<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system’s states. We suggest a methodology that uses Tikhonov’s regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game’s mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.</p>
</abstract>

The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system’s states. We suggest a methodology that uses Tikhonov’s regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game’s mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.

Computing a Mechanism for a Bayesian and Partially Observable Markov Approach

Department of Automatic Control, Center for Research and Advanced Studies

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Computing a Mechanism for a Bayesian and Partially Observable Markov Approach"}

The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework....

Computing a Mechanism for a Bayesian and Partially Observable Markov Approach

Published Online: Sep 21, 2023

Page range: 463 - 478

Received: Jul 11, 2022

Accepted: Feb 27, 2023

DOI: https://doi.org/10.34768/amcs-2023-0034

Keywords
dynamic mechanism design, partially observable Markov chains, games with private information, Bayesian equilibrium, regularization

© 2023 Julio B. Clempner et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Computing a Mechanism for a Bayesian and Partially Observable Markov Approach

Published Online: Sep 21, 2023

Page range: 463 - 478

Received: Jul 11, 2022

Accepted: Feb 27, 2023

DOI: https://doi.org/10.34768/amcs-2023-0034

Keywordsdynamic mechanism design, partially observable Markov chains, games with private information, Bayesian equilibrium, regularization

© 2023 Julio B. Clempner et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
dynamic mechanism design, partially observable Markov chains, games with private information, Bayesian equilibrium, regularization