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
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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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
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