Lipschitz Continuity and Approximate Equilibria

In this paper, we study games with continuous action spaces and non-linear payoff functions. Our key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in these games. We begin by studying Lipschitz games, which encompass, f...

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Vydáno v:Algorithmica Ročník 82; číslo 10; s. 2927 - 2954
Hlavní autoři: Deligkas, Argyrios, Fearnley, John, Spirakis, Paul
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.10.2020
Springer Nature B.V
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Continuity (mathematics)
Data Structures and Information Theory
Game theory
Mathematics of Computing
Norms
Penalty function
Polynomials
Theory of Computation
Approximate equilibria
Lipschitz games
Penalty games
Biased games
ISSN:0178-4617, 1432-0541
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Shrnutí:In this paper, we study games with continuous action spaces and non-linear payoff functions. Our key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in these games. We begin by studying Lipschitz games, which encompass, for example, all concave games with Lipschitz continuous payoff functions. We provide an efficient algorithm for computing approximate equilibria in these games. Then we turn our attention to penalty games, which encompass biased games and games in which players take risk into account. Here we show that if the penalty function is Lipschitz continuous, then we can provide a quasi-polynomial time approximation scheme. Finally, we study distance biased games, where we present simple strongly polynomial time algorithms for finding best responses in L 1 and L 2 2 biased games, and then use these algorithms to provide strongly polynomial algorithms that find 2/3 and 5/7 approximate equilibria for these norms, respectively.
Bibliografie:ObjectType-Article-1
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00709-3