Expected Motion in 2x2 Symmetric Games Played by Reinforcement Learners

This chapter discusses several classes of potential games that are common in the literature and how to derive the Nash equilibrium for such games. It first considers identical interests games and dummy games before turning to decoupled games and bilateral symmetric games. It then describes congestion games, in which all players are equal, in the sense that the cost associated with each resource only depends on the total number of players using that resource and not on which players use it. It also presents other potential games, including the Sudoku puzzle, and goes on to analyze the distributed resource allocation problem, the computation of Nash equilibria for potential games, and fictitious play. It concludes with practice exercises and their corresponding solutions, along with additional exercises.

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Symmetric games

Topology of 2x2 Games ◽

10.4324/9780203340271-7 ◽

2004 ◽

pp. 77-92

Keyword(s):

Symmetric Games

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Symmetric Games

Luck, Logic, and White Lies ◽

10.1201/9781003092872-39 ◽

2021 ◽

pp. 381-396

Author(s):

Jörg Bewersdorff ◽

David Kramer

Keyword(s):

Symmetric Games

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Evolutionary Game Theory: A Generalization of the ESS Definition

International Game Theory Review ◽

10.1142/s0219198919500051 ◽

2019 ◽

Vol 21 (04) ◽

pp. 1950005

Author(s):

Elvio Accinelli ◽

Filipe Martins ◽

Jorge Oviedo

Keyword(s):

Game Theory ◽

Strategic Planning ◽

Evolutionary Game Theory ◽

Replicator Dynamics ◽

Evolutionary Game ◽

Previous Literature ◽

Evolutionarily Stable Strategies ◽

Symmetric Games ◽

Two Populations ◽

Evolutionarily Stable

In this paper, we study the concept of Evolutionarily Stable Strategies (ESSs) for symmetric games with [Formula: see text] players. The main properties of these games and strategies are analyzed and several examples are provided. We relate the concept of ESS with previous literature and provide a proof of finiteness of ESS in the context of symmetric games with [Formula: see text] players. We show that unlike the case of [Formula: see text], when there are more than two populations an ESS does not have a uniform invasion barrier, or equivalently, it is not equivalent to the strategy performing better against all strategies in a neighborhood. We also construct the extended replicator dynamics for these games and we study an application to a model of strategic planning of investment.

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