Repeated Prisoner's Dilemma Game Research Articles

Private list sharing leads to cooperation and central hubs emergence in ABM

We introduce an agent based model framework to investigate how an alternative to classic image score and gossip can support the emergence of cooperation in a repeated prisoner dilemma game with agents employing mixed strategies. We debate the universality of image scores, arguing that they cannot be considered an objective property of the agents observed but rather a subjective property of each observer. From this assumption, we develop a private list mechanism for opponent selection and gossip sharing among the population of the simulation. The results show that the private list mechanism is able to foster the emergence of cooperation, and that for various levels of list usage different levels of cooperation correspond in the system. Finally, we observe interesting topological properties emerging, with networks characterised by one ‘super-hub’ connected to every other node, suggesting the emergence of centralized entities to support cooperation.

Zero-determinant strategies under observation errors in repeated games.

Zero-determinant (ZD) strategies are a novel class of strategies in the repeated prisoner's dilemma (RPD) game discovered by Press and Dyson. This strategy set enforces a linear payoff relationship between a focal player and the opponent regardless of the opponent's strategy. In the RPD game, games with discounting and observation errors represent an important generalization, because they are better able to capture real life interactions which are often noisy. However, they have not been considered in the original discovery of ZD strategies. In some preceding studies, each of them has been considered independently. Here, we analytically study the strategies that enforce linear payoff relationships in the RPD game considering both a discount factor and observation errors. As a result, we first reveal that the payoffs of two players can be represented by the form of determinants as shown by Press and Dyson even with the two factors. Then, we search for all possible strategies that enforce linear payoff relationships and find that both ZD strategies and unconditional strategies are the only strategy sets to satisfy the condition. We also show that neither Extortion nor Generous strategies, which are subsets of ZD strategies, exist when there are errors. Finally, we numerically derive the threshold values above which the subsets of ZD strategies exist. These results contribute to a deep understanding of ZD strategies in society.

Cooperation through communication: Teams and individuals in finitely repeated Prisoners’ dilemma games

For both two person teams and individuals unrestricted communication between opponents in a finitely repeated prisoner dilemma game results in stage-one cooperation rates of between 95–100%. Content analysis of between opponent communication focuses on the increased earnings cooperation can achieve, with minimal discussion of punishment for failing to cooperate. Restoring cooperation after an early stage-game defection typically requires compensating the aggrieved agent.

Cooperation Through Communication: Teams and Individuals in a Finitely Repeated Prisonerss Dilemma Game

For both two person teams and individuals unrestricted communication between opponents in a finitely repeated prisoner dilemma game results in stage-one cooperation rates of between 95-100%. Content analysis of between opponent communication focuses on the increased earnings cooperation can achieve, with minimal discussion of punishment for failing to cooperate. Restoring cooperation after an early stage-game defection typically requires compensating the aggrieved player. Between opponent discussions underlying cooperation focus on the mutual benefit from cooperation (earning more money and fairer than competing), with threats for failing to live up to agreements coming in a distant third.

Individual Characteristics vs. Experience: An Experimental Study on Cooperation in Prisoner's Dilemma.

Cooperative behavior is often assumed to depend on individuals' characteristics, such as altruism and reasoning ability. Evidence is mixed about what the precise impact of these characteristics is, as the subjects of study are generally randomly paired, generating a heterogeneous mix of the two characteristics. In this study we ex-ante create four different groups of subjects by factoring their higher or lower than the median scores in both altruism and reasoning ability. Then we use these groups in order to analyze the joint effect of the two characteristics on the individual choice of cooperating and on successful paired cooperation. Subjects belonging to each group play first 10 one-shot prisoner's dilemma (PD) games with ten random partners and then three consecutive 10-round repeated PD games with three random partners. In all games, we elicit players' beliefs regarding cooperation using an incentive compatible method. Individuals with high altruism are more optimistic about the cooperative behavior of the other player in the one-shot game. They also show higher individual cooperation and paired cooperation rates in the first repetitions of this game. Contrary to the one-shot PD games where high reasoning ability reduces the probability of playing cooperatively, the sign of the relationship is inverted in the first repeated PD game, showing that high reasoning ability individuals better adjust their behavior to the characteristics of the game they are playing. In this sense, the joint effect of reasoning ability and altruism is not linear, with reasoning ability counteracting the cooperative effect of altruism in the one-shot game and reinforcing it in the first repeated game. However, experience playing the repeated PD games takes over the two individual characteristics in explaining individual and paired cooperation. Thus, in a (PD) setting, altruism and reasoning ability significantly affect behavior in single encounters, while in repeated interactions individual and paired cooperation reach similarly high levels independently of these individual characteristics.

