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Paper details
Number 3 - September 2023
Volume 33 - 2023
Computing a mechanism for a Bayesian and partially observable Markov approach
Julio B. Clempner, Alexander S. Poznyak
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.
Keywords
dynamic mechanism design, partially observable Markov chains, games with private information, Bayesian equilibrium, regularization