Dynamic Models of Search and Learning

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SBR-9422988 Lones Smith In most markets buyers and sellers do not meet at some central site, but must constantly seek each other out. Economists usually ignore the search process when analyzing market outcomes and simply assume that in equilibrium the market-clearing price is common knowledge. The process by which equilibrium is attained and the equilibrium price becomes common knowledge is treated as a "black box." The first part of this research project opens up this black box to more careful scrutiny. The P.I. investigates the whole class of employment matching models and provides a coherent theory underlying the efficient and equilibrium outcomes when individuals are inherently different. Thirty years ago, Professor George Stigler suggested that oligopolies were unstable and proposed a process of "secret" price cuts that would seem to cause any oligopoly agreement to unravel toward the competitive outcome. Yet despite many efforts the implicit game remains unsolved and so Stigler's conjectured equilibrium remains a conjecture. All the recent progress in this area has been on the quantity-setting version of Stigler's game in which prices were observable and output unobservable. Such games have a recursive structure to which dynamic programming can be successfully applied. The second part of this research project is an attempt to solve the original much harder Stigler pricing game. This is done indirectly by examining an unsolved problem from the search literature known as the Rendezvous problem. This problem has much of the same formal structure as Stigler's oligopoly game, namely it is a repeated game with imperfect monitoring and privately observed signals, yet appears to be more tractable.