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Unformatted text preview: Lecture XIV: Applications of Repeated Games Markus M. Mobius April 28, 2004 Gibbons, chapter 2.3.D,2.3.E Osborne, chapter 14 1 Introduction We have quite thoroughly discussed the theory of repeated games. In this lecture we discuss applications. The selection of problems is quite eclectic and include: collusion of firms efficiency wages monetary policy theory of gift giving For all these applications we analyze equilibria which are similar to the basic grim-trigger strategy equilibrium which we first studied in the repeated Prisoners Dilemma context. 2 Collusion of Firms 2.1 Some Notes on Industrial Organization Industrial organization is a subfield of economics which concerns itself with the study of particular industries. The standard setting is one where there 1 are many consumers but only a few firms (usually more than one). This environment is called an oligopoly (in contrast to a monopoly). Classical economics usually assumes perfect competition where there are many firms and consumers and all of them are price-takers. This simplifies analysis a lot because it gets rid of strategic interactions - a firm which is small relative to the market and hence has an infinitesimal impact on price does not have to worry about the reactions of other firms to its own actions. Oligopolies are more intriguing environments because strategic interac- tions do matter now. Therefore, game theory has been applied extremely successfully in IO during the past 30 years. 2.2 The Bertrand Paradox We have already discussed static Bertrand duopoly where firms set prices equal to marginal cost (as long as they have symmetric costs). Many economists think that this result is counterintuitive - if it would literally hold then firms would not be able to recoup any fixed costs (such as R&D, building a factory etc.) and would not develop products in the first place. One solution is to assume that firms engage instead in Cournot compe- tition. However, the assumption that firms set prices rather than quantities is appropriate for industries without significant capacity constraints (such as joghurts versus airplanes). Repeated games provide an alternative resolution of the Bertrand para- dox: firms can cooperate and set prices above marginal cost in each period. If a firm defects they both revert to static Nash pricing at marginal cost. This equilibrium is an example of tacit collusion . 1 2.3 Static Bertrand Lets recall the static Bertrand game: Two firms have marginal cost of production c > 0. They face a downward sloping demand curve q = D ( p ). Firms can set any price p 0. The unique NE of the game is p 1 = p 2 = c . 1 Its called tacit collusion because it is a Nash equilibrium and self-enforcing....
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This note was uploaded on 05/19/2010 for the course DFDAS 220 taught by Professor Ding during the Fall '10 term at Academy of Art University.
- Fall '10