Statistics Papers

Document Type

Journal Article

Date of this Version

5-2007

Publication Source

Machine Learning

Volume

67

Issue

1

Start Page

7

Last Page

22

DOI

10.1007/s10994-006-9713-5

Abstract

We consider a group of agents on a graph who repeatedly play the prisoner’s dilemma game against their neighbors. The players adapt their actions to the past behavior of their opponents by applying the win-stay lose-shift strategy. On a finite connected graph, it is easy to see that the system learns to cooperate by converging to the all-cooperate state in a finite time. We analyze the rate of convergence in terms of the size and structure of the graph. Dyer et al. (2002) showed that the system converges rapidly on the cycle, but that it takes a time exponential in the size of the graph to converge to cooperation on the complete graph. We show that the emergence of cooperation is exponentially slow in some expander graphs. More surprisingly, we show that it is also exponentially slow in bounded-degree trees, where many other dynamics are known to converge rapidly.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s10994-006-9713-5.

Keywords

games on graphs, learning, prisoner's dilemma game, win-stay lose-shift, oriented percolation, emergence of cooperation

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Date Posted: 27 November 2017

This document has been peer reviewed.