| dc.description.abstract | This dissertation consists of three individual chapters. The first chapter applies lattice theoretic techniques in order to establish fundamental properties of Bayesian games of strategic substitutes (GSS) when the underlying type space is ordered either in increasing or decreasing first-order stochastic dominance. Existence and uniqueness of equilibria is considered, as well as the question of when such equilibria can be guaranteed to be monotone in type, a property which is used to guarantee monotone comparative statics. The second chapter uses the techniques of the first and combines them with the existing results for strategic complements (GSC) in order to extend the literature on global games under both GSC and GSS. In particular, the model of Carlsson and Van Damme (1993) is extended from 22 games to GSS or GSC involving a finite amount of players, each having a finite action space. Furthermore, the possibility that groups of players receive the same signal is allowed for, a condition which is new to the literature. It is shown that under this condition, the power of the model to resolve the issue of multiplicity is unambiguously increased. The third chapter considers stability of mixed strategy Nash equilibria in GSS. Chapter 1 analyzes Bayesian games of strategic substitutes under general conditions. In particular, when beliefs are order either increasingly or decreasingly by first order stochastic dominance, the existence and uniqueness, monotonicity, and comparative statics in this broad class of games are addressed. Unlike their supermodular counterpart, where the effect of an increase in type augments the strategic effect between own strategy and opponent’s strategy, submodularity produces competing effects when considering optimal responses. Using adaptive dynamics, conditions are given under which such games can be guaranteed to exhibit Bayesian Nash equilibria, and it is shown that in many applications these equilibria will be a profile of monotone strategies. Comparative statics of parametrized games is also analyzed using results from submodular games which are extended to incorporate incomplete information. Several examples are provided. The framework of Chapter 1 is applied to global games in Chapter 2. Global games methods are aimed at resolving issues of multiplicity of equilibria and coordination failure that arise in game theoretic models by relaxing common knowledge assumptions about an underlying parameter. These methods have recently received a lot of attention when the underlying complete information game is a GSC. Little has been done in this direction concerning GSS, however. This chapter complements the existing literature in both cases by extending the global games method developed by Carlsson and Van Damme (1993) to multiple player, multiple action GSS and GSC, using a p-dominance condition as the selection criterion. This approach helps circumvent recent criticisms to global games by relaxing some possibly unnatural assumptions on payoffs and parameters necessary to conduct analysis under current methods. The second part of this chapter generalizes the model by allowing groups of players to receive homogenous signals, which, under certain conditions, strengthens the model’s power of predictability. Chapter 3 analyzes the learning and stability of mixed strategy Nash equilibria in GSS, complementing recent work done in the case of GSC. Mixed strategies in GSS are of particular interest because it is well known that such games need not exhibit pure strategy Nash equilibria. First, a bound on the strategy space which indicate where randomizing behavior may occur in equilibrium is established. Second, it is shows that mixed strategy Nash equilibria are generally unstable under a wide variety of learning rules. | |
