Dynamic Mechanism Design for Repeated Markov Games with Hidden Actions: Computational Approach

Abstract

This paper introduces a dynamic mechanism design tailored for uncertain environments where incentive schemes are challenged by the inability to observe players’ actions, known as moral hazard. In these scenarios, the system operates as a Markov game where outcomes depend on both the state of payouts and players’ actions. Moral hazard and adverse selection further complicate decision-making. The proposed mechanism aims to incentivize players to truthfully reveal their states while maximizing their expected payoffs. This is achieved through players’ best-reply strategies, ensuring truthful state revelation despite moral hazard. The revelation principle, a core concept in mechanism design, is applied to models with both moral hazard and adverse selection, facilitating optimal reward structure identification. The research holds significant practical implications, addressing the challenge of designing reward structures for multiplayer Markov games with hidden actions. By utilizing dynamic mechanism design, researchers and practitioners can optimize incentive schemes in complex, uncertain environments affected by moral hazard. To demonstrate the approach, the paper includes a numerical example of solving an oligopoly problem. Oligopolies, with a few dominant market players, exhibit complex dynamics where individual actions impact market outcomes significantly. Using the dynamic mechanism design framework, the paper shows how to construct optimal reward structures that align players’ incentives with desirable market outcomes, mitigating moral hazard and adverse selection effects. This framework is crucial for optimizing incentive schemes in multiplayer Markov games, providing a robust approach to handling the intricacies of moral hazard and adverse selection. By leveraging this design, the research contributes to the literature by offering a method to construct effective reward structures even in complex and uncertain environments. The numerical example of oligopolies illustrates the practical application and effectiveness of this dynamic mechanism design.

Keywords

• optimal dynamic mechanism design
• hidden actions
• Markov games with private information
• Bayesian equilibrium
• regularization