Reactive strategies: an inch of memory, a mile of equilibria
type: Item
instance of: scholarly article
title: Reactive strategies: an inch of memory, a mile of equilibria
zbMATH Open document ID: 1479.91004
published in: Games
publication date: 2021-11-26T00:00:00Z
review text: Summary: We explore how an incremental change in complexity of strategies (``an inch of memory'') in repeated interactions influences the sets of Nash equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players' actions depends only on the opponent's preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) reactive strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (``a mile of equilibria'') Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory.
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A20
Mathematics Subject Classification ID: 91A10
zbMATH DE Number: 7434041
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: 1-memory or memory-one strategies
zbMATH Keywords: infinitely repeated games
author: A. P. Baklanov
MaRDI profile type: Publication
full work available at URL: g12020042
OpenAlex ID: W3162962776
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DOI: 10.3390/G12020042
description: scientific article; zbMATH DE number 7434041