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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem
Author(s): Li, Jiawei
Kendall, Graham
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Issue Date: 19-Aug-2015
Date Deposited: 11-Jun-2016
Citation: Li J & Kendall G (2015) On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem. PLoS ONE, 10 (8), Art. No.: e0136032.
Abstract: In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games.
DOI Link: 10.1371/journal.pone.0136032
Rights: © 2015 Li, Kendall. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
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