Some notes on possibilistic randomisation with t-norm based joint distributions in strategic-form games
Some notes on possibilistic randomisation with t-norm based joint distributions in strategic-form games
This article continues the investigation started in [18] on the role of possibilistic mixed strategies in strategic-form games. In this earlier work we assumed, as standard in possibility theory, that joint possibility distributions were computed by combining possibilistic mixed strategies with the minimum t-norm. In this paper, we investigate the consequences of defining joint possibility distributions by using any continuous t-norm, with players' expected utilities based on the Choquet integral. We characterise under which conditions a pair of possibilistic mixed strategies is an equilibrium, generalising the results first presented in [18], and also show that the set of equilibria in possibilistic mixed strategies depends on the set of idempotent elements of a t-norm and not just on the chosen t-norm.
Mixed Strategies, Nash Equilibria, Possibilistic Expected Utility, Possibilistic Randomisation, Triangular Norms, Mixed strategies, Triangular norms, Nash equilibria, Possibilistic expected utility, Possibilistic randomisation
Corsi, Esther Anna
fc3bbea2-76be-41ee-8163-98aaf844ab33
Hosni, Hykel
5fea876f-a264-4ea6-8026-da7507f970c8
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
March 2024
Corsi, Esther Anna
fc3bbea2-76be-41ee-8163-98aaf844ab33
Hosni, Hykel
5fea876f-a264-4ea6-8026-da7507f970c8
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Corsi, Esther Anna, Hosni, Hykel and Marchioni, Enrico
(2024)
Some notes on possibilistic randomisation with t-norm based joint distributions in strategic-form games.
International Journal of Approximate Reasoning, 166, [109109].
(doi:10.1016/j.ijar.2023.109109).
Abstract
This article continues the investigation started in [18] on the role of possibilistic mixed strategies in strategic-form games. In this earlier work we assumed, as standard in possibility theory, that joint possibility distributions were computed by combining possibilistic mixed strategies with the minimum t-norm. In this paper, we investigate the consequences of defining joint possibility distributions by using any continuous t-norm, with players' expected utilities based on the Choquet integral. We characterise under which conditions a pair of possibilistic mixed strategies is an equilibrium, generalising the results first presented in [18], and also show that the set of equilibria in possibilistic mixed strategies depends on the set of idempotent elements of a t-norm and not just on the chosen t-norm.
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Accepted/In Press date: 19 December 2023
e-pub ahead of print date: 2 January 2024
Published date: March 2024
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© 2023 The Authors
Keywords:
Mixed Strategies, Nash Equilibria, Possibilistic Expected Utility, Possibilistic Randomisation, Triangular Norms, Mixed strategies, Triangular norms, Nash equilibria, Possibilistic expected utility, Possibilistic randomisation
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Local EPrints ID: 486337
URI: http://eprints.soton.ac.uk/id/eprint/486337
ISSN: 0888-613X
PURE UUID: df80ed34-40ff-418a-b7c7-94bd280ffaa8
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Date deposited: 18 Jan 2024 18:31
Last modified: 26 Mar 2024 17:46
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Author:
Esther Anna Corsi
Author:
Hykel Hosni
Author:
Enrico Marchioni
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