A Study of Nash Equilibria in Multi-Objective Normal-Form Games: JAAMAS Track

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Abstract

We present a detailed analysis of Nash equilibria in multi-objective normal-form games, which are normal-form games with vectorial payoffs. Our approach is based on modelling each player's utility using a utility function that maps a vector to a scalar utility. For mixed strategies, we can apply the utility function before calculating the expectation of the payoff vector as well as after, resulting in two distinct optimisation criteria. We show that when computing the utility from the expected payoff, a Nash equilibrium can be guaranteed when players have quasiconcave utility functions. In addition, we show that when players have quasiconvex utility functions, pure strategy Nash equilibria are equal under both optimisation criteria. We extend this to settings where some players optimise for one criterion, while others optimise for the second. We combine these results and formulate an algorithm that computes all pure strategy Nash equilibria given quasiconvex utility functions.
Original languageEnglish
Title of host publicationThe 22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2023)
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages269-271
Number of pages3
ISBN (Electronic)978-1-4503-9432-1
Publication statusPublished - May 2023
EventThe 22nd International Conference on Autonomous Agents and Multiagent Systems - London, United Kingdom
Duration: 29 May 20232 Jun 2023
https://aamas2023.soton.ac.uk

Conference

ConferenceThe 22nd International Conference on Autonomous Agents and Multiagent Systems
Abbreviated titleAAMAS 2023
Country/TerritoryUnited Kingdom
CityLondon
Period29/05/232/06/23
Internet address

Keywords

  • Multi-objective
  • Game theory
  • Nash equilibrium

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