Quitting games and linear complementarity problems

Eilon Solan; Omri N. Solan

doi:https://doi.org/10.1287/moor.2019.0996

Quitting games and linear complementarity problems

Eilon Solan, Omri N. Solan

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that every multiplayer quitting game admits a sunspot ε-equilibrium for every ε > 0, that is, an ε-equilibrium in an extended game in which the players observe a public signal at every stage. We also prove that, if a certain matrix that is derived from the payoffs in the game is not a Q-matrix in the sense of linear complementarity problems, then the game admits a uniform ε-equilibrium for every ε > 0.

Original language	English
Pages (from-to)	434-454
Number of pages	21
Journal	Mathematics of Operations Research
Volume	45
Issue number	2
DOIs	https://doi.org/10.1287/moor.2019.0996
State	Published - May 2020

Keywords

Linear complementarity problems
Q-matrices
Quitting games
Stochastic games
Stopping games
Sunspot equilibrium

All Science Journal Classification (ASJC) codes

Mathematics(all)
Computer Science Applications
Management Science and Operations Research

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https://doi.org/10.1287/moor.2019.0996

Cite this

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title = "Quitting games and linear complementarity problems",

abstract = "We prove that every multiplayer quitting game admits a sunspot ε-equilibrium for every ε > 0, that is, an ε-equilibrium in an extended game in which the players observe a public signal at every stage. We also prove that, if a certain matrix that is derived from the payoffs in the game is not a Q-matrix in the sense of linear complementarity problems, then the game admits a uniform ε-equilibrium for every ε > 0.",

keywords = "Linear complementarity problems, Q-matrices, Quitting games, Stochastic games, Stopping games, Sunspot equilibrium",

author = "Eilon Solan and Solan, {Omri N.}",

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doi = "https://doi.org/10.1287/moor.2019.0996",

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AU - Solan, Omri N.

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N2 - We prove that every multiplayer quitting game admits a sunspot ε-equilibrium for every ε > 0, that is, an ε-equilibrium in an extended game in which the players observe a public signal at every stage. We also prove that, if a certain matrix that is derived from the payoffs in the game is not a Q-matrix in the sense of linear complementarity problems, then the game admits a uniform ε-equilibrium for every ε > 0.

AB - We prove that every multiplayer quitting game admits a sunspot ε-equilibrium for every ε > 0, that is, an ε-equilibrium in an extended game in which the players observe a public signal at every stage. We also prove that, if a certain matrix that is derived from the payoffs in the game is not a Q-matrix in the sense of linear complementarity problems, then the game admits a uniform ε-equilibrium for every ε > 0.

KW - Linear complementarity problems

KW - Q-matrices

KW - Quitting games

KW - Stochastic games

KW - Stopping games

KW - Sunspot equilibrium

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M3 - مقالة

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SP - 434

EP - 454

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

IS - 2

ER -

Quitting games and linear complementarity problems

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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