Learning to cooperate in the Iterated Prisoner’s Dilemma by means of social attachments

Ana L C Bazzan,Juan C Burguillo,Ana Peleteiro

doi:10.1007/s13173-011-0038-2

Abstract

AbstractThe Iterated Prisoner’s Dilemma (IPD) has been used as a paradigm for studying the emergence of cooperation among individual agents. Many computer experiments show that cooperation does arise under certain conditions. In particular, the spatial version of the IPD has been used and analyzed to understand the role of local interactions in the emergence and maintenance of cooperation. It is known that individual learning leads players to the Nash equilibrium of the game, which means that cooperation is not selected. Therefore, in this paper we propose that when players have social attachment, learning may lead to a certain rate of cooperation. We perform experiments where agents play the spatial IPD considering social relationships such as belonging to a hierarchy or to coalition. Results show that learners end up cooperating, especially when coalitions emerge.

Highlights

The concept of evolution of cooperation has been successfully studied using metaphors such as the Iterated Prisoner’s Dilemma (IPD), which is the repeated version of the PD game
13: receive reward 14: update Qijnd m times 15: end if 16: end for 17: for all Si ∈ S do 18: observe state, action, and reward for each Lj 19: compute the average reward r 20: if tuple at, st, r not yet in case base 21: add tuple at, st, r 22: else 23: if r > rold 24: replace by tuple at, st, r 25: end if 26: end if 27: end for 28: end while multiagent systems literature, but here we focus on coalition formation because it is a well-established approach from game theory, having solid mathematical grounds
Despite the obvious limitations and simplifications, the twoagent PD can be seen as an abstraction of very simple social situations that deal with cooperation

Summary

Introduction

The concept of evolution of cooperation has been successfully studied using metaphors such as the Iterated Prisoner’s Dilemma (IPD), which is the repeated version of the PD game. In the PD, two individuals are questioned separately over their involvement on a crime They have a simple choice: either to confess a mutual crime (thereby implicating the other) and accept the consequences, or to deny all involvement and hope that the other does likewise. We remark that by confessing there is a penalty reduction as it will be clear when the payoff matrix is introduced. This game models a more general situation in which two individuals have to decide, in an isolated way, whether to cooperate or to defect. The game is so formulated that mutual cooperation yields the highest joint payoff, but there is a high incentive for individual defection

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Conclusion