Essays on Evolutionary Game Theory and Its Applications

Book excerpt: This dissertation consists of three essays on evolutionary game theory and its applications. The first essay considers mechanism design in the evolutionary game-theoretic framework. The second essay studies equilibrium selection of coordination games by using an evolutionary game-theoretic concept. The third essay formulates a multi-regional economic growth model as an evolutionary game and characterizes the stability of its equilibria under an evolutionary dynamic. The summaries of each essay are provided below. In the first essay, I consider an implementation problem in a class of congestion games with players that have heterogeneous costs of taking actions. One application is to traffic congestion with drivers having heterogeneous time costs. The planner would like to design a price scheme under which the economy converges to an epsilon-optimum from any initial state when he does not have full knowledge of the cost functions, and he can observe only the aggregate strategy distribution. Although the planner would like to internalize the externalities, the informational constraints compel him to estimate their values. Using the optimality and equilibrium conditions, I construct a practical estimation procedure that yields the true values of externalities in the long-run. Moreover, I show that our scheme makes the epsilon-optimum globally stable under the best response dynamic if the externalities among players taking the same action are sufficiently large relative to those among players taking different actions. In the second essay, I study the long-run outcomes of noisy asynchronous repeated games with players that are heterogeneous in in terms of their patience. The players repeatedly play a 2-by-2 coordination game with random pair-wise matching. The games are noisy because the players may make mistakes when choosing their actions and are asynchronous because only one player can move in each period. I characterize the long-run outcomes of Markov perfect equilibrium that are robust to the mistakes and show that if there is a sufficiently patient player, the efficient state can be the unique robust outcome even if it is risk-dominated. Because I need heterogeneity for the result, I argue that it enables the most patient player in effect to be the leader. In the third essay, I consider a microfounded urban growth model with two regions and a mass of mobile workers to study interactions among growth, agglomeration, and urban congestion. Unlike previous research in the urban growth literature, I formulate the model as a one-shot game and take an evolutionary game-theoretic approach for stability analysis. My approach enables us to analyze the stability of nonstationary equilibria in which populations of each region are not constant over time. I show that if both the expenditure share for housing and inter-regional transport cost are small, a stable stationary equilibrium does not exist. Moreover, in such a case, I show that there can exist a stable nonstationary equilibrium in which mobile workers agglomerate in one region at first but some of them migrate to the other region later. I argue that such a nonstationary location pattern is related to return migration.