Tempered best response dynamics

We propose a new deterministic evolutionary dynamic—the tempered best response dynamic (tBRD)—to capture two features of economic decision making: optimization and continuous sensitivity to incentives. That is, in the tBRD, an agent is more likely to revise his action when his current payoff is further from the optimal payoff, and he always switches to an optimal action when revising. The tBRD is a payoff monotone selection like the replicator dynamic, which makes medium and long-run outcomes more consistent with predictions from equilibrium refinement than the BRD in some situations. The technical contribution of the tBRD is continuous sensitivity, which allows us to apply results of a system of piecewise differential equations in order to obtain conditions for uniqueness and stability of solutions.