The good, the finite, and the infinite

Abstract

Many interesting behaviours in the animal and human world involve cooperation among individuals. Yet, cooperating individuals are often susceptible to exploitation by cheaters. Because cheaters do better than the cooperators they exploit, the evolution and persistence of cooperation has been a challenging topic of study in biology, sociology and economics. Studies often abstract from real cooperative interactions, and construct simple games in which players can choose either cooperation with other players, or defection, e.g., the well known prisoner’s dilemma and the snowdrift game. In these games and other social dilemmas, mutual cooperation yields greater payoffs than mutual defection, but individuals are still tempted to defect (because of the possibility that if they cooperate, the other player will defect). Similar dilemmas also arise in situations where multiple individuals may be affected by the actions of one (such as volunteering for community service or evading taxes), and the main theme of this thesis is cooperation in groups. In chapter 2, we analyze pre-emptive vaccination for an outbreak of smallpox (following a bioterrorist attack or accidental release), from the public health (i.e., group) and individual perspectives. Chapters 3 and 4 deal with an extension of the snowdrift game to n interacting players and continuous strategy sets (where individuals decide on their degree of cooperation): in chapter 3, we analyze global evolutionary stability of cooperative strategies in a large class of n-player snowdrift games in infinite populations; chapter 4 analyzes general continuous n-person snowdrift games in finite populations, and compares the evolutionary dynamics with their infinite population analogues. In chapter 5, we present a general framework to model selection processes in finite populations, necessary for the analysis in chapter 4.