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. / Thesis / Doctor of Philosophy (PhD)

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Indirect reciprocity describes a class of reputation-based mechanisms which may explain the prevalence of cooperation in groups where partners meet only once. The first model for which this has analytically been shown was the binary image scoring mechanism, where one's reputation is only based on one's last action. But this mechanism is known to fail if errors in implementation occur. It has thus been claimed that for indirect reciprocity to stabilize cooperation, reputation assessments must be of higher order, i.e. contingent not only on past actions, but also on the reputations of the targets of these actions. We show here that this need not be the case. A simple image scoring mechanism where more than just one past action is observed provides ample possibilities for stable cooperation to emerge even under substantial rates of implementation errors. (authors' abstract) / Series: Department of Economics Working Paper Series

Indirect reciprocity describes a class of reputation-based mechanisms which may explain the prevalence of cooperation in large groups where partners meet only once. The first model for which this has been demonstrated was the image scoring mechanism. But analytical work on the simplest possible case, the binary scoring model, has shown that even small errors in implementation destabilize any cooperative regime. It has thus been claimed that for indirect reciprocity to stabilize cooperation, assessments of reputation must be based on higher-order information. Is indirect reciprocity relying on frst-order information doomed to fail? We use a simple analytical model of image scoring to show that this need not be the case. Indeed, in the general image scoring model the introduction of implementation errors has just the opposite effect as in the binary scoring model: it may stabilize instead of destabilize cooperation.

This thesis contains four essays that analyze the behaviors that evolve when populations of boundedly rational individuals interact strategically for a long period of time. Individuals are boundedly rational in the sense that their strategy choices are determined by simple rules of adaptation -- learning rules. Convergence results for general finite games are first obtained in a homogenous setting, where all populations consist either of stochastic imitators, who almost always imitate the most successful strategy in a sample from their own population's past strategy choices, or stochastic better repliers, who almost always play a strategy that gives at least as high expected payoff as a sample distribution of all populations' past play. Similar results are then obtained in a heterogeneous setting, where both of these learning rules are represented in each population. It is found that only strategies in certain sets are played in the limit, as time goes to infinity and the mutation rate tends to zero. Sufficient conditions for the selection of a Pareto efficient such set are also provided. Finally, the analysis is extended to natural selection among learning rules. The question is whether there exists a learning rule that is evolutionarily stable, in the sense that a population employing this learning rule cannot be invaded by individuals using a different rule. Monte Carlo simulations for a large class of learning rules and four different games indicate that only a learning rule that takes full account of hypothetical payoffs to strategies that are not played is evolutionarily stable in almost all cases. / Diss. Stockholm : Handelshögsk., 2001