cooperative behavior is prevalent in human societies, yet it is often undermined by selfish individuals. Within the framework of evolutionary game theory, pro-social incentives are often considered to be an effective means of promoting cooperation. In fact, however, the resources (including human resources, budget, etc.) to implement incentives are often limited for the institutions. Based on the public goods game, this paper introduces the concept of limited (negative or positive) incentive pool, in which the number of punishers/rewarders that the incentive pool can accommodate is limited. When the capacity of the incentive pool reaches the maximum, the remaining individuals who want to perform the punish/reward behavior will automatically withdraw from the game. Experimental simulations show that the introduction of positive/negative incentive facilitates the promotion and maintenance of cooperation, and that negative incentive is more effective in promoting cooperation and inhibit defection than positive incentives.

The team allocator game: Allocation power in public goods games

We analyze linear, weakest-link and best-shot public goods games where a distinguished team member, the team allocator, has property rights over the benefits from the public good to distribute it among team members. Our team allocator games are intended to capture natural asymmetries in hierarchical teams facing social dilemmas, such as those in work teams. We show that introducing a team allocator leads to increased contributions in linear and best-shot public-good games. No effect can be found in the weakest-link public good. The team allocator uses her power to distribute benefits in a way that motivates people to contribute. Re-allocating team payoffs allows her to reward contributing team members and to sanction non-cooperating members at no efficiency losses from explicit sanctioning costs. Thus, team profits are higher in the linear team allocator game but not in the best-shot case, where coordination problems lower the welfare for the remaining team members.