2×2 Zero-Sum Games with Commitments and Noisy Observations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2023

2×2 Zero-Sum Games with Commitments and Noisy Observations

Abstract

In this paper, 2 × 2 zero-sum games are studied under the following assumptions: (1) One of the players (the leader) commits to choose its actions by sampling a given probability measure (strategy); (2) The leader announces its action, which is observed by its opponent (the follower) through a binary channel; and (3) the follower chooses its strategy based on the knowledge of the leader's strategy and the noisy observation of the leader's action. Under these conditions, the equilibrium is shown to always exist. Interestingly, even subject to noise, observing the actions of the leader is shown to be either beneficial or immaterial for the follower. More specifically, the payoff at the equilibrium of this game is upper bounded by the payoff at the Stackelberg equilibrium (SE) in pure strategies; and lower bounded by the payoff at the Nash equilibrium, which is equivalent to the SE in mixed strategies. Finally, necessary and sufficient conditions for observing the payoff at equilibrium to be equal to its lower bound are presented. Sufficient conditions for the payoff at equilibrium to be equal to its upper bound are also presented.
Fichier principal
Vignette du fichier
Perlaza-VFinal-ISIT2023.pdf (384.96 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04091712 , version 1 (08-05-2023)
hal-04091712 , version 2 (11-05-2023)

Licence

Attribution

Identifiers

Cite

Ke Sun, Samir M. Perlaza, Alain Jean-Marie. 2×2 Zero-Sum Games with Commitments and Noisy Observations. ISIT 2023 - IEEE International Symposium on Information Theory, Jun 2023, Taipei, Taiwan. ⟨10.1109/ISIT54713.2023.10206806⟩. ⟨hal-04091712v2⟩
75 View
154 Download

Altmetric

Share

Gmail Facebook X LinkedIn More