EDP-0638 - Economics Discussion Paper EDP-0638 On a...

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Unformatted text preview: Economics Discussion Paper EDP-0638 On a foundation for Cournot equilibrium By Alex Dickson and Roger Hartley November 2006 Download paper from: http://www.socialsciences.manchester.ac.uk/economics/research/discuss.htm Economics School of Social Sciences The University of Manchester Oxford Road Manchester M13 9PL United Kingdom On a foundation for Cournot equilibrium A. Dickson * and R. Hartley Economics, School of Social Sciences University of Manchester Oxford Road Manchester, UK M13 9PL November 28, 2006 Abstract We show in the context of a bilateral oligopoly where all agents are al- lowed to behave strategically the unexpected result that when the number of buyers becomes large the outcomes in a strategic market game do not converge to those at the Cournot equilibrium. However, convergence to Cournot outcomes is restored if the game is sequential: sellers move simul- taneously as do buyers, but the former always move before the latter. This suggests that the ability to commit to supply decisions is an essential feature of Cournot equilibrium. Keywords : Cournot competition, strategic market game, strategic founda- tion. JEL codes : C72, D43, D51, L13. Corresponding author: e-mail alex.dickson@manchester.ac.uk, tel: +44 (0)161 275 4810. Supported by ESRC PhD studentship/postdoctoral fellowship. 1 1 Introduction Cournot competition has become a widely used model of imperfect competition in modern economic theory. Its premise is that whilst firms behave strategically, buyers act as price takers. Just as in Walrasian models, this price-taking assump- tion requires a strategic foundation in order to be judged valid. A strategic market game with strategies as quantities is an appropriate framework within which to provide this foundation, in which we need to show that when the number of buyers increases outcomes in the market game tend to those at the Cournot equilibrium. When the sellers move at the same time as the buyers in the market game we show that this convergence does not generally occur. Conversely, in a sequential two-stage game in which sellers move simultaneously as do buyers, but the former move before the latter, convergence to Cournot outcomes is restored. This suggests that in order to provide the Cournot equilibrium concept with a strategic founda- tion, the sellers must have an opportunity to commit before the buyers make their choices, implying an essential feature of Cournot equilibrium is the ability of firms to commit to supply decisions. The framework we use is that of bilateral oligopoly in which there are two com- modities, the second thought of as money, and agents have a corner endowment. Those agents endowed with the first commodity are called sellers , whilst those en- dowed with the second commodity are called buyers . In a strategic market game signals are quantity-based: each agent decides on a proportion of her endowment to send to the market to be exchanged for the other commodity. For sellers we call this an offer...
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This note was uploaded on 10/21/2010 for the course ECON 1530 taught by Professor Ohly during the Spring '10 term at