Classic Prisoner Research Articles

An asymptotic analysis of the evolutionary spatial prisoner’s dilemma on a path

In this paper, we consider the Evolutionary Spatial Prisoner’s Dilemma (ESPD) in which players are modelled by the vertices of an underlying graphG representing some spatial organisational structure amongst the players. During each round of the ESPD every pair of adjacent players in G play a classical prisoner’s dilemma against each other, and they update their strategies from one round to the next based on the perceived success achieved by the strategies of neighbouring players during the previous round. In this way, players are able to adapt and learn from each other’s strategies as the game progresses without being able to rationalise good strategies. We characterise all steady states of the ESPD for the case where G is a path, and we also characterise the structures of those initial states that lead to the emergence of persistent substates of cooperation over time. We finally determine analytically (i.e. without using simulation) the probability that the game’s states will evolve from a randomly generated initial state towards a steady state which accommodates some form of persistent cooperation. More specifically, we show that there exists a range of game parameters for which the likelihood of the emergence of persistent cooperation increases to almost certainty as the length of the path increases.

New Nash Equilibrium Based on Generic Risk Element Transmission Theory

Nash equilibrium is the foundation of traditional game theory, while the benefits of game players under the Nash equilibrium are constant, so the core idea of generic risk transmission was applied to traditional static game. Accordingly a risk static game model, in which the benefits of players were subject to triangular distribution, was constructed. Then we obtained different equilibrium states under the different risk types of players. Furthermore, the classic Prisoners’ Dilemma was used to demonstrate the practice value of risk game. Through analyzing and solving the risk Prisoners’ Dilemma model which changed from the classic Prisoner's Dilemma model according to actual situation, the Pareto improvement strategy combination could be achieved. The new equilibrium result can give an appropriate explanation why there is always some prisoners conceal the corpus delicti in adventure

Split or Steal? Cooperative Behavior When the Stakes Are Large

We examine cooperative behavior when large sums of money are at stake, using data from the television game show Golden Balls. At the end of each episode, contestants play a variant on the classic prisoner's dilemma for large and widely ranging stakes averaging over $20,000. Cooperation is surprisingly high for amounts that would normally be considered consequential but look tiny in their current context, what we call a “big peanuts” phenomenon. Utilizing the prior interaction among contestants, we find evidence that people have reciprocal preferences. Surprisingly, there is little support for conditional cooperation in our sample. That is, players do not seem to be more likely to cooperate if their opponent might be expected to cooperate. Further, we replicate earlier findings that males are less cooperative than females, but this gender effect reverses for older contestants because men become increasingly cooperative as their age increases. This paper was accepted by Brad Barber, Teck Ho, and Terrance Odean, special issue editors.

A model of political information-processing and learning cooperation in the repeated Prisoner’s Dilemma

A model of political information processing drawn from the studies of political behavior and psychology is applied to the emergence of cooperation observed in classic repeated Prisoner’s Dilemma (PD) game experiments. The results show that the model can robustly account for the learning of cooperation observed in the experiments when players are aware of the strategic nature of the game and make choices over immediate actions. In effect, basic psychological learning mechanisms, well-established in political behavior and psychology research, together tend to lead players to learn to cooperate over time under quite general conditions. In particular, the evaluative affect players develop towards choice objects and a belief learning that weighs an actually obtained outcome more than a forgone outcome play a central role in these processes.

Prisoner's Dilemma and the Nuisance Suit

When a nuisance suit survives a motion to dismiss, defendant corporations are faced with a variant of the classic prisoner’s dilemma. If all corporations refused to settle and put their resources towards litigating frivolous claims, then the incentive of plaintiff’s firms to file these suits would diminish. However, if only one corporation chooses to litigate (and the rest settle), then litigating is a costly, futile, and self-destructive response. Although litigating and deterring frivolous suits would be better for all corporations, no individual corporation would be acting rationally in refusing to settle. So the optimal choice for each corporation individually leads to a worse outcome for all corporations. This paper argues that there is a way for corporations to both behave rationally and act collectively when it comes to nuisance suits. By analyzing the nuisance suit as a prisoner’s dilemma for corporations and understanding how the dilemma is solved, this note will illustrate how corporations can build a litigation strategy that will effectively deter nuisance suits.

