Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game

Abstract We study a simple model for social-learning agents in a restless multiarmed bandit (rMAB). The bandit has one good arm that changes to a bad one with a certain probability. Each agent stochastically selects one of the two methods, random search (individual learning) or copying information f...

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Autores principales:	Kazuaki Nakayama, Masato Hisakado, Shintaro Mori
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/9e250b018c12484b82a9e9fc551d2d65
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spelling	oai:doaj.org-article:9e250b018c12484b82a9e9fc551d2d652021-12-02T15:05:24ZNash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game10.1038/s41598-017-01750-z2045-2322https://doaj.org/article/9e250b018c12484b82a9e9fc551d2d652017-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-01750-zhttps://doaj.org/toc/2045-2322Abstract We study a simple model for social-learning agents in a restless multiarmed bandit (rMAB). The bandit has one good arm that changes to a bad one with a certain probability. Each agent stochastically selects one of the two methods, random search (individual learning) or copying information from other agents (social learning), using which he/she seeks the good arm. Fitness of an agent is the probability to know the good arm in the steady state of the agent system. In this model, we explicitly construct the unique Nash equilibrium state and show that the corresponding strategy for each agent is an evolutionarily stable strategy (ESS) in the sense of Thomas. It is shown that the fitness of an agent with ESS is superior to that of an asocial learner when the success probability of social learning is greater than a threshold determined from the probability of success of individual learning, the probability of change of state of the rMAB, and the number of agents. The ESS Nash equilibrium is a solution to Rogers’ paradox.Kazuaki NakayamaMasato HisakadoShintaro MoriNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-8 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Kazuaki Nakayama Masato Hisakado Shintaro Mori Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game
description	Abstract We study a simple model for social-learning agents in a restless multiarmed bandit (rMAB). The bandit has one good arm that changes to a bad one with a certain probability. Each agent stochastically selects one of the two methods, random search (individual learning) or copying information from other agents (social learning), using which he/she seeks the good arm. Fitness of an agent is the probability to know the good arm in the steady state of the agent system. In this model, we explicitly construct the unique Nash equilibrium state and show that the corresponding strategy for each agent is an evolutionarily stable strategy (ESS) in the sense of Thomas. It is shown that the fitness of an agent with ESS is superior to that of an asocial learner when the success probability of social learning is greater than a threshold determined from the probability of success of individual learning, the probability of change of state of the rMAB, and the number of agents. The ESS Nash equilibrium is a solution to Rogers’ paradox.
format	article
author	Kazuaki Nakayama Masato Hisakado Shintaro Mori
author_facet	Kazuaki Nakayama Masato Hisakado Shintaro Mori
author_sort	Kazuaki Nakayama
title	Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game
title_short	Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game
title_full	Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game
title_fullStr	Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game
title_full_unstemmed	Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game
title_sort	nash equilibrium of social-learning agents in a restless multiarmed bandit game
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/9e250b018c12484b82a9e9fc551d2d65
work_keys_str_mv	AT kazuakinakayama nashequilibriumofsociallearningagentsinarestlessmultiarmedbanditgame AT masatohisakado nashequilibriumofsociallearningagentsinarestlessmultiarmedbanditgame AT shintaromori nashequilibriumofsociallearningagentsinarestlessmultiarmedbanditgame
_version_	1718388849769447424

Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game

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