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On the Bertrand core and equilibrium of a market

  • Economics


Microsoft Word - EDP-1004 Economics Discussion Paper Series EDP-1017 On the Bertrand core and equilibrium of a market Robert Routledge August 2010 Economics School of Social Sciences The University of Manchester Manchester M13 9PL On the Bertrand core and equilibrium of a market Robert R. Routledge∗ University of Manchester August, 2010 Abstract A remarkable result in economic theory is that price competition between a small number of sellers producing a homogeneous good may result in the perfectly competi- tive market outcome. We return to the issue of what prices constitute a pure strategy Bertrand equilibrium when we admit the possibility of coalitional deviations from the market. We consider a market with a finite number of buyers and sellers and standard market primitives. In this context we introduce a new core notion which we term the Bertrand core. A trading price is said to be in the Bertrand core if all sellers quoting this price constitutes a pure strategy Bertrand equilibrium and no subset of traders, buyers and sellers, can leave the market and improve their outcomes by engaging in Bertrand price competition by themselves. Under standard assumptions we show that the Bertrand core is non-empty. Moreover, we are able to obtain a partial equilibrium analogue of the well-known Debreu-Scarf (1963) result by showing that as the set of market traders is replicated then any price other than the competitive equilibrium can be blocked by some subset of traders provided that the market is replicated sufficiently many times. Keywords: equilibrium existence, core convergence, price-taking behaviour. JEL Classification: D43, C72. ∗Email:[email protected] Tel:07506 187 938. 1 1 Introduction A central problem in economic theory is to establish under what market conditions we might expect economic outcomes to be close to the equilibrium when agents have no market power. The origin

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