Approximate nash equilibria of imitation games: Algorithms and complexity

Aniket Murhekar, Ruta Mehta

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A two-player finite game is represented by two payoff matrices (A, B), one for each player. Imitation games are a subclass of two-player games in which B is the identity matrix, implying that the second player gets a positive payoff only if she “imitates" the first. Given that the problem of computing a Nash equilibrium (NE) is known to be provably hard, even to approximate, we ask if it is any easier for imitation games. We show that much like the general case, for any c > 0, computing a n1c -approximate NE of imitation games remains PPAD-hard, where n is the number of moves available to the players. On the other hand, we design a polynomial-time algorithm to find ε-approximate NE for any given constant ε > 0 (PTAS). The former result also rules out the smooth complexity being in P, unless PPAD ⊂ RP.

Original languageEnglish (US)
Title of host publicationProceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2020
EditorsBo An, Amal El Fallah Seghrouchni, Gita Sukthankar
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages887-894
Number of pages8
ISBN (Electronic)9781450375184
StatePublished - 2020
Event19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2020 - Virtual, Auckland, New Zealand
Duration: May 19 2020 → …

Publication series

NameProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume2020-May
ISSN (Print)1548-8403
ISSN (Electronic)1558-2914

Conference

Conference19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2020
CountryNew Zealand
CityVirtual, Auckland
Period5/19/20 → …

Keywords

  • Imitation games
  • Nash equilibrium
  • PPAD-hardness
  • PTAS
  • Two-player games

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering

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