In this paper , we investigate gains from strategy revisions in deterministic evolutionary dynamics. To clarify the gain from revision, we propose a framework to reconstruct an evolutionary dynamic from optimal decision with stochastic (possibly restricted) available action set and switching cost. Many major dynamics and interesting new dynamicscan be constructed in this framework. We formally define net gains from revisions and obtain several general properties of the gain function, which leads to Nash stability of contractive games---generalization of concave potential games---and local asymptotic stability of a regular evolutionary stable state. The unifying framework allows us to apply the Nash stability to mixture of heterogeneous populations, whether heterogeneity is in payoffs or in revision protocols. While the analysis here is confined to general strategic-form games , we finally discuss that the idea of reconstructing evolutionary dynamics from optimization with switching costs and focusing on net revision gains for stability is promising for further applications to more complex situations.
The goal of this paper is to present a universal and intuitive approach to link static stability with dynamic stability, i.e., asymptotic stability of equilibrium, through economic principles behind evolutionary dynamics. In economics, static stability is traditionally defined as a notion about how incentives respond to choices: for a population game, it means that, on average, the payoff of a strategy responds negatively to an increase in the share of the strategy. This is characterized by negative definiteness of the Hessian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS. We say an evolutionary dynamic is economically reasonable, if an agent's choice of a new strategy can be justified as an optimal choice possibly by introducing additional costs and constraints; for example, inertia can be justified by switching costs, and switches to suboptimal strategies can be by restriction to available strategies. This class of dynamics includes not only the best response dynamic, pairwise payoff comparison dynamics and excess payoff dynamics. The key in our proof is a net gain from revision of the strategy, i.e., the payoff improvement by the revision minus the switching cost. Static stability implies that the aggregate net gain monotonically decreases over time under an economic reasonable dynamic and thus can be used as a Lyapunov function. Our Lyapunov function allows us to extend the dynamic stability to mixture of heterogeneous populations, who may follow different dynamics or different payoff functions. While our analysis here is confined to normal form games for clear illustration of our approach, we argue that our approach is promising for further applications to more complex situations.
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In this paper , we investigate gains from strategy revisions in deterministic
The goal of this paper is to present a universal and intuitive approach to link static stability with dynamic stability, i.e., asymptotic stability of equilibrium, through economic principles behind
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To clarify the gain from revision, we propose a framework to reconstruct an evolutionary dynamic from optimal decision with stochastic (possibly restricted) available action set and switching cost. Many major dynamics and interesting new dynamicscan be constructed in this framework. We formally define net gains from revisions and obtain several general properties of the gain function, which leads to Nash stability of contractive games---generalization of concave potential games---and local asymptotic stability of a regular evolutionary stable state. The unifying framework
In economics, static stability is traditionally defined as a notion about how incentives respond to choices: for a population game, it means that, on average, the payoff of a strategy responds negatively to an increase in the share of the strategy. This is characterized by negative definiteness of the Hessian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS. We say an evolutionary dynamic is economically reasonable, if an agent's choice of a new strategy can be justified as an optimal choice possibly by introducing additional costs and constraints; for example, inertia can be justified by switching costs, and switches to suboptimal strategies can be by restriction to available strategies. This class of dynamics includes not only the best response dynamic, pairwise payoff comparison dynamics and excess payoff dynamics. The key in our proof is a net gain from revision of the strategy, i.e., the payoff improvement by the revision minus the switching cost. Static stability implies that the aggregate net gain monotonically decreases over time under an economic reasonable dynamic and thus can be used as a Lyapunov function. Our Lyapunov function
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apply the Nash
extend the dynamic
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whether heterogeneity is in payoffs or in revision protocols. While the
who may follow different dynamics or different payoff functions. While our
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general strategic-form games , we finally discuss that the idea of reconstructing evolutionary dynamics from optimization with switching costs and focusing on net revision gains for stability
normal form games for clear illustration of our approach, we argue that our approach