Since the seminal work of John Nash, convex combinations of actions are known to guarantee the existence of equilibria in strategic-form games. This paper introduces an alternative notion of randomisation among actions – possibilistic randomisation – and investigates the mathematical consequences of doing so. The framework of possibility theory gives rise to two distinct notions of equilibria both of which are characterised in our main results: a qualitative one based on the Sugeno integral and a quantitative one based on the Choquet integral. Then the two notions of equilibrium are compared against a coordination game with payoff-distinguishable equilibria known as the Weak-link game.

Possibilistic randomisation in strategic-form games / H. Hosni, E. Marchioni. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 114(2019 Nov), pp. 204-225. [10.1016/j.ijar.2019.08.008]

Possibilistic randomisation in strategic-form games

H. Hosni
Primo
;
2019

Abstract

Since the seminal work of John Nash, convex combinations of actions are known to guarantee the existence of equilibria in strategic-form games. This paper introduces an alternative notion of randomisation among actions – possibilistic randomisation – and investigates the mathematical consequences of doing so. The framework of possibility theory gives rise to two distinct notions of equilibria both of which are characterised in our main results: a qualitative one based on the Sugeno integral and a quantitative one based on the Choquet integral. Then the two notions of equilibrium are compared against a coordination game with payoff-distinguishable equilibria known as the Weak-link game.
Mixed strategies; Nash equilibria; Possibilistic expected utility; Possibilistic randomisation; Selection of multiple equilibria; Weak-link game
Settore M-FIL/02 - Logica e Filosofia della Scienza
Settore INF/01 - Informatica
Settore MAT/01 - Logica Matematica
   Dipartimenti di Eccellenza 2018-2022 - Dipartimento di FILOSOFIA
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
nov-2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/679710
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