Three essays on extensive-form games and strategic complements

Abstract

Games with strategic complements have the property that best response set of a player is increasing in the strategies of opponents in the standard lattice set order. Normal form games with strategic complements have been extensively studied in the literature. Such property in extensive form games are less well studied and turns out to be hard to analyze. This dissertation studies strategic complements in extensive form games. Echenique (2004) has a definition for extensive form game with strategic complements. We show in Chapter 2 that there are many cases of interest that are beyond his definition. Even simple two-stage $2\times 2$ game does not satisfy his definition. More generally, we characterize when two-stage $2\times 2$ game have strategic complements. This shows the aspects of strategic complements not captured by standard definition. Another way to analyze 2-stage games is to look at their reduced normal form (Mailath, Samuelson and Swinkels (1993)). In Chapter 3, we show that standard ordinal strategic complementarity conditions imposed on the reduced normal form are not sufficient to generate strategic complements in the extensive form. Semi no crossing conditions are added to make it sufficient. Moreover, I provide conditions on the reduced normal form to characterize strategic complements in the two-stage games. I also show how to recover the extensive form from the reduced normal form by applying the algorithm in (MSS (1994)). In Chapter 4, I study strategic complements in more general two-player multi-stage games. I show that in response to different classes of opponent's strategies, the corresponding best response sets must include strategies that can generate certain paths of play once the conditions are met. I then characterize the structure of best response sets necessary to exhibit strategic complements.