Abstract:

This paper investigates evolutionary adaptation in a coordination game with strategic uncertainty. Coordination games with strategic uncertainty are usually analyzed in the context of a team-production model in which players make decisions about the level of effort they want to contribute towards production of a joint final good. When making their decisions, players do not have information on the actions taken by their fellow participants. The amount of final good produced is determined by the minimum amount of effort. Players obtain the highest payoff when each player contributes the maximum feasible amount of effort, but there is an element of strategic uncertainty since players are not sure about what the others will do. Thus, these games are characterized by multiplicity of equilibria that can be Pareto ranked. Criteria for choosing equilibrium strategies include payoff dominance and risk dominance.

Evidence from the experiments with human subjects suggests that neither the payoff dominance nor risk dominance equilibrium selection criteria can be used as an equilibrium selection device. The results of the experiments with human subjects in which the above described game was simulated are described in Van Huyck, Battalio, and Beil (1990). These results showed that the number of players was important determinant for equilibrium selection. The evidence from these experiments demonstrated that a small number of players (group size equal to 2) could coordinate on a payoff dominant equilibrium while a large number of players (group size equal to 14) coordinates on an equilibrium with the lowest payoff.

Following this experimental work, Berninghaus and Ehrhart (1998) showed that the number of repetitions of the game in the experiments with human subjects was another important determinant for equilibrium selection. Large number of repetitions of a period coordination game favor the payoff dominant equilibrium outcome even in games with `many' (group size equal to 6) players. By sufficiently reducing the number of repetitions, Berninghaus and Ehrhart were able to reproduce Van Huyck et al. experimental results for large groups.

This paper uses an evolutionary model to examine the issues related to the equilibrium selection, long-run behavior and the impact of different variables on the dynamics of adaptation in a coordination game with strategic uncertainty. The equilibria of the model are neutrally stable which implies that invading strategies will not necessarily be driven out of a population. Because these equilibria are neutrally stable, transition from one Nash equilibrium to the other is possible through the effects of mutation and genetic drift. To gain an understanding of the basic underlying evolutionary dynamics, I first analyze evolutionary stability of equilibria in case of monomorphic populations of strategies with infinite number of players and then their evolutionary stability in case of polymorphic populations with finite number of players. The results of this analysis show that there is a negative relationship between the group size and the amount of time spent in the high effort equilibria.

Finally, the evolutionary dynamics are examined in simulations in which players use the genetic algorithm to update their strategies. The results of simulations show that mutation and genetic drift take populations of strategies through different Nash equilibria regardless of the group size.

The results of simulations also show that populations with small and large group sizes spend fractions of time close to each of the Nash equilibria of the game. Small group sizes spend more time in high effort equilibria, while large group sizes spend more time in the low effort equilibria. This behavior is due to the effect of the genetic drift which takes the populations through different equilibria. The transition from the low effort to the high effort equilibrium is more likely for small groups than for large groups. Likewise, the transition from the high effort to the low effort equilibrium is less likely for small groups than for large groups.