Analytical Method for Mechanism Design in Partially Observable Markov Games

Abstract

A theme that become common knowledge of the literature is the difficulty of developing a mechanism that is compatible with individual incentives that simultaneously result in efficient decisions that maximize the total reward. In this paper, we suggest an analytical method for computing a mechanism design. This problem is explored in the context of a framework, in which the players follow an average utility in a non-cooperative Markov game with incomplete state information. All of the Nash equilibria are approximated in a sequential process. We describe a method for the derivative of the player’s equilibrium that instruments the design of the mechanism. In addition, it showed the convergence and rate of convergence of the proposed method. For computing the mechanism, we consider an extension of the Markov model for which it is introduced a new variable that represents the product of the mechanism design and the joint strategy. We derive formulas to recover the variables of interest: mechanisms, strategy, and distribution vector. The mechanism design and equilibrium strategies computation differ from those in previous literature. A numerical example presents the usefulness and effectiveness of the proposed method.

Keywords

• dynamic mechanism design
• incentive-compatible mechanisms
• Markov games with private information
• partially observable Markov chains
• incomplete state information