On the Evolution of Preferences: Multi-population and Multi-mutation Scenarios

• Main Authors: Yu-Sung Tu, 凃又菘
• Other Authors: 莊委桐
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/73836075175176633778

博士 === 國立臺灣大學 === 經濟學研究所 === 104 === We use the indirect evolutionary approach to study the evolution of preferences. Each player has subjective preferences concerning outcomes, and chooses a best response based on his own preferences and the information about the opponents. However, the players'' actual fitness for each strategy profile is assigned by a material payoff function. In Chapter 2, we study the features of stable outcomes in a multi-population setting under various observability. Players may observe their opponents'' preferences with some fixed probability p. We examine necessary and sufficient conditions for evolutionary stability for p = 1 and p = 0. We also check the robustness of these results against a small perturbation in p for the case of pure-strategy outcomes. In Chapter 3, we study the evolution of preferences under complete information with multiple mutations in multi- and single-population settings, respectively. Multiple mutations would be introduced to refine the evolutionarily stable outcomes. In the two population settings, respectively, we examine necessary and sufficient conditions for stability against multiple mutations; we characterize the relations between the order of stability and the level of efficiency. In Chapter 4, the range of a payoff function in a game is investigated, especially the noncooperative payoff region. A novel tool, the notion of extreme points of non-convex sets, is introduced to analyze noncooperative payoff regions; we try to characterize the noncooperative payoff region in terms of its extreme points and supporting hyperplanes. The main theorem says that all extreme points of a payoff region can be generated by pure-strategy profiles, and it helps us to achieve meaningful results.