Alternative Approaches to Analyzing Markets with Asymmetric Information: Reply

Shiro Yabushita's comment on "The Theory of Screening" (Stiglitz, 1975) raises some interesting questions which have arisen in a number of different contexts: How should one model markets with imperfect information? What are appropriate behavioral postulates and equilibrium concepts? To restructure the question in terms of game theoretic language: Who are the active players? What are their strategy spaces? Do the players move simultaneously, or does one move before the other? These questions do not have simple answers: different equilibrium notions are appropriate for different economic contexts. Yabushita's comment illustrates how one can obtain markedly different results using alternative assumptions. Although we believe that for the particular context examined in Stiglitz (1975), the equilibrium concept employed there is better than the alternative implicitly proposed by Yabushita, his formulation merits attention, and there are other contexts in which his would be the appropriate formulation. In order to illuminate how the Yabushita model differs from the Stiglitz model, it is useful to reformulate their analyses in game theoretic terms. The strategies of individuals entail decisions as to whether or not to screen themselves (go to school), while the strategies of firms are wage offers conditioned on whether or not the individual has screened himself, and the result of that screening. An individual goes to work for the firm which offers him the highest wage. Thus, the payoff to the firm is zero, if it doesn't obtain the worker, and the difference between the worker's productivity and his wage if it obtains the worker. The payoff to the individual is his maximum wage offer minus his screening costs. There are two alternative ways of viewing the difference between the Yabushita and Stiglitz formulations of the education market. One way is to view Yabushita and Stiglitz as differing in their assumptions about whether firms or individuals move first. The choice of a schooling program is typically made by individuals before a wage offer is received. The Stiglitz model attempts to capture this natural temporal sequence of decision making by formulating a two-period model; in the first period, individuals decide whether or not to screen themselves, while in the second, profit-maximizing firms offer wages to both screened and unscreened individuals (who, in turn, go to work for the firm offering them the highest wage). The wage offer of each firm is assumed to be the profit-maximizing response to the screening decision of workers, given the wage offers of other firms. Hence, if any high ability worker screens himself he will receive a wage equal to his expected productivity 9k. ' If no workers screen themselves, the unscreened workers receive a wage equal to their expected productivity of 0, and if the type 1 workers screen themselves, the unscreened workers receive a wage of 02, their expected productivity. In each case, higher wages would incur losses; and a lower wage could not be an equilibrium, since there would be an opportunity for some other firm to increase its profits by offering a higher wage.2