Prisoner's Dilemma Game Research Articles

Research on the Iterated Prisoner Dilemma Based on Combinations of Two-side Strategies

The endless prisoner's dilemma game is described as a "primer" using the perspectives of the bilateral parties. Current research focuses on which player responds most effectively, which is a kind of self-protect behavior. Content analysis and mathematical justification were undertaken for the prisoners dilemma iteration to understand better how to improve the game in a partially competitive and cooperative collaborative setting. This aims to apply the two-side strategies to the real world, especially the political events in which the whole human outcome should be maximized. Participants, who were mostly chosen from game theory specialists from an experiment, provided the decision parameters and rules, in which they have to decide among certain personal strategy choices. The comparisons findings show that two-sided cooperation produces the best results. Still, two-sided inaction results in the poorest, and single cooperation and single noncooperation result from personal sacrifice and personal selfishness, which is a psychological phenomenon.

Government and Polluting Companies Game Strategies in the Context of Green Finance A Prisoners Dilemma Game Model

Promoting the development of green industries to facilitate the growth of green finance has become a consensus among various sectors of society. This article focuses on the game theory strategies between governments and polluting companies in the context of green finance. Taking the Prisoner's Dilemma game model as an example, we discuss if polluting companies, under different types of governments, would choose to allocate loans towards improving production and environmental projects. Furthermore, we analyze whether the preferences of the general public towards eco-friendly products would influence the game strategies of governments and polluting companies. Through solving the model, we find that when governments increase penalties for polluting projects, reduce the costs of environmental project research and development for polluting companies, enhance environmental awareness among the general public, and stimulate their preference for eco-friendly products, they can strengthen corporate social responsibility and promote green investments. Consequently, polluting companies are more likely to invest in environmental projects to gain greater returns.

The influence of environment-based reputation on cooperation in spatial prisoner's dilemma game

Research has shown that reputation mechanism can be effective in facilitating the generation and maintenance of cooperation in social dilemmas. In the traditional reputation mechanism, the amount of change in reputation is fixed. However, in real life, people's impression scores of a player are often influenced by the environment in which he lives. In other words, we prefer to celebrate the cooperative heroes who are surrounded by defectors and spurn the defectors who are hidden among the many cooperators. Thus, this paper proposes an environment-based reputation model, in which the increment of a player's reputation will be influenced by the local and global environment. The results of the research indicate that the greater the intensity of the environmental influence, the more it promotes the evolution of cooperation. It is worth noting that the local and global environmental focus shows peculiarities. Focusing on the global environment can improve the fraction of cooperators at low defection temptations while focusing on the local environment will facilitate cooperators’ survival at higher defection temptations.

Coupling injunctive social norms with evolutionary games

Human behaviors are strongly influenced by social norms. This work couples injunctive social norms with evolutionary games. Injunctive norms refer to behaviors which individuals should conform to and thereby entail social pressure to adhere to a particular action. Here we investigate impact of such social norms on both pairwise and multi-player games. It is shown that injunctive norms can enforce the system to either extreme, meaning that they give rise to the possibility of bi-stability (two stable equilibrium states) in evolutionary games. We derive the condition for such bi-stability in the mean-field limit. While investigating pairwise games with social norms, we observe that —besides other possibilities—Prisoner's dilemma (PD), snow-drift (SD), and Trivial (TR) games may experience the bi-stability like the stag-hunt (SH) game. Interestingly, SD game with social norms exhibits four possible asymptotic outcomes: all-cooperation (AllC), all-defection (AllD), either AllC or AllD (bi-stable), and coexistence. However, its multi-player variant does not manifest a unique coexistence equilibrium. Moreover, it demonstrates another bi-stable equilibrium, comprising either coexistence or AllC, besides other outcomes observed in the two-player case. Conversely, PD and its multi-player variant, i.e., public goods game with injunctive norms show identical evolutionary outcomes (AllD or bi-stable).

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.

Interaction state Q-learning promotes cooperation in the spatial prisoner's dilemma game

Many recent studies have used reinforcement learning methods to investigate the behavior of agents in evolutionary games. Q-learning, in particular, has become a mainstream method during this development. Here we introduce Q-learning agents into the evolutionary prisoner's dilemma game on a square lattice. Specifically, we associate the state space of Q-learning agents with the strategies of their neighbors, and we introduce a neighboring reward information sharing mechanism. We thus provide Q-learning agents with the payoff information of their neighbors, in addition to their strategies, which has not been done in previous studies. Through simulations, we show that considering neighborhood payoff information can significantly promote cooperation in the population. Moreover, we show that for an appropriate strength of neighborhood payoff information sharing, a chessboard pattern emerges on the lattice. We analyze in detail the reasons for the emergence of the chessboard pattern and the increase in cooperation frequency, and we also provide a theoretical analysis based on the pair approximation method. We hope that our research will inspire effective approaches for resolving social dilemmas by means of sharing more information among reinforcement learning agents during evolutionary games.

