Reputation : The New Palgrave Dictionary

We explain what reputation effects are, how they arise and the factors that limit or strenghten them. Signalling activity has an increased importance in a dynamic setting because signals sent will affect current and future behavior of other parties; this is called the reputation effect. The literature on reputation has two main themes. The first is that introducing a small amount of incomplete information in a dynamic game can dramatically change the set of equilibrium payoffs: introducing something to signal can have big implications in a dynamic model. These kind of results can also be interpreted as providing a robustness check. Dynamic and repeated games typically have many equilibria and reputation results allow us to determine which equilibria continue to be played when a game is " close " to complete information. The second theme of the literature on reputations is that introducing incomplete information in a dynamic game may introduce new and important signalling dynamics in the players' strategies. Thus reputation effects tells us something about behavior. This theme is particularly important in applications to macroeconomics and to industrial organization, for example. For either of these themes to be relevant it is necessary to have a dynamic game with incomplete information, so work on reputation has been influenced by, and influences, the larger literature on repeated and dynamic games of incomplete information. An excellent detailed treatment of reputation can be found in Mailath and Samuelson (2006). Most of the results below will be described in the context of a simple infinitely repeated trading game. The row player is a seller who can produce high or low quality. The column player is a buyer. Producing high quality is always expensive for the seller, so she would rather produce low quality, the buyer, however, only wants to buy a high quality product. The only non-standard element is that the buyer regrets not buying a high quality product. The trading game (Figure 1) has a unique equilibrium (L, N).