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

Evolution of trust in the N-player trust game with transformation incentive mechanism

Trust game is commonly used to study the evolution of trust among unrelated individuals. It offers valuable insights into human interactions in a range of disciplines, including economics, sociology and psychology. Previous research has revealed that reward and punishment systems can effectively promote the evolution of trust. However, these investigations overlook the gaming environment, leaving unresolved the optimal conditions for employing distinct incentives to effectively facilitate trust level. To bridge this gap, we introduce a transformation incentive mechanism in an N-player trust game, where trustees are given different forms of incentives depending on the number of trustees in the group. Using the Markov decision process approach, our research shows that as incentives increase, the level of trust rises continuously, eventually reaching a high level of coexistence between investors and trustworthy trustees. Specifically, in the case of smaller incentives, rewarding trustworthy trustees is more effective. Conversely, in the case of larger incentives, punishing untrustworthy trustees is more effective. Additionally, we find that moderate incentives have a positive impact on increasing the average payoff within the group.

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.

Investigating the impact of environmental feedback on the optional prisoner's dilemma for insights into cyclic dominance and evolution of cooperation

This study incorporates environmental feedback into the optional prisoner's dilemma and rock-paper-scissors games to examine the mutual influence of eco-evolutionary outcomes and strategy dynamics. A novel game-theoretic model is developed that integrates the optional prisoner's dilemma and rock-paper-scissors games by incorporating an environmental state variable. By adjusting feedback parameters, chaos, oscillations and coexistence are observed that surpass the usual outcomes of social dilemmas when the environment transitions between depleted and replenished states. Defection is no longer advantageous in evolution; cooperation, abstention and cyclic dominance arise. The observed transitions align with natural economics, ecology and sociology phenomena. The inclusion of abstention options and environmental feedback has a significant impact on collective outcomes when compared with conventional games. This has important implications for studying adaptation and decision-making in situations with ecological constraints.

A new sociology of humans and machines

From fake social media accounts and generative artificial intelligence chatbots to trading algorithms and self-driving vehicles, robots, bots and algorithms are proliferating and permeating our communication channels, social interactions, economic transactions and transportation arteries. Networks of multiple interdependent and interacting humans and intelligent machines constitute complex social systems for which the collective outcomes cannot be deduced from either human or machine behaviour alone. Under this paradigm, we review recent research and identify general dynamics and patterns in situations of competition, coordination, cooperation, contagion and collective decision-making, with context-rich examples from high-frequency trading markets, a social media platform, an open collaboration community and a discussion forum. To ensure more robust and resilient human-machine communities, we require a new sociology of humans and machines. Researchers should study these communities using complex system methods; engineers should explicitly design artificial intelligence for human-machine and machine-machine interactions; and regulators should govern the ecological diversity and social co-development of humans and machines.

Emergence of cooperation in the one-shot Prisoner's dilemma through Discriminatory and Samaritan AIs

As artificial intelligence (AI) systems are increasingly embedded in our lives, their presence leads to interactions that shape our behaviour, decision-making and social interactions. Existing theoretical research on the emergence and stability of cooperation, particularly in the context of social dilemmas, has primarily focused on human-to-human interactions, overlooking the unique dynamics triggered by the presence of AI. Resorting to methods from evolutionary game theory, we study how different forms of AI can influence cooperation in a population of human-like agents playing the one-shot Prisoner's dilemma game. We found that Samaritan AI agents who help everyone unconditionally, including defectors, can promote higher levels of cooperation in humans than Discriminatory AI that only helps those considered worthy/cooperative, especially in slow-moving societies where change based on payoff difference is moderate (small intensities of selection). Only in fast-moving societies (high intensities of selection), Discriminatory AIs promote higher levels of cooperation than Samaritan AIs. Furthermore, when it is possible to identify whether a co-player is a human or an AI, we found that cooperation is enhanced when human-like agents disregard AI performance. Our findings provide novel insights into the design and implementation of context-dependent AI systems for addressing social dilemmas.

