Incentive-based control of networked evolutionary coordination games under asynchronous best-response dynamics

Incentive-based control mechanisms in game-theoretic models aim to steer players toward socially desirable strategies through appropriately designed utility rewards or penalties. In this paper, we propose an algebraic framework for incentive-based control in networked evolutionary coordination games (NECGs) under asynchronous myopic best-response dynamics. We establish a fundamental connection between the reward policy and the attainability of a desired equilibrium, demonstrating that a fully cooperative equilibrium is implementable if and only if there exists a reward vector that makes it reachable from the initial fully non-cooperative strategies in the incentivized NECG. Moreover, leveraging the strategy profile reachability sets, we demonstrate that the incentive control problem reduces to verifying the reachability of the set associated with the desired equilibrium. We prove that the reachable set of the desired equilibrium in the original NECG is contained within that of its incentivized counterpart. This, to some extent, simplifies the verification for computing the reachable set of the desired equilibrium in the incentivized NECG. Finally, we show an example to illustrate the proposed result.