Social metacognition drives willingness to commit.

Showing or telling others that we are committed to cooperate with them can boost social cooperation. But what makes us willing to signal our cooperativeness, when it is costly to do so? In two experiments, we tested the hypothesis that agents engage in social commitments if their subjective confidence in predicting the interaction partner's behavior is low. In Experiment 1 (preregistered), 48 participants played a prisoner's dilemma game where they could signal their intentions to their co-player by enduring a monetary cost. As hypothesized, low confidence in one's prediction of the co-player's intentions was associated with a higher willingness to engage in costly commitment. In Experiment 2 (31 participants), we replicate these findings and moreover provide causal evidence that experimentally lowering the predictability of others' actions (and thereby confidence in these predictions) motivates commitment decisions. Finally, across both experiments, we show that participants possess and demonstrate metacognitive access to the accuracy of their mentalizing processes. Taken together, our findings shed light on the importance of confidence representations and metacognitive processes in social interactions. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Asymmetry of individual activity promotes cooperation in the spatial prisoner's dilemma game.

We consider an aspiration-based asymmetric individual activity co-evolutionary prisoner's dilemma game model on the square lattice. In detail, each player has an individual weight that evolves with its strategy. We introduce an asymmetric setting that only μ fractions of players in the network chosen to be active can update their individual weights according to whether their payoffs satisfy their aspirations. Therefore, our individual weights can be regarded as a type of intrinsic motivation satisfaction. Through Monte Carlo simulations on the square lattice, our co-evolution mechanism has been proven to significantly promote cooperation. Furthermore, we find that the moderate μ leads to the highest cooperation level. By dividing the players into four types according to their strategies and weights, we prove that the inversion of the dominant relationship between cooperators and defectors with low weights leads to a conversion cycle of the four types of players, which enhances spatial reciprocity to promote cooperation. Moderate μ results in an appropriate number of low-weight players in this cycle. Interestingly, our results show that higher weight heterogeneity does not lead to higher levels of cooperation, which is contrary to the intuition formed in the previous work.

Switching global correlations on and off in a many-body quantum state by tuning local entanglement.

A quantum many-body state built on a classical 1D Ising model with locally entangled qubits is considered. This setup can model an infinite player quantum Prisoner's dilemma game with each site representing two entangled players (or qubits). The local entanglement γ between two qubits placed on a site in the 1D Ising model and classical coupling between adjacent sites of the Ising model have an apposite influence on qubits. It points to a counter-intuitive situation wherein local entanglement at a site can exactly cancel global correlations, signaling an artificial quantum many-body state wherein, by locally tuning the entanglement at a particular site, one can transition from a strongly correlated quantum state to an uncorrelated quantum state and then to a correlated classical state. In other words, we can simulate a state similar to a type II superconducting state via local tuning of entanglement in a 1D Ising chain with entangled qubits.

Unravelling the relation between altruistic cooperativeness trait, smiles, and cooperation: a mediation analysis.

Human cooperativeness is an important personality trait. However, the mechanism through which people cooperate remains unclear. Previous research suggests that one of the proposed functions of smiling is to advertise altruistic dispositions, leading to successful cooperation. In particular, studies have reported that Duchenne smiles are honest signals of cooperative intent because they are not easy to produce voluntarily. This study aimed to examine the predictive relationships among altruistic cooperativeness traits, Duchenne smiles, and cooperative behavior. A total of 90 people were randomly assigned to dyads and filmed while they participated in a ten-minute, unstructured conversation followed by a prisoner's dilemma game to measure their cooperative behaviors. Their smiles during conversations were classified as Duchenne or non-Duchenne. Participants' altruistic dispositions were measured before the conversation began using an anonymous prisoner's dilemma game. The results of our linear regression analyses support previous findings that individual's Duchenne smiles and their own cooperative behavior are positively correlated. However, when we controlled for altruistic cooperativeness, Duchenne smiles no longer correlated with cooperative behavior. The results of the mediation analyses showed that Duchenne smiles and smile synchrony did not mediate the predictive relationship between altruistic cooperativeness and cooperative behavior. Our results suggest that human cooperative behavior may be predetermined by altruistic cooperativeness. This calls for the reconsideration of the Duchenne smile as an underlying behavioral mechanism that is effective for signaling altruistic cooperative intent.

