In this thesis we investigate formal economic models of repeated interactions where some players might be able to establish and/or maintain a reputation for choosing certain actions. In Chapter 1 of the thesis we review the literature on reputation models;In Chapter 2 we extend the basic chain-store game to the two-incumbent case. We consider a highly stylized model where two incumbents populate a finite number of markets. In each of these markets there is a threat of potential entry by a different competitor. In case of entry, each of the two incumbents simultaneously and independently decides whether to meet entry by aggressive (costly in the short-run) or a peaceful response. We investigate a model where each of the incumbents may have an initial reputation for being a "tough" type that enjoys fighting. We show that over some range of initial reputations a weak incumbent's pay off is a decreasing function of its reputation. This interesting result stands in sharp contrast to the predictions of the existing literature on reputation effects;In Chapter 3 we analyze issues of time consistency associated with strategic trade. From the results on time consistency, we know that ability to revise announcements can lead to suboptimal outcomes. Mechanisms are then explored that impose a "cost" for the failure to honor the initial commitment. Both trading parties gain, if these mechanisms are perfectly enforceable. We also examine a model in which the commitment mechanism is present, but imperfectly enforceable. We show that if the parties trade for sufficiently many periods and/or the initial reputation for being a commitment type is sufficiently high, then reputation effects dominate the play of the game. Both players gain compared to the case in which the commitment mechanisms are absent. Finally, we observe that the model of strategic trade has required innovations in the game theoretic formulation. The most important of these follow from the "personality" of the "commitment" type.