Spatial prisoner's dilemma games with zealous cooperators

Cooperative bots exhibit nuanced effects on cooperation across strategic frameworks

The positive impact of cooperative bots on cooperation within evolutionary game theory is well-documented. However, prior studies predominantly use discrete strategic frameworks with deterministic actions. This article explores continuous and mixed strategic approaches. Continuous strategies use intermediate probabilities for varying degrees of cooperation and focus on expected payoffs, while mixed strategies calculate immediate payoffs from actions taken within these probabilities. Using the prisoner's dilemma game, this study examines the effects of cooperative bots on human cooperation in both well-mixed and structured populations across these strategic approaches. Our findings reveal that cooperative bots significantly enhance cooperation in both population types under weak imitation scenarios, where players are less concerned with material gains. Conversely, under strong imitation scenarios, cooperative bots do not alter the defective equilibrium in well-mixed populations but have varied impacts in structured populations. Specifically, they disrupt cooperation under discrete and continuous strategies but facilitate it under mixed strategies. These results highlight the nuanced effects of cooperative bots within different strategic frameworks and underscore the need for careful deployment, as their effectiveness is highly sensitive to how humans update their actions and their chosen strategic approach.

Beyond a binary theorizing of prosociality

Stylized experiments, the public goods game and its variants thereof, have taught us the peculiar reproducible fact that humans tend to cooperate (or contribute to shared resources) more than expected from economically rational assumptions. There have been two competing explanations for this phenomenon: Either cooperating is an innate human trait (the prosocial preference hypothesis) or a transitory effect while learning the game (the confused learner hypothesis). We use large-scale experimental data in the two-player version of the public goods game-the prisoner's dilemma-from an experimental design to distinguish between these two hypotheses. By monitoring the effects of zealots (persistently cooperating bots) and varying the participants' awareness of them, we find a considerably more complex scenario than previously reported. People indeed have a prosocial bias, but not to the degree that they always forego taking action to increase their profit. While our findings end the simplistic theorizing of prosociality, an observed positive, cooperative response to zealots has actionable policy implications.

Prosocial punishment bots breed social punishment in human players

Prosocial punishment, an important factor to stabilize cooperation in social dilemma games, often faces challenges like second-order free-riders-who cooperate but avoid punishing to save costs-and antisocial punishers, who defect and retaliate against cooperators. Addressing these challenges, our study introduces prosocial punishment bots that consistently cooperate and punish free-riders. Our findings reveal that these bots significantly promote the emergence of prosocial punishment among normal players due to their 'sticky effect'-an unwavering commitment to cooperation and punishment that magnetically attracts their opponents to emulate this strategy. Additionally, we observe that the prevalence of prosocial punishment is greatly enhanced when normal players exhibit a tendency to follow a 'copying the majority' strategy, or when bots are strategically placed in high-degree nodes within scale-free networks. Conversely, bots designed for defection or antisocial punishment diminish overall cooperation levels. This stark contrast underscores the critical role of strategic bot design in enhancing cooperative behaviours in human/AI interactions. Our findings open new avenues in evolutionary game theory, demonstrating the potential of human-machine collaboration in solving the conundrum of punishment.

Facilitating cooperation in human-agent hybrid populations through autonomous agents

Cooperative AI has shown its effectiveness in solving the conundrum of cooperation. Understanding how cooperation emerges in human-agent hybrid populations is a topic of significant interest, particularly in the realm of evolutionary game theory. In this article, we scrutinize how cooperative and defective Autonomous Agents (AAs) influence human cooperation in social dilemma games with a one-shot setting. Focusing on well-mixed populations, we find that cooperative AAs have a limited impact in the prisoner's dilemma games but facilitate cooperation in the stag hunt games. Surprisingly, defective AAs can promote complete dominance of cooperation in the snowdrift games. As the proportion of AAs increases, both cooperative and defective AAs have the potential to cause human cooperation to disappear. We then extend our investigation to consider the pairwise comparison rule and complex networks, elucidating that imitation strength and population structure are critical for the emergence of human cooperation in human-agent hybrid populations.

Small bots, big impact: solving the conundrum of cooperation in optional Prisoner's Dilemma game through simple strategies

Cooperation plays a crucial role in both nature and human society, and the conundrum of cooperation attracts the attention from interdisciplinary research. In this study, we investigated the evolution of cooperation in optional Prisoner's Dilemma games by introducing simple bots. We focused on one-shot and anonymous games, where the bots could be programmed to always cooperate, always defect, never participate or choose each action with equal probability. Our results show that cooperative bots facilitate the emergence of cooperation among ordinary players in both well-mixed populations and a regular lattice under weak imitation scenarios. Introducing loner bots has no impact on the emergence of cooperation in well-mixed populations, but it facilitates the dominance of cooperation in regular lattices under strong imitation scenarios. However, too many loner bots on a regular lattice inhibit the spread of cooperation and can eventually result in a breakdown of cooperation. Our findings emphasize the significance of bot design in promoting cooperation and offer useful insights for encouraging cooperation in real-world scenarios.

