The first chapter presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how, for a population of myopic agents with homogeneous preferences, changes in the environment caused by current aggregate behavior may affect future payoffs and hence alter future behavior. The interaction between the agents is based on a symmetric two-strategy game with positive externalities and negative feedback from aggregate behavior to payoffs, so that at every point in time the population has an incentive to coordinate, whereas over time the more popular strategy becomes less appealing. Under the best response dynamics and the logit dynamics with small noise levels the joint trajectories of preferences and behavior converge to closed orbits around the unique steady state, whereas for large noise levels the steady state of the logit dynamics becomes a sink. Under the replicator dynamics the unique steady state of the system is repelling and the trajectories are unbounded unstable spirals.

The second chapter generalizes the model of Kranton (1996), who demonstrated that in optimal monomorphic equilibria i) cooperative behavior can be supported by strategies involving no more than two levels of cooperation, with the lower level employed at most once in the interaction; ii) there is no value in delaying cooperation in the hopes of cooperating at higher levels. Our interest in these results is motivated by the fact that the set of possible cooperation levels in Kranton's model is bounded, and the highest level of cooperation is feasible after just one period of interaction even for impatient agents. By allowing for an unbounded action set we investigate whether these results rely on the choice of upper bound. We confirm both findings, but demonstrate that the bounded action set is inadequate for the second result, and that in general the highest feasible level of cooperation is never optimal.

The third chapter introduces an imitative evolutionary dynamic with minimal information requirements. Agents in a large population are matched to play a symmetric game. An agent who receives a revision opportunity observes one opponent from the population at random and switches to that opponent's strategy whenever the opponent's realized payoff is higher than his own. This behavioral rule imitate the better realization (IBR) generates an ordinal mean dynamics which is polynomial in strategy utilization frequencies and does not possess any of the standard cardinal properties such as Nash stationarity or payoff monotonicity. Under the IBR dynamics pure strategies iteratively strictly dominated by pure strategies are eliminated, and strict equilbria are locally stable. In two-strategy games and in games with only two distinct payoffs the IBR dynamics is equivalent to the replicator dynamics. In Rock-Paper- Scissors games we conjecture that both dynamics exhibit one of the three possible types of behavior: global convergence to the rest point, global convergence to the boundary, or closed orbits around the rest point, but the partitions into these convergence classes are based on different criteria. Thus, the behavior of the replicator dynamics in a game need not coincide with the behavior of the IBR dynamics in its ordinal counterpart. In other cases, for instance in Zeeman's game, the number of interior rest points the two dynamics possess is different.