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Multiple Oracle Algorithm to Solve Continuous Games

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Multiple Oracle Algorithm to Solve Continuous Games

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

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

Result continuities

  • Project

    <a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>

  • Continuities

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

Others

  • Publication year

    2023

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

    Decision and Game Theory for Security

  • ISBN

    978-3-031-26369-9

  • ISSN

    0302-9743

  • e-ISSN

    1611-3349

  • Number of pages

    19

  • Pages from-to

    149-167

  • Publisher name

    Springer International Publishing

  • Place of publication

    Cham

  • Event location

    Pittsburgh

  • Event date

    Oct 26, 2022

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article