Academic journal article International Journal of Business and Management Science

Repeated Prisoners' Dilemma with Local Interaction: A Simulation Model

Academic journal article International Journal of Business and Management Science

Repeated Prisoners' Dilemma with Local Interaction: A Simulation Model

Article excerpt

Abstract:

We study a simulation model of the prisoner's dilemma game played locally by agents situated on a two dimensional lattice. Agents interact simultaneously with players in its Von Neuman neighborhood (r = 1), behaving as one of the four of automata strategy types including simple cooperation, simple defect, TFT (tit for tat) and TF2T (tit for two tats). Our research seeks to study the effect of including reciprocal players like TFT and TF2T on the survival rate of simple cooperation under different scenarios of learning rate and payoff structures. We show that presence of reciprocal-strategy (TFT and TF2T) players and learning delay positively affects the survival of single state cooperators.

Keywords: Game Theory, Prisoner's Dilemma, local action, automata, simulation

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INTRODUCTION

There are many instances of economic behavior where the players engage in playing the same game of competition against many other players at the same time and sometimes repeatedly over finite or infinite periods of time. A genre of such games is typified by the ubiquitous Prisoner's Dilemma (PD) game. The emergence and flourishing of human society is set on foundations of cooperation and at the same time guided by economic rationalism, particularly rational selfishness. This simultaneous engagement of two opposing forces is a puzzle that continues to baffle economists even to-day. The PD game captures the quintessential contradiction between the instinct to cooperate and rational economic choice of selfishness. Interestingly the latter follows in the shadow of the former, but the question remains as to however did we arrive at the union of these two disparate forces that simultaneously sustain and energize the human civilization?

The PD game has a unique Nash equilibrium of (defect, defect) for both the players, an outcome that leaves none better off. Obviously, both can be better off playing (cooperate, cooperate), but such an outcome is imperiled by the selfish inclination of cheating on a trusting partner. Can there never be cooperation, then? Well, it can possibly happen but only when players engage in an infinite series of PD game between themselves. For infinitely repeated PD games between two players, trigger strategies can virtually guarantee cooperation as an equilibrium strategy. The cost of playing a trigger strategy, however, could be very high in terms of information processing and book-keeping. Is it reasonable to assume such complex skills on the part of all players? The real world has many instances of similar interactions with a multiplicity of players playing with each other simultaneously and indeed 'cooperation' is seen very well to exist, and that without the use of any bookkeeping, or any other mechanisms to mitigate the non-cooperative settings. How do we explain the survival of the strategy of 'cooperation' among a group of ordinary unsophisticated players?

An approach that has recently gained much adherence, is the assumption of bounded rationality, that is, players when repeatedly playing the same game simultaneously against a multiplicity of players defined as neighbors, play more or less like machines or cellular automata (CA). They tend to play the same action against all players, and if they can apply action with discrimination against their neighbors based on the neighbor's previous action, then they do so with limited recall of previous play by the neighbor, and update their strategies using some uniform rule of thumb. Economists are increasingly beginning to appreciate that 'rationality' is a strong assumption in many game contexts. This assumption has been applied to the study of cooperation to population of players playing the PD game against other members of the population, with whom either they are randomly matched or happen to share a small local neighborhood.

It is easy to see instances of PD in the social context. …

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