Nash Equilibria in Multi-Agent Motor Interactions

Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.

Harm to Others: The Social Cost of Antibiotics in Agriculture

It has become increasingly clear that the use of antibiotics in conventionally raised livestock contributes to the emergence of antibiotic-resistant bacteria. In this paper, I argue that the harm principle of classical liberalism should guide agricultural policy in general, and the regulation of antibiotics in livestock in particular. After developing an interpretation of the harm principle, and framing the choice to produce and consume animals treated with antibiotics as a classic prisoner's dilemma, I consider some policy responses to the problem, including a ban on the non-therapeutic use of antibiotics.

Are women better mindreaders? Sex differences in neural correlates of mentalizing detected with functional MRI

BackgroundThe ability to mentalize, i.e. develop a Theory of Mind (ToM), enables us to anticipate and build a model of the thoughts, emotions and intentions of others. It has long been hypothesised that women differ from men in their mentalizing abilities. In the present fMRI study we examined the impact of (1) gender (women vs. men) and (2) game partner (human vs. computer) on ToM associated neural activity in the medial prefrontal cortex. Groups of men (n = 12) and women (n = 12) interacted in an iterated classical prisoner's dilemma forced choice situation with alleged human and computer partners who were outside the scanner.ResultsBoth the conditions of playing against putative human as well as computer partners led to activity increases in mPFC, ACC and rTPJ, constituting the classic ToM network. However, mPFC/ACC activity was more pronounced when participants believed they were playing against the alleged human partner. Differences in the medial frontal lobe activation related to the sex of the participants could be demonstrated for the human partner > computer partner contrast.ConclusionOur data demonstrate differences in medial prefrontal brain activation during a ToM task depending on both the gender of participants and the game partner.

The Problem of Clean Hands

The problem of dirty hands concerns the apparently inevitable need for effective politicians to do what is ethically wrong. This essay discusses a related problem in democratic elections of politicians being unwilling to commit themselves to precise positions on controversial policy issues. Given certain plausible assumptions, I demonstrate using a simple game theoretic model that there is an incentive structure for political candidates that is damaging to the public good. I contrast this problem with the classic prisoner’s dilemma and then go on to discuss some possible strategies for overcoming this problem by an improved system of political debates.

Institutions matter! Why the Herder Problem is not a Prisoner’s Dilemma

In the game theory literature, Garrett Hardin’s famous allegory of the “tragedy of the commons” has been modeled as a variant of the Prisoner’s Dilemma, labeled the Herder Problem (or, sometimes, the Commons Dilemma). This brief paper argues that important differences in the institutional structures of the standard Prisoner’s Dilemma and Herder Problem render the two games different in kind. Specifically, institutional impediments to communication and cooperation that ensure a dominant strategy of defection in the classic Prisoner’s Dilemma are absent in the Herder Problem. Their absence does not ensure that players will achieve a welfare-enhancing, cooperative solution to the Herders Problem, but does create far more opportunity for players to alter the expected payoffs through cooperative arrangements. In a properly modeled Herder Problem—along the lines of an assurance game—defection would not always be the dominant strategy. Consequently, the Herder Problem is not in the nature of a Prisoner’s Dilemma.

Institutions Matter! Why the Herder Problem is Not a Prisoner's Dilemma

In the game theory literature, Garrett Hardin's famous allegory of the tragedy of the commons has been modeled as a variant of the Prisoner's Dilemma, labeled the Herder Problem (or, sometimes, the Commons Dilemma). This brief paper argues that important differences in the institutional structures of the archetypal Prisoner's Dilemma and Herder Problem render the two games different in kind. Specifically, institutional impediments to communication and cooperation that ensure a dominant strategy of defection in the classic Prisoner's Dilemma are absent in the Herder Problem. Their absence does not ensure that players will achieve a welfare-enhancing, cooperative solution to the Herders Problem, but does create far more opportunity for players to alter the expected payoffs through cooperative arrangements. In a properly modeled Herder Problem, defection would not always be the dominant strategy. Consequently, the Herder Problem is not in the nature of a Prisoner's Dilemma.