Reciprocity in Human-Robot Interaction: A Quantitative Approach Through the Prisoner’s Dilemma and the Ultimatum Game

Reciprocity is an important factor in human-human interaction, so it can be expected that it should also play a major role in human-robot interaction (HRI). Participants in our study played the Repeated Prisoner's Dilemma Game (RPDG) and the mini Ultimatum Game (mUG) with robot and human agents, with the agents using either Tit for Tat (TfT) or Random strategies. As part of the study we also measured the perceived personality traits in the agents using the TIPI test after every round of RPDG and mUG. The results show that the participants collaborated more with humans than with a robot, however they tended to be equally reciprocal with both agents. The experiment also showed the TfT strategy as the most profitable strategy; affecting collaboration, reciprocation, profit and joint profit in the game. Most of the participants tended to be fairer with the human agent in mUG. Furthermore, robots were perceived as less open and agreeable than humans. Consciousness, extroversion and emotional stability were perceived roughly the same in humans and robots. TfT strategy became associated with an extroverted and agreeable personality in the agents. We could observe that the norm of reciprocity applied in HRI has potential implications for robot design.

Evolution of Conformity in Social Dilemmas.

People often deviate from their individual Nash equilibrium strategy in game experiments based on the prisoner’s dilemma (PD) game and the public goods game (PGG), whereas conditional cooperation, or conformity, is supported by the data from these experiments. In a complicated environment with no obvious “dominant” strategy, conformists who choose the average strategy of the other players in their group could be able to avoid risk by guaranteeing their income will be close to the group average. In this paper, we study the repeated PD game and the repeated m-person PGG, where individuals’ strategies are restricted to the set of conforming strategies. We define a conforming strategy by two parameters, initial action in the game and the influence of the other players’ choices in the previous round. We are particularly interested in the tit-for-tat (TFT) strategy, which is the well-known conforming strategy in theoretical and empirical studies. In both the PD game and the PGG, TFT can prevent the invasion of non-cooperative strategy if the expected number of rounds exceeds a critical value. The stability analysis of adaptive dynamics shows that conformity in general promotes the evolution of cooperation, and that a regime of cooperation can be established in an AllD population through TFT-like strategies. These results provide insight into the emergence of cooperation in social dilemma games.

An evolutionary game-theoretic model for ethno-religious conflicts between two groups

Ethno-religious conflict in multi-cultural societies has been one of the major causes of loss of life and property in recent history. In this paper, we present and analyze a multi-agent game theoretic model for computational study of ethno-religious conflicts in multi-cultural societies. Empirical fact-based research in sociology and conflict resolution literature have identified (a) ethno-religious identity of the population, (b) spatial structure (distribution) of the population, (c) existing history of animosity, and (d) influence of leaders as some of the salient factors causing ethno-religious violence. It has also been experimentally shown by Lumsden that multi-cultural conflict can be viewed as a Prisoner's Dilemma (PD) game. Using the above observations, we model the multi-cultural conflict problem as a variant of the repeated PD game in graphs. The graph consists of labeled nodes corresponding to the different ethno-religious types and the topology of the graph encodes the spatial distribution and interaction of the population. We assume the structure of the graph to have the statistical properties of a social network with the high degree nodes representing the leaders of the society. The agents play the game with neighbors of their opponent type and they update their strategies based on neighbors of their same type. This strategy update dynamics, where the update neighborhood is different from the game playing neighborhood, distinguishes our model from conventional models of PD games in graphs. We present simulation results showing the effect of various parameters of our model to the propensity of conflict in a population consisting of two ethno-religious groups. We also compare our simulation results to real data of occurrence of ethno-religious violence in Yugoslavia.

Evolving densities in continuous strategy games through particle simulations

Many cases of strategic interaction between agents involve a continuous set of choices. It is natural to model these problems as continuous space games. Consequently, the population of agents playing the game will be represented with a density function defined over the continuous set of strategy choices. Simulating evolutionary dynamics on continuous strategy spaces is a challenging problem. The classic approach of discretizing the strategy space is ineffective for multidimensional strategy spaces. We present a principled approach to simulation of adaptive dynamics in continuous space games using sequential Monte Carlo methods. Sequential Monte Carlo methods use a set of weighted random samples, also named particles to represent density functions over multidimensional spaces. Sequential Monte Carlo methods provide computationally efficient ways of computing the evolution of probability density functions. We employ resampling and smoothing steps to prevent particle degeneration problem associated with particle estimates. The resulting algorithm can be interpreted as an agent based simulation with elements of natural selection, regression to mean and mutation. We illustrate the performance of the proposed simulation technique using two examples: continuous version of the repeated prisoner dilemma game and evolution of bidding functions in first-price closed-bid auctions.

Can the Repeated Prisoner's Dilemma Game Be Used As a Tool to Enhance Moral Reasoning?

The Treadway Commission examined the causes offraudulent financial reporting and maderecommendations to curb its occurrence. In itsrecommendations to educators, the TreadwayCommission (1987) stated that ``(b)usinessschools should encourage business andaccounting faculty to develop their ownpersonal competence as well as classroommaterials for conveying information, skills,and ethical values that can help prevent,detect, and deter fraudulent financialreporting'' (p. 83). The purpose of this studywas to determine whether the repeatedprisoner's dilemma game could be used as a toolto increase individuals' moral reasoning. Itwas hoped that this exercise would encouragetrust (Rapoport and Chammah, 1965) andreciprocal altruism (Dawes, 1988) as theylearned to cooperate with one another in orderto maximize their payoffs.