Evolutionary robustness of dominant strategy implementation

Evolutionary robustness of dominant strategy implementation

Sarvesh Bandhu, Ratul Lahkar

Journal: Economic Theory 

Abstract: Evolutionary game theory studies the behavior of large populations of agents who repeatedly engage in strategic interactions. Changes in behavior in these populations are driven either by natural selection or by the bounded rationality of decision rules by individual agents. Then, it studies how the social state changes as agents change their strategies over time. Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change. This is influenced by the frequency of the competing strategies in the population. 

In this paper, the researchers consider dominant strategy implementation in a large population aggregative game. The model has strategic complementarities which generates multiple Nash equilibria. Moreover, externalities are positive due to which, all equilibria are socially inefficient. The planner, therefore, constructs a direct mechanism and assigns efficient strategies and transfer levels to agents. Truthful revelation then becomes strictly dominant, which implements efficiency. In their new evolutionary approach to this mechanism, the reported type distribution evolves under dynamics satisfying monotone percentage growth. Such dynamics eliminate dominated strategies thereby ensuring convergence to truthful revelation by all agents. Dominant strategy implementation is, therefore, robust under such evolutionary dynamics. The evolutionary approach differs from existing models of evolutionary implementation based on potential games. That approach may fail to implement efficiency under strategic complementarities as a Pareto inferior Nash equilibrium can remain asymptotically stable under evolutionary dynamics. The researchers’ evolutionary approach is effective even under such strategic complementarities. 

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