Unions and the Coordination Problem in an Integrated Economy

This work represents an extension of the model presented by Olivier Blanchard in occasion of the Lionel Robbins Lectures (2000) given at M.I.T. It analyzes the transnational cooperative behavior of trade unions in a two symmetric country-model with monopolistic competition firms present in the two markets under the possibility to shift production (i.e. through an increase in investments). In the case of technological shocks firms are able to capture the advantage in wage differentials between the two countries. The country facing the shock has a loss in employment, while the other one faces a gain. But, if trade unions cooperate, in absence of transaction costs (costs to coordinate union activities), they are able to reduce the total loss of employment. If transaction costs are present unions face a classical Prisoner’s Dilemma where the Nash equilibrium of the game is no cooperation. hut this result is not Pareto-efficient.

Evolutionary escape from the prisoner's dilemma

The classic prisoner's dilemma model of game theory is modified by introducing occasional variations on the options available to players. Mutation and selection of game options reliably change the game matrix, gradually, from a prisoner's dilemma game into a byproduct mutualism one, in which cooperation is stable, and “temptation to defect” is replaced by temptation to cooperate. This result suggests that when there are many different potential ways of interacting, exploring those possibilities may make escape from prisoner's dilemmas a common outcome in the world. A consequence is that persistent prisoner's dilemma structures may be less common than one might otherwise expect.

Friend or Foe?A Natural Experiment of the Prisoner's Dilemma

Abstract This study examines data drawn from the game show Friend or Foe? which is similar to the classic prisoner's dilemma tale: partnerships are endogenously determined, and players work together to earn money, after which they play a one-shot prisoner's dilemma game over large stakes: varying from $200 to (potentially) more than $22,000. The data reveal several interesting insights; perhaps most provocatively, they suggest that even though the game is played in front of an audience of millions of viewers, some of the evidence is consistent with a model of discrimination. The observed patterns of social discrimination are unanticipated, however.

Simulating Two-Level Negotiations

International negotiations can be modeled as a two-level process that involves competing interests within and between groups. This modified simulation of the classic prisoner's dilemma introduces students to the negotiation process and challenges them to consider how different de- cision structures can affect outcomes. Students fill both leadership and negotiation roles and gain an active learning experience that exposes them to important international relations concepts. All of the instruc- tions, handouts, and materials are included to provide instructors of international relations or comparative politics with a resource that can be utilized with groups of varying size, ability, and composition. International negotiation is a complex process that is often discussed at an abstract level in introductory courses to international relations. Using simulations of this process can place the relevance of key concepts discussed in international relations theory, such as absolute versus relative gains, into perspective for the participants. Role playing also increases the participant's awareness of these complexities. The prisoner's dilemma has often been used as a tool to simulate international bar- gaining as the game has integral commonalities with the international system. Both situations lack a sovereign to enforce agreements. Therefore, the dominant strategy for the individual or state is often to defect. For example, the U.S. benefits from other nations signing the Kyoto Protocol even though America does not have to reduce emissions or spend more on protecting the environment. Defecting from the Kyoto treaty while other developed nations cooperate has the greatest benefits and the least costs for the United States. In the classic, single play or one-shot, prisoner's dilemma (PD) cooperation is highly unlikely as neither participant knows whether they can trust the other party in the game. In an iterated prisoner's dilemma (IPD) cooperation becomes more likely as groups know that interaction will occur in the future. This ''shadow of the future'' encourages groups or individuals to cooperate (Axelrod 1984). This sim- ulation is a finite IPD. It has been utilized in primary schools and high schools as well as in undergraduate courses at both Florida State University and the University of Connecticut. What makes this simulation unique is the intergroup nature of the dilemma as well as the inclusion of diplomats and the incorporation of various regime types. Students gain direct experience with small group decision making in a democracy or an authoritarian regime.

