Asymmetric Information Acquisition Games

TL;DR

This paper models a complex stochastic game where agents with asymmetric, partial information optimize their search strategies for acquiring opportunities, using advanced control and decision process techniques to find equilibrium policies.

Contribution

It introduces a novel approach combining optimal control and MDP tools to solve asymmetric information acquisition games with infinite states and actions, providing closed-form equilibrium solutions.

Findings

Derived closed-form Nash Equilibria in special cases

Reduced infinite-dimensional game to finite state with 1D actions

Provided asymptotic expressions for equilibrium policies

Abstract

We consider a stochastic game with partial, asymmetric and non-classical information, where the agents are trying to acquire as many available opportunities/locks as possible. Agents have access only to local information, the information updates are asynchronous and our aim is to obtain relevant equilibrium policies. Our approach is to consider optimal open-loop control until the information update, which allows managing the belief updates in a structured manner. The agents continuously control the rates of their Poisson search clocks to acquire the locks, and they get rewards at every successful acquisition; an acquisition is successful if all the previous stages are successful and if the agent is the first one to complete. However, none of them have access to the acquisition status of the other agents, leading to an asymmetric information game. Using standard tools of optimal control theory and Markov decision process (MDP) we solved a bi-level control problem; every stage of the dynamic programming equation of the MDP is solved using optimal control tools. We finally reduced the game with an infinite number of states and infinite-dimensional actions to a finite state game with one-dimensional actions. We provided closed-form expressions for Nash Equilibrium in some special cases and derived asymptotic expressions for some more.