Zealous cooperation does not always promote cooperation in public goods games

There is a conventional belief that prosocial behaviors cannot arise through selfish human nature, because defection always exploits cooperation to achieve a higher payoff at an individual level. Unyieldingly, some people hope to move society to cooperation through their zealous cooperation, regardless of payoffs. From the perspective of spatial evolutionary games, however, such zealous behavior is unnecessary because cooperation can emerge from selfish human nature by aggregating in evolution. Yet, to what extent can zealous cooperation induce others to cooperate? We assume a fraction of zealous agents in spatial public goods games who always cooperate. The results show that a moderate proportion of these zealous cooperators can diminish the cooperation level in the system, and cooperation is only promoted when zealots are many. Regarding spatial behaviors, the areas of zealous cooperation in a medium density can prevent evolutionary cooperation from passing through and aggregating. The phenomenon of zealous cooperation impeding cooperation becomes more pronounced when agents become less random and more selfish. This is because dotted zealous cooperation provides significant payoffs to neighboring defection, making them more solid in fitness. In this way, we also find that when zealous cooperators have low productivity, the neighbors receive fewer benefits by exploitation, thus allowing cooperation to spread. We also study replicator dynamics in unstructured populations where zealous cooperation always promotes cooperation, agreeing that zealous cooperation hindering cooperation is a spatial effect.

Social Dilemma Analysis of the Spread of Infectious Disease

Understanding and controlling the spread of infectious disease is a pressing issue for our society. Contemporary globally connected civilization is more at risk from various modern infectious diseases than classical ones such as pests, cholera, and tuberculosis. Over the last few years, pandemic outbreaks of highly virulent influenza, possibly related to avian flu, severe acute respiratory syndrome (SARS), and middle-eastern respiratory syndrome coronavirus (MARSE) have been a threat. Beyond this, the intentional spread of infectious disease, e.g., “bioterrorism”, has come to be recognized as being just as dangerous as nuclear weapons. An infectious disease spreads on human social networks. Each individual can protect himself through several measures. Pre-emptive vaccination is thought to be most effective, although it incurs a partial cost to each individual. This brings about a social dilemma, because an individual may be able to rely on so-called “herd immunity” to avoid his own infection without himself being vaccinated. Also, besides vaccination, there may be several practical ways to protect against contagion, such as wearing a mask, keeping away from crowds, and self-isolation by leaving the home less often, which may be less costly and less effective than vaccination. In any case, there is a human-decision-making process regarding what steps should be taken, while the dynamics of infectious-disease spread can themselves be evaluated as a diffusion problem that has been well-studied in physics for many years. Thus, based on the concept of human–environment–social interaction, a basic-physics model for this diffusion problem that considers evolutionary game theory (EGT) may lead us to obtain some meaningful solutions that can be proposed to our society. Following the previous chapter explaining how EGT can be applied to traffic-flow analysis, this chapter describes this practical problem.

The co-evolution of networks and prisoner's dilemma game by considering sensitivity and visibility

Strategies adopted by individuals in a social network significantly impact the network, and they strongly affect relationships between individuals in the network. Links between individuals also heavily influence their levels of cooperation. Taking into account the evolution of each individual's connection, we explore how sensitivity and visibility affect the prisoner's dilemma game. The so-called 'sensitivity' and 'visibility' respectively present one's self-protection consciousness and the ability of gaining information. We find that at moderate levels of player sensitivity cooperative behavior increases, but that at high levels it is inhibited. We also find that the heterogeneity of the weight of individuals at the end of the game is higher when sensitivity and visibility are increased, but that the successful-defection-payoff has less impact on the weight of individuals and on the relationship between the heterogeneity of the weight of individuals and the density of cooperators. This framework can be used to clarify the interaction mechanism between the micro-level of individual behavior and the macro-level of individual co-evolutionary processes.

Role-separating ordering in social dilemmas controlled by topological frustration

''Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

From degree-correlated to payoff-correlated activity for an optimal resolution of social dilemmas

An active participation of players in evolutionary games depends on several factors, ranging from personal stakes to the properties of the interaction network. Diverse activity patterns thus have to be taken into account when studying the evolution of cooperation in social dilemmas. Here we study the weak prisoner's dilemma game, where the activity of each player is determined in a probabilistic manner either by its degree or by its payoff. While degree-correlated activity introduces cascading failures of cooperation that are particularly severe on scale-free networks with frequently inactive hubs, payoff-correlated activity provides a more nuanced activity profile, which ultimately hinders systemic breakdowns of cooperation. To determine optimal conditions for the evolution of cooperation, we introduce an exponential decay to payoff-correlated activity that determines how fast the activity of a player returns to its default state. We show that there exists an intermediate decay rate at which the resolution of the social dilemma is optimal. This can be explained by the emerging activity patterns of players, where the inactivity of hubs is compensated effectively by the increased activity of average-degree players, who through their collective influence in the network sustain a higher level of cooperation. The sudden drops in the fraction of cooperators observed with degree-correlated activity therefore vanish, and so does the need for the lengthy spatiotemporal reorganization of compact cooperative clusters. The absence of such asymmetric dynamic instabilities thus leads to an optimal resolution of social dilemmas, especially when the conditions for the evolution of cooperation are strongly adverse.