Win-Stay-Lose-Shift as a self-confirming equilibrium in the iterated Prisoner's Dilemma.

Minjae Kim,Jung-Kyoo Choi,Seung Ki Baek

doi:10.1098/rspb.2021.1021

Abstract

Evolutionary game theory assumes that players replicate a highly scored player’s strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someone’s strategy just by observing the behaviour. In this work, we consider players with memory-one stochastic strategies in the iterated Prisoner’s Dilemma, with an assumption that they cannot directly access each other’s strategy but only observe the actual moves for a certain number of rounds. Based on the observation, the observer has to infer the resident strategy in a Bayesian way and chooses his or her own strategy accordingly. By examining the best-response relations, we argue that players can escape from full defection into a cooperative equilibrium supported by Win-Stay-Lose-Shift in a self-confirming manner, provided that the cost of cooperation is low and the observational learning supplies sufficiently large uncertainty.

Highlights

Evolutionary game theorists often assume that behavioural traits can be genetically transmitted across generations [1]
The notion of self-confirming equilibrium (SCE) has been proposed by incorporating such imperfectness of observation in learning [11]: when an SCE strategy is played, some of the possible information sets may not be reached, so the players do not have exact knowledge but only certain untested belief about what their co-players would do at those unreached sets
It is sustained as an equilibrium in the sense that no player can expect a better payoff by unilaterally deviating from it once given such belief, and that the beliefs do not conflict with observed moves

Summary

Introduction

Evolutionary game theorists often assume that behavioural traits can be genetically transmitted across generations [1]. We will identify the best-response dynamics in this space and examine how the dynamics should be modified when observational learning introduces uncertainty in Bayesian inference about strategies.

Results

Conclusion