Title: Utilitarian and Rawlsian preferences in vector bimatrix games

Authors: Asunción Zapata; Luisa Monroy; Amparo M. Mármol

Addresses: Departamento de Economía Aplicada III, Facultad de Ciencias Económicas y Empresariales, Universidad de Sevilla, Avda. Ramón y Cajal, 1, 41018-Sevilla, Spain ' Departamento de Economía Aplicada III, Facultad de Ciencias Económicas y Empresariales, Universidad de Sevilla, Avda. Ramón y Cajal, 1, 41018-Sevilla, Spain ' Departamento de Economía Aplicada III, Facultad de Ciencias Económicas y Empresariales, Universidad de Sevilla, Avda. Ramón y Cajal, 1, 41018-Sevilla, Spain

Abstract: In this paper the equilibria of bimatrix games with multi-dimensional payoffs are analysed. In order to derive a description of the sets of equilibria for these games, two approaches are studied. The first one, the utilitarian approach, considers the preferences of the players represented by a weighted sum of the payoffs. The second one, the Rawlsian approach, relies on a maxmin representation of the preferences of the players. The whole sets of equilibria of these vector-valued bimatrix games are characterised in terms of the parameters involved in the representation of the preferences in both cases. We also show how the additional information on the preferences can be introduced in both models and analyse the effect that this information has in the equilibria for some interesting cases. The theoretical results are illustrated with an example of a two-criteria two-person game.

Keywords: vector bimatrix games; equilibria; best response; utilitarian preferences; Rawlsian preferences.

DOI: 10.1504/IJMCDM.2024.143248

International Journal of Multicriteria Decision Making, 2024 Vol.10 No.1, pp.23 - 46

Received: 14 Sep 2022
Accepted: 21 Dec 2023
Published online: 11 Dec 2024 *

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