Impact of Social Preferences, Trust and Behavioural Norms on Cooperation: Experimental Evidence from Prisoner’s Dilemma Game

The main objective of the study is to evaluate the impact of social preferences, trust and behavioural norms on strategic choices made by economic agents using the framework of a one-shot Prisoner’s Dilemma (PD) game. The standard neoclassical economics model predicts that all players will choose a strategy of non-cooperation, establishing it as the Nash equilibrium. We examine how social preferences and behavioural norms influence the player’s expectations from others and their own choices, by experimentally testing for the same using a 2 × 2 factorial design with the following three levels of partner selection arrangements: (i) game playing with stranger, (ii) face-to-face game playing with peer, and (iii) game playing with friend. The experimental results reveal significant deviations from the standard predictions of the one-shot PD game. The experimental data revealed that (i) players while interacting with a peer cooperated significantly more than playing with a stranger and (ii) players playing with a friend cooperated significantly more than playing with a peer. These changes in the social preferences of the players were further investigated in terms of trust/distrust and four behavioural norms—positive reciprocity, negative reciprocity, exploitation and altruism, and how these factors interact in influencing decision-making with respect to cooperation. JEL Codes: C72, C91, D01, D91

Spontaneous humanization of robots in passive observation of human-robot interaction: A path toward ethical consideration and human-robot cooperation

As humanoid robots become more prevalent, understanding how people form initial representations of and attitudes towards these agents is crucial. This study investigated whether observing a human's emotional reactions towards a robot in a passive human-robot interaction influences the spontaneous humanization and mental state attributions of the robot, and subsequent ethical considerations and cooperation. In Experiment 1, Japanese and British participants observed videos of a human interacting emotionally or neutrally with a Pepper robot and then assessed the robot. Results showed the emotional video elicited more humanization and intentionality attributions towards the robot, subsequently predicting greater ethical concern, especially among Japanese participants. In Experiment 2, observing human emotional engagement increased cooperation with the robot in a Prisoner's Dilemma game through enhanced humanization and intentionality attributions. The findings suggest that passive observation of human-robot interactions can shape the representation, attribution, and treatment of robots based on culture and situational cues. This highlights the need to consider social factors that may influence people's developing relationships with robots.

IN THE MULTIPLAYER PRISONER'S DILEMMA, A PLAYER EMPLOYING A ZERO-DETERMINANT STRATEGY SECURES ADVANTAGEOUS OUTCOMES FOR THE ENTIRE GROUP.

When there is an interaction between the level of choice of an individual and a group, there is no favorite but to refer to the problem of a multi-member prisoner's dilemma game. Also in real life, there is a widespread need for cooperation or defection amongst a group of population in the matter of choice. The problem of multiplayer prisoner's dilemma is widely used in real life. We conducted this study to find out how people cooperate in a multiplayer interaction in the prisoner's dilemma game. In this study, we examine the interaction between an individual and a group of population and look for the Zero-Determinant strategies in the case of multiplayer prisoner's dilemma game.

Direct emotional interaction in prisoner's dilemma game

In this paper, we develop a prisoner's dilemma game model with three types of strategies and six types of emotions. We propose a direct emotional interaction mechanism considering memory effect in which a player's favorability serves as an index of emotions and directly impacts payoffs and emotions. Our model enables that individuals gradually increase the tendency to loneliness or defection in the face of unfriendly people, and increase the tendency to cooperation in the face of friendly people. By simulations, we further show that both direct emotional interaction and memory have the effect of enhancing the competitive advantage of cooperators and individuals with friendly emotions. Besides, the proportion of friendly groups increases if the degree of direct emotional interaction increases. Also, the impact of memory on cooperation has a non-monotonic characteristic. As a result, direct emotional interaction with memory effect leads to the improvement of social average favorability, increases the number of friendly populations, improves the overall level of social cooperation, and enables friendly people to gain advantages in evolution. Therefore, our work contributes to understanding the role of emotional factors in the evolution of social cooperation.

Let justice be silent no more: A study of “courage behaviors for a just cause” based on repeated game and evolutionary game model

In this paper, an empirical method based on game theory is employed to investigate the necessity and strategy of righteousness and courage. Firstly, a single prisoner's dilemma game model is established, and its limitations are analyzed. Secondly, the number of games is expanded, and the repeated game model is utilized to examine the optimal strategy for individuals. Next, the concept of finite rationality is introduced, and the characteristics of strategy superiority and inferiority are considered. The positive effects of brave behavior for righteousness on social groups are studied using the evolutionary game model. Finally, based on the empirical results, corresponding suggestions are offered, including encouraging residents to establish a concept of morality and integrity, rather than simply being "good people", and urging the government to foster a harmonious atmosphere in society and improve the legal protection system for righteous and courageous acts, with the aim of motivating people to take courageous actions that promote righteousness.

How do the joint effects of aspiration and social influence promote cooperation in the prisoner’s dilemma game?

