|Cooperation Prisoner's Dilemma evolutionary game theory replicator dynamics experimental economics learning|
This thesis starts at the observation that cooperative behaviour is a robust phenomenon in economic experiments. Chapter 2 provides a closer look at experimental data which allows the identification of three distict behavioral types, namely a strictly non-cooperative type, a strictly cooperative type and a weak, or, conditional cooperative type. These three behavioral dispositions seem to co-exist in experimental populations in a stable manner. Of course the question arises of how to explain this stable symbiosis. Chapter 3 refers the standard theoretical results concerning this question. Robert Frank (1987) proposed a quasi-evolutionary model for explaining the co-existence of a cooperative and a non-cooperative type. His model employs signals about a player's underlying disposition on which cooperative types can condition their decision to cooperate or not. The Frank model has been criticized by Harrington (1988) since its results are based on an implicit and implausible assumption. Harrington has shown that the main results depend on the assumption of a range in the signal's support where the type of a player can be identified with certainty. Chapter 3 also provides evidence from economic and psychological experimnets that raises doubts whether signals empirically play an important role in identifying behavioral dispositions. Hence, the signalling approach is completely abandoned. In this thesis, an alternative approach for explaining the survival of cooperative behavior is provided. The main idea is that players may learn the types of other players during the course of action. Based on this information cooperative players may be able to identify defective players later in in time and may reject interaction with them. Chapter 4 develops a model for experience based learning which is applicable to random matching games. In Chapter 5, this model is introduced to an evolutionary Prisoner's Dilemma, where, additionally to the strictly cooperative and non-cooperative players, a knowledgeable cooperative type appears on the scene. This type is assumed to be able to learn other players' types and to be exploitation-averse, i.e. the knowledgeable type rejects interactions with known defectors. The dynamic analysis shows that there exists a fully mixed, interior equilibrium, i.e. a population state in which all three behavioral types co-exist. This interior solution is globally stable for appropriate parameter constellations. Particularly, the intelligible cooperative type must learn sufficiently succesful. For less favorable learning conditions a two-type population equilibrium state exists where intellgible cooperators and non-cooperative types co-exist. Chapter 6 shows that these results are essentially robust with respect to the introduction of a further mutant which is assumed to be knowledgeable, too, but to be a defector. Chapter 7 shows that the results are robust to a change of the modelling framework. It is shown that the switch from a completely deterministic dynamic to a stochastic framework cannot destroy the basic result of survival of cooperative behavior. Chapter 8 concludes.