Essays on equilibrium selection

Abstract

The first two chapters of this thesis explore how coordination happens in simple games. The first chapter models the adaptive play of a 2 x 2 game by pairs of agents matched together from a large population. In contrast with the existing literature, I assume that agents have some control over who they are matched with - specifically, I give them the option to sometimes continue playing against the same opponent. This renewal option allows agents playing efficiently to isolate themselves from those who are not. Perhaps counterintuitively, efficient play may be less likely to survive in the long run when agents have this additional instrument, even in games with common interests. This is because isolation has two effects: it raises the returns to an efficient but fragile strategy, but it also "ghettoizes" agents playing inefficiently - they rarely learn about the efficient strategy and when they do learn about it, they rarely hear good news. I look at an extension in which agents have long memories about the performance of a strategy. With long memories, good news about an efficient strategy will be more likely to trickle down to ghettoized agents, mitigating the bias in learning. With this bias removed, long run survival of efficient play becomes more likely - even when it is not a static Nash equilibrium. Essentially, agents learn to use the renewal option to punish non-cooperators. However, the speed of learning may still be quite slow, so that ghettoization persists for a long time.

(cont.) The second chapter investigates the interaction of strategic uncertainty and timing in a coordination game. Carlsson and van Damme have shown that small departures from common knowledge of the game being played can dramatically alter the equilibrium set. In the game I look at, there are two equilibria, but only the risk dominant equilibrium survives such a perturbation. I augment this model by giving agents a costly option to delay choosing a strategy (thereby observing any actions that were taken without delay). Strategic uncertainty gives agents a reason to exercise this option (under complete information, it never would be). In turn, the fact that Agent B sometimes waits and chooses an action after observing Agent A's choice, mitigates the risk that A faces when taking an action that is efficient but sensitive to coordination. As a result, the efficient equilibrium is played more often; in fact, as the cost of delay vanishes, it is always played. In Chapter 3, I explore the interaction between imperfect consumer information and the endogenous level of product differentiation in a non-spatial model of monopolistic competition with horizontally differentiated products. A principle of extreme differentiation is derived: firms will always choose to differentiate either maximally or minimally. In equilibrium, differentiation is maximal when search costs are low and minimal when search costs are high, providing a new interpretation of Hotelling's classic result.