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A Dynamic Mechanism Design for Controllable and Ergodic Markov Games

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  • Julio B. Clempner

    (Instituto Politécnico Nacional (National Polytechnic Institute))

Abstract

This paper suggests an analytical method for computing Bayesian incentive-compatible mechanisms where the private information is revealed following a class of controllable Markov games. We consider a dynamic environment where decision are taken after several finite periods. Our method incorporates a new variable that represents the product of the mechanism design, the strategies, and the distribution vector. We derive the relations to analytically compute the variables of interest. The introduction of this variable makes the problem computationally tractable. The method involves a Reinforcement Learning approach which computes the near-optimal mechanism in equilibrium with the resulting strategy of the game with high profit maximization. We use the standard notion of Bayesian–Nash equilibrium as the equilibrium concept for our game. An interesting challenge is that for the objective of profit maximization there is no single optimal mechanism because there are multiple equilibria. We use Tikhonov’s method to provide a regularization parameter to solve this problem. We demonstrate the game’s equilibrium and convergence to a single incentive-compatible mechanism. This generates novel and considerably better findings for many game theory problem areas, as well as incentive-compatible mechanisms that match the game’s equilibrium. We present a numerical example in the realm of a dynamic public finance model with partial information to demonstrate the suggested technique.

Suggested Citation

  • Julio B. Clempner, 2023. "A Dynamic Mechanism Design for Controllable and Ergodic Markov Games," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1151-1171, March.
    • Handle: RePEc:kap:compec:v:61:y:2023:i:3:d:10.1007_s10614-022-10240-y
    DOI: 10.1007/s10614-022-10240-y
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    References listed on IDEAS

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    1. Dirk Bergemann & Juuso V‰lim‰ki, 2010. "The Dynamic Pivot Mechanism," Econometrica, Econometric Society, vol. 78(2), pages 771-789, March.
    2. Julio B. Clempner & Alexander S. Poznyak, 2021. "Analytical Method for Mechanism Design in Partially Observable Markov Games," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    3. Susan Athey & Ilya Segal, 2013. "An Efficient Dynamic Mechanism," Econometrica, Econometric Society, vol. 81(6), pages 2463-2485, November.
    4. Julio B. Clempner & Alexander S. Poznyak, 2020. "Finding the Strong Nash Equilibrium: Computation, Existence and Characterization for Markov Games," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 1029-1052, September.
    5. Alessandro Pavan & Ilya Segal & Juuso Toikka, 2014. "Dynamic Mechanism Design: A Myersonian Approach," Econometrica, Econometric Society, vol. 82(2), pages 601-653, March.
    6. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    7. Julio B. Clempner, 2021. "A Proximal/Gradient Approach for Computing the Nash Equilibrium in Controllable Markov Games," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 847-862, March.
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