Inducing Desired Equilibria in Constrained Noncooperative Games via Nudging

Abstract

This paper explores nudge schemes for a central regulator aimed at incentivizing players in constrained noncooperative games to reach desired equilibria. Unlike traditional intervention mechanisms where players update their actions by blindly following signals from the regulator, the nudge mechanism comprehensively integrates players’ rational judgment by incorporating trust variables into players’ models. This implies that players update their actions by evaluating the signals from the regulator and their own expectations to the incentive mechanisms. If the regulator’s signals significantly deviate from the players’ expectations, players decrease trust in the regulator and rely more on the their expectations when updating their actions. Conversely, if the signals align closely with their expectations, players tend to increase trust in the regulator and place greater emphasis on the regulator’s signals. It should be noted that each player does not have access to other players’ actions, which means that it updates its action in a distributed manner by only observing the actions of its neighbors through a directed balanced graph. Furthermore, static and dynamic nudges are designed based on different information available to the regulator, which are also extended to an online case with the desired equilibrum being time-varying. Finally, an application to the robot formation control is shown to validate the obtained results.