Bayesian learning in fish wars: dynamic estimation of unknown states and private information

Jiangjing Zhou ; Ovanes Petrosian

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 2, pp. 92-112.

Résumé

This paper investigates a unique variant of the «fish war» game, where participants are required to estimate unknown environmental parameters and the private information of adversaries based on received signals. We develop a dynamic game model where the evolution of the fish population is influenced by an unknown parameter, $\epsilon$, and each player's payoff function incorporates their private information, $\delta$. Utilizing Bayesian learning methods, we demonstrate how participants can update their estimates of these unknown parameters over time. We prove that these estimates converge to true values as time progresses. The paper further presents a Nash Equilibrium with Bayesian learning, providing a solution to this specialized game. Numerical simulations are included to illustrate the convergence of beliefs among players and to compare their control strategies under various scenarios.

Détail

Keywords: dynamic Bayesian learning, «fish war» game, private information, unknown parameters.

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