Essays in Game Theory

This thesis explores interactions among agents whose rationality is bounded in distinct ways. It consists of three self-contained chapters/papers. Chapters 2 and 3 consider myopic and hard-wired strategy revisions based on evolutionary game dynamics, while Chapter 4 deals with rationally inattentive agents who acquire costly information in a flexible manner. The thesis, thus, spans two extremes of the range of models with boundedly rational agents. The first paper proposes a novel way to formalize matching mechanisms in evolutionary games. The proposed formalization nests group selection models such as the haystack (Maynard Smith, 1964) and trait-group models (Wilson, 1975). It is shown that evolutionary optima can be obtained as Nash equilibria under appropriately defined matching rules. In the second paper matching rules are endogenized and the co-evolution of cooperation and matching is studied in social dilemma situations. It turns out that only full-or-null assortativity levels are evolutionarily stable. The extent to which efficient outcomes are achieved by this endogenization process is evaluated, which crucially depends on the structure of the particular interaction considered. The third paper extends recent models of flexible information acquisition to an uncountable-action-space setting: a beauty contest coordination game. Necessary conditions for the existence of equilibria with well-behaved strategies are derived. It is established that affine equilibria exist only if the fundamental is normally distributed. A higher coordination motive, a more concentrated prior distribution of the fundamental and higher information costs lead to less attention being paid to the fundamental. Moreover, flexible information acquisition technology is shown to result in equilibrium multiplicity under certain parameter combinations.