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A utility-based analysis of equilibria in multi-objective normal-form games

Published online by Cambridge University Press:  30 June 2020

Roxana Rădulescu
Artificial Intelligence Lab, Vrije Universiteit Brussel, Pleinlaan 2, Brussels1050, Belgium, e-mails:,
Patrick Mannion
School of Computer Science, National University of Ireland Galway, GalwayH91 TK33, Ireland, e-mail:
Yijie Zhang
Universiteit van Amsterdam, Amsterdam, The Netherlands, e-mail:
Diederik M. Roijers
Artificial Intelligence Lab, Vrije Universiteit Brussel, Pleinlaan 2, Brussels1050, Belgium, e-mails:, Microsystems Technology, HU University of Applied Sciences Utrecht, Heidelberglaan 15, 3584CSUtrecht, The Netherlands, e-mail:
Ann Nowé
Artificial Intelligence Lab, Vrije Universiteit Brussel, Pleinlaan 2, Brussels1050, Belgium, e-mails:,


In multi-objective multi-agent systems (MOMASs), agents explicitly consider the possible trade-offs between conflicting objective functions. We argue that compromises between competing objectives in MOMAS should be analyzed on the basis of the utility that these compromises have for the users of a system, where an agent’s utility function maps their payoff vectors to scalar utility values. This utility-based approach naturally leads to two different optimization criteria for agents in a MOMAS: expected scalarized returns (ESRs) and scalarized expected returns (SERs). In this article, we explore the differences between these two criteria using the framework of multi-objective normal-form games (MONFGs). We demonstrate that the choice of optimization criterion (ESR or SER) can radically alter the set of equilibria in a MONFG when nonlinear utility functions are used.

Adaptive and Learning Agents
© The Author(s), 2020. Published by Cambridge University Press

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This article extends an earlier unpublished paper (Rădulescu et al., 2019) that was originally presented at the Adaptive and Learning Agents Workshop 2019.


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