Young, Selfish and Male: Field Evidence of Social Preferences

This study examines social preferences in three distinct field environments. In the first field setting, I allow consumers of all age and education levels to participate in one-shot and multiple-shot public goods games in a well-functioning marketplace. The second field study, an actual university capital campaign, gathers data from mail solicitations sent to 2,000 Central Florida residents. In the third field experiment, I examine data from an uncontrolled environment, a television gameshow, which closely resembles the classic prisoner's dilemma game. Several insights emerge; perhaps the most provocative is that age and social preferences appear linked.

The Economic Viability of Frequency Reward Programs in a Strategic Competitive Environment

We examine the conditions that enhance the economic viability of frequency reward programs in a strategic competitive environment. We focus particularly on conditions related to consumer behavior, namely the extent to which consumers value the future benefits offered by the reward, the expandability of the category, and consumers’ preferences for competing brands. Consumers maximize utility over a long-term time horizon, taking into account the value of the reward. Two firms maximize profits over a long-term time horizon. They first decide between implementing a frequency reward program or a traditional pricing policy (a constant price), and then decide on the specific prices. We numerically solve for the sub-game perfect equilibrium for this two-stage game. We find that a brand is more likely to find reward programs to be viable strategies if consumers value future benefits, if reward programs can expand the market, and if the brand has a higher preference. The market expandability finding is particularly interesting. If the sales increases generated by reward programs represent category growth, the power of frequency reward programs makes them an effective vehicle for generating profits. However, if gains come mainly from competitors, the power of frequency reward programs precipitates a strong competitive response that erodes profits in a classic prisoner’s dilemma. We use the airline industry to explore our market expandability finding. We find evidence that the “major” airlines introduced reward programs to counter-act a stronger outside category (new entrants), and in doing so, they expanded their market.

Reciprocity-Induced Cooperation

Many legal systems foster metarules of reciprocity to facilitate cooperative outcomes. This paper considers the role of reciprocity rules in various strategic environments. We start by considering the effect of reciprocity constraints in a classic prisoners' dilemma with two symmetric parties and linear payoffs. We extend the analysis to continuous strategies and then further extend the basic model of reciprocity to (a) asymmetric players and (b) nonlinear payoff functions. Then we examine the welfare properties of the reciprocity-induced equilibrium. In many game-theoretic situations, reciprocity constraints facilitate the achievement of cooperative outcomes. Yet the reciprocity-induced equilibrium is not always socially optimal.

Reciprocity-Induced Cooperation

The concept of reciprocity gains importance where there is no external authority to enforce agreements. Many legal systems foster meta-rules of reciprocity to facilitate cooperative outcomes. This paper considers the role of reciprocity rules in various strategic environments. We start by considering the effect of reciprocity constraints in a classic prisoner's dilemma with two symmetric parties and linear payoffs. We extend the analysis to continuous strategies and then further extend the basic model of reciprocity to a) asymmetric players, and (b) non-linear payoff functions. Then we examine the welfare properties of the reciprocity-induced equilibrium. In many game-theoretic situations, reciprocity facilitates the achievement of cooperative outcomes. Yet the reciprocity-induced equilibrium is not always socially optimal.

The Economic Viability of Frequency Reward Programs in a Strategic Competitive Environment

We examine the conditions that enhance the economic viability of frequency reward programs in a strategic competitive environment. We focus particularly on conditions related to consumer behavior namely the extent to which consumers value the future benefits offered by the reward, the expandability of the category, and Consumers' preferences for competing brands. Consumers maximize utility over a long-term time horizon, taking into account the value of the reward. Two firms maximize profits over a long-term time horizon. They first decide between implementing a frequency reward program or a traditional pricing policy (a constant price), and then decide on the specific prices. We numerically solve for the sub-game perfect equilibrium for this two-stage game. We find that a brand is more likely to find reward programs to be viable strategies if consumers value future benefits, if reward programs can expand the market, and if the brand has a higher preference. The market expandability finding is particularly interesting. If the sales increases generated by reward programs represent category growth, the power of frequency reward programs makes them an effective vehicle for generating profits. However, if gains come mainly from competitors, the power of frequency reward programs precipitates a strong competitive response that erodes profits in a classic prisoner's dilemma. We use the airline industry to explore our market expandability finding. We find evidence that the major airlines introduced reward programs to counter-act a stronger outside category (new entrants), and in doing so, they expanded their market.