Multiple Oracle Algorithm to Solve Continuous Games

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00364558" target="_blank" >RIV/68407700:21230/23:00364558 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-26369-9_8" target="_blank" >https://doi.org/10.1007/978-3-031-26369-9_8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-26369-9_8" target="_blank" >10.1007/978-3-031-26369-9_8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multiple Oracle Algorithm to Solve Continuous Games

Popis výsledku v původním jazyce

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium computation are known only for particular classes of continuous games, such as two-player polynomial games or games in which pure equilibria are guaranteed to exist. This contribution focuses on the computation and approximation of a mixed strategy equilibrium for the whole class of multiplayer general-sum continuous games. We vastly extend the scope of applicability of the double oracle algorithm, initially designed and proved to converge only for two-player zero-sum games. Specifically, we propose an iterative strategy generation technique, which splits the original problem into the master problem with only a finite subset of strategies being considered, and the subproblem in which an oracle finds the best response of each player. This simple method is guaranteed to recover an approximate equilibrium in finitely many iterations. Further, we argue that the Wasserstein distance (the earth mover’s distance) is the right metric for the space of mixed strategies for our purposes. Our main result is the convergence of this algorithm in the Wasserstein distance to an equilibrium of the original continuous game. The numerical experiments show the performance of our method on several classes of games including randomly generated examples.

Název v anglickém jazyce

Multiple Oracle Algorithm to Solve Continuous Games

Popis výsledku anglicky

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium computation are known only for particular classes of continuous games, such as two-player polynomial games or games in which pure equilibria are guaranteed to exist. This contribution focuses on the computation and approximation of a mixed strategy equilibrium for the whole class of multiplayer general-sum continuous games. We vastly extend the scope of applicability of the double oracle algorithm, initially designed and proved to converge only for two-player zero-sum games. Specifically, we propose an iterative strategy generation technique, which splits the original problem into the master problem with only a finite subset of strategies being considered, and the subproblem in which an oracle finds the best response of each player. This simple method is guaranteed to recover an approximate equilibrium in finitely many iterations. Further, we argue that the Wasserstein distance (the earth mover’s distance) is the right metric for the space of mixed strategies for our purposes. Our main result is the convergence of this algorithm in the Wasserstein distance to an equilibrium of the original continuous game. The numerical experiments show the performance of our method on several classes of games including randomly generated examples.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Výzkumné centrum informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Decision and Game Theory for Security

ISBN

978-3-031-26369-9

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

19

Strana od-do

149-167

Název nakladatele

Springer International Publishing

Místo vydání

Cham

Místo konání akce

Pittsburgh

Datum konání akce

26. 10. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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