Mechanism Design

This chapter presents an analytical method for computing Bayesian incentive-compatible mechanisms where the private information is revealed following a class of controllable Markov games. We take into account a dynamic setting where decisions are made after a number of limited time periods. Our approach includes a new variable that denotes the outcome of the distribution vector, the strategies, and the mechanism design. We develop the relationships needed to calculate the relevant variables analytically. The issue becomes computationally tractable with the addition of this variable. The technique uses a Reinforcement Learning (RL) methodology to calculate a mechanism that is nearly optimum and in equilibrium with the game’s winning strategy. We employ the Bayesian-Nash equilibrium concept as the default equilibrium idea in the game. There are several equilibria, which presents an intriguing problem because there isn’t a single mechanism that is ideal for the goal of profit maximization. To address this issue, we apply Tikhonov’s approach and offer a regularization parameter. We show the game’s equilibrium and convergence to a single mechanism that is compatible with incentives. This results in numerous game theory issue areas having unique and significantly improved results, as well as incentive-compatible processes that are consistent with the equilibrium of the game. To illustrate the recommended method, we provide a numerical example in the context of a dynamic public finance model with incomplete knowledge.