Various mechanisms have been proposed to promote cooperation in evolutionary games, including aspiration and social influence. However, the joint effects of aspiration and social influence have so far been ignored in the literature. Thus, we discuss the joint effects of aspiration and social influence on promoting cooperation in the Prisoner’s Dilemma Game (PDG). We introduce different aspiration tags as different aspirations and different types of neighborhoods as different social influences to reveal how the level of cooperation changes in four heterogeneous micro-environments composed of diverse aspirations and social influences. The Fermi function is adopted as the priority strategy updating rule. Simulation results show that aspiration and social influence mechanisms are jointly effective at improving cooperation in the PDG. More precisely, the aspiration mechanism promotes cooperation unconditionally, but that the social influence mechanism promotes it conditionally.

Prisoner's dilemma and the free operant: John Nash, I'd like you to meet Fred Skinner.

In separate chambers, responding by two pairs of pigeons was reinforced under concurrent random-ratio schedules of reinforcement. For each pair, the birds' schedules were coupled in such a manner that left- and right-key reinforcement probabilities were determined by the key being pecked by the other pigeon of the pair. In this way, a reinforcement matrix, like that of the popular Prisoner's Dilemma game of game theory, was created. The responding of all subjects soon gravitated to the choice combination identified by the mathematician John Nash as the equilibrium of the Prisoner's Dilemma game. This was found both before and after reversal of contingencies on the keys. In a second experiment, with a single pair of pigeons, stimuli signaling the choice of the paired pigeon had little lasting effect: responding again gravitated to the game's equilibrium. The results affirm earlier findings, demonstrating that Skinner's principle of positive reinforcement, together with Nashian mathematics, entirely accounts for iterative game-theoretic behavior. They extend these findings to the so-called free operant: to schedules of reinforcement in which responding is not constrained by stimulus-response sequencing (i.e., a trials procedure). The coupled schedule of reinforcement introduced here offers significant promise for the experimental analysis of economic and social behaviors.

Antisocial behavior-based environmental feedback in spatial prisoner's dilemma game

The environment, people, and behavior are interdependent and always interactive influence. In reality, a higher cooperation level may change the environment in a way that is beneficial for all competitors. Herein, this work proposed a coevolutionary model in the prisoner's dilemma game where the community environment determines the anti-social revenue structure. Moreover, to capture this phenomenon that behavioral changes induced by the individual's perception of the external environment, the memory effect is also taken into account in this work. It suggests that individuals' stored information about community cooperative level (referred to as indirect experience) can trigger antisocial behavior by influencing their perceptions of antisocial revenue, and that their own past strategic information (referred to as direct experience) also plays a similar role. Numerous simulations show that the proposed mechanism significantly improves cooperation, especially when sensitivity to the environment is taken into account. Furthermore, when memory is considered, a lack of experience and insufficient environmental information may result in different optimal cooperative levels corresponding to different b. In addition, the impact of the sufficient indirect experience and the immediate environmental feedback on cooperation are nearly identical. When individuals have sufficient direct and indirect experiences, their roles can be interchangeably in decision-making. Finally, we discovered that the proposed mechanism exhibits good robustness. Overall, this study demonstrates an innovative use of quantitative calculations to describe the conclusions of qualitative analysis, which have theoretical and practical implications.

Humans perceive warmth and competence in artificial intelligence

Artificial intelligence (A.I.) increasingly suffuses everyday life. However, people are frequently reluctant to interact with A.I. systems. This challenges both the deployment of beneficial A.I. technology and the development of deep learning systems that depend on humans for oversight, direction, and regulation. Nine studies (N= 3,300) demonstrate that social-cognitive processes guide human interactions across a diverse range of real-world A.I. systems. Across studies, perceived warmth and competence emerge prominently in participants' impressions of A.I. systems. Judgments of warmth and competence systematically depend on human-A.I. interdependence and autonomy. In particular, participants perceive systems that optimize interests aligned with human interests as warmer and systems that operate independently from human direction as more competent. Finally, a prisoner's dilemma game shows that warmth and competence judgments predict participants' willingness to cooperate with a deep-learning system. These results underscore the generality of intent detection to perceptions of a broad array of algorithmic actors.

Intergroup competition, group status, and individuals’ cooperation behavior: Evidence from a laboratory experiment

Intergroup competition has been proven to increase ingroup cooperation, but it will also divide individuals into high-status groups and low-status groups, which may lead to group-level conflict and affect cooperation behavior among different status group members. In this paper, we conduct a laboratory experiment to find how group status caused by intergroup competition changes individuals’ cooperation behavior in two representative social dilemma frameworks, the public goods game and the prisoner's dilemma game. Experimental results show that both high-status group members and low-status group members will improve ingroup cooperation, and there exists the framing effect of cooperation which affects different status group members’ decisions under different situations. Specifically, the increase of ingroup cooperation occurs among low-status group members in the public goods game and high-status group members in the prisoner's dilemma game. Besides, we find no evidence of any significant change in outgroup cooperation among different status group members.