Essays on cooperation, coordination, and conformity

by Xue, Jun.

This thesis consists of three essays, discussing three related aspects of human behavior, namely, cooperation, coordination, and conformity. The …rst essay studies the repeated Prisoner’s Dilemma in a local interaction setup. We construct a sequential equilibrium in pure strategies that sustains cooperation for su¢ ciently patient players. The notion of sequential equilibrium is extended to extensive form games with in…nite time horizon and additive payo¤s across time. The strategy is embedded in an explicitly de…ned expectation system, which is a more compact way to describe strategies than machines in the local interaction setup, although essentially the expectation system can also be viewed as a …nite state automaton. The belief system is derived by perturbing the strategy appropriately and following the principle that parsimonious explanations receive all the weight. The equilibrium has the property that after any global history, full cooperation will be restored after a …nite number of periods. Therefore, the explicitly de…ned expectation system serves as a social norm. What matters is not a common observation of a physical outcome, what matters is a common understanding of the social norm, the understanding that everybody knows the norm and is willing to follow it after any history. The second essay deals with coordination games. By adding a small amount of noise to the information structure, the theory of global games is able to select a unique equilibrium in coordination games with a …nite number of players and two actions, a safe action and a risky action. As the noise vanishes, however, it is often the case that positive amount of ine¢ ciency remains in the selected equilibrium. This essay argues that this is partly due to the simultaneity of the moves. If the game is played sequentially with the order of moves determined endogenously, and if the risky action is irreversible and the safe action is reversible, then e¢ ciency will be asymptotically restored as the noise vanishes. However, if the safe action is irreversible, then dynamics will not make much di¤erence to the possible ine¢ ciency of equilibria. Thus two coordination games may look very similar if they are treated as simultaneous move games, yet they can be very di¤erent if they are treated as sequential move games. For example, there has been much recent interest in the phenomenon of currency attacks and its similarity to the well-known model of bank runs. However, we show that these games are quite di¤erent in the dynamic setting and endogenous timing might help to resolve ine¢ ciencies in the …rst but not the second. In the third essay we propose to use Polya urn processes to model the emergence of order in an environment where people interact with each other sequentially and indirectly, through a common physical facility. Examples include rewinding video tapes, erasing blackboards, and ‡ushing toilets, etc. We …nd that a minimum amount of imitation is able to generate a maximum level of conformity. iii