Three applications of game theory

The methods of game theory are used to discuss three features pertinent to numerous economic interactions. Explicitly recognizing these features offers new insights into many issues previously studied in economics. In Chapter 1, I study the behavior of agents confronted with a variety of different games, but who cannot fully analyze each of these games individually. This requires first defining similarity of games. Because of the fundamental relationship between similarity and decision making, the only acceptable way to do this is to use definitions generated endogenously, much in the way beliefs are held and updated by decision makers. I show that taking explicit account of similarity in this way and imposing a mild bounded rationality constraint on agents rules out certain equilibria which a repeated game framework admits. In Chapter 2, it is established that interaction requires coordination on certain behavioral standards. Typically, this coordination comes at a cost. This cost is incurred by both the individual attempting to achieve coordination and other members of society. A random matching model in which agents exchange endowments is used. Agents choose a standard of behavior, knowing that the gains from trade are higher if two trading agents have chosen the same standard. Agents preferring a particular standard are considered to be a community. It is shown that in some cases, total welfare of a minority community decreases when a trade barrier is lifted between it and the majority community. An example is also offered of a case in which, where no dominant culture exists, members of both communities may be worse off when trade barriers are lifted. In Chapter 3, I study the problem of modeling collective negotiations as two-player bargaining games, when the players in the negotiating groups have differing preferences over the outcome of the negotiation. I show that it is generally necessary to represent the group by a player with preferences significantly more extreme than those of a player with median preferences, even if the group makes decisions using majority rule voting. How much more extreme this representative should be depends upon the parameters of the game