Stochastic Control Approach to Reputation Games

Abstract

Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the information of the short-lived players is nested in that of the long-lived player. This nested information structure is obtained through an appropriate monitoring structure. Under this monitoring structure, we show that, given mild assumptions, the set of Perfect Bayesian Equilibrium payoffs coincide with Markov Perfect Equilibrium payoffs, and hence a dynamic programming formulation can be obtained for the computation of equilibrium strategies of the strategic long-lived player in the discounted setup. We also consider the undiscounted setup where we obtain an optimal equilibrium strategy of the strategic long-lived player. We then use this optimal strategy in the undiscounted setup as a tool to obtain an upper payoff bound for the arbitrarily patient long-lived player in the discounted setup. Finally, by using measure concentration techniques, we obtain a refined lower payoff bound on the value of reputation in the discounted setup. We also establish the continuity of equilibrium payoffs in the prior beliefs.

An improved ellipsoid optimization algorithm in subspace predictive control

“…In (Casini and Garulli, 2017), a new multivariable adaptive control scheme is designed for plants with an arbitrary relative degree, which does not require a stringent symmetry assumption related to the plat high-frequency gain matrix. An adaptive controller makes use of a closed-loop reference model as an observer (Dalkiran, 2020) and guarantees global stability or asymptotic output tracking. A reference model robust adaptive controller and a linear quadratic regulator are combined to obtain high performance and robust control system (Lan and Liu, 2020).…”

Controller design for the closed loop system with non-interaction condition

“…By comparing these two strategies, this direct data-driven method is worth studying deeply in future. But now as the first model-based design strategy is more applied widely, and then we need to do much research on closed loop system identification (Dalkiran, 2020). The performance of model-based control system is often limited.…”