Enhancing social cohesion with cooperative bots in societies of greedy, mobile individuals

Addressing collective issues in social development requires a high level of social cohesion, characterized by cooperation and close social connections. However, social cohesion is challenged by selfish, greedy individuals. With the advancement of artificial intelligence (AI), the dynamics of human-machine hybrid interactions introduce new complexities in fostering social cohesion. This study explores the impact of simple bots on social cohesion from the perspective of human-machine hybrid populations within network. By investigating collective self-organizing movement during migration, results indicate that cooperative bots can promote cooperation, facilitate individual aggregation, and thereby enhance social cohesion. The random exploration movement of bots can break the frozen state of greedy population, help to separate defectors in cooperative clusters, and promote the establishment of cooperative clusters. However, the presence of defective bots can weaken social cohesion, underscoring the importance of carefully designing bot behavior. Our research reveals the potential of bots in guiding social self-organization and provides insights for enhancing social cohesion in the era of human-machine interaction within social networks.

Santos F, Simoens P, Lenaerts T. The art of compensation: How hybrid teams solve collective-risk dilemmas

It is widely known how the human ability to cooperate has influenced the thriving of our species. However, as we move towards a hybrid human-machine future, it is still unclear how the introduction of artificial agents in our social interactions affect this cooperative capacity. In a one-shot collective risk dilemma, where enough members of a group must cooperate in order to avoid a collective disaster, we study the evolutionary dynamics of cooperation in a hybrid population. In our model, we consider a hybrid population composed of both adaptive and fixed behavior agents. The latter serve as proxies for the machine-like behavior of artificially intelligent agents who implement stochastic strategies previously learned offline. We observe that the adaptive individuals adjust their behavior in function of the presence of artificial agents in their groups to compensate their cooperative (or lack of thereof) efforts. We also find that risk plays a determinant role when assessing whether or not we should form hybrid teams to tackle a collective risk dilemma. When the risk of collective disaster is high, cooperation in the adaptive population falls dramatically in the presence of cooperative artificial agents. A story of compensation, rather than cooperation, where adaptive agents have to secure group success when the artificial agents are not cooperative enough, but will rather not cooperate if the others do so. On the contrary, when risk of collective disaster is low, success is highly improved while cooperation levels within the adaptive population remain the same. Artificial agents can improve the collective success of hybrid teams. However, their application requires a true risk assessment of the situation in order to actually benefit the adaptive population (i.e. the humans) in the long-term.

Tax thresholds yield multiple optimal cooperation levels in the spatial public goods game

Income redistribution, which involves transferring income from certain individuals to others, plays a crucial role in human societies. Previous research has indicated that tax-based redistribution can promote cooperation by enhancing incentives for cooperators. In such a tax system, all individuals, irrespective of their income levels, contribute to the tax system, and the tax revenue is subsequently redistributed to everyone. In this study, we relax this assumption by introducing a tax threshold, signifying that only individuals with incomes exceeding the threshold will be subject to taxation. In particular, we employ the spatial public goods game to investigate the influence of tax rates-the percentage of income allocated to tax-and tax thresholds, which determine the income level at which individuals become taxable, on the evolution of cooperation. Our extensive numerical simulations disclose that tax thresholds produce complex outcomes for the evolution of cooperation, depending on tax rates. Notably, at low tax rates (i.e., below 0.41), as the tax threshold increases, discontinuous phase transitions in cooperation performance suggest the presence of multiple intervals of effective tax thresholds that promote peak cooperation levels. Nevertheless, irrespective of the chosen tax rate, once the tax threshold surpasses a critical threshold, the redistribution mechanism fails, causing the collapse of cooperation. Evolutionary snapshots show that self-organized redistribution forms an intermediary layer on the peripheries of cooperative clusters, effectively shielding cooperators from potential defectors. Quantitative analyses shed light on how self-organized redistribution narrows the income gap between cooperators and defectors through precise identification of tax-exempt entities, thereby amplifying the cooperative advantage. Collectively, these findings enhance our comprehension of how income redistribution influences cooperation, highlighting the pivotal role of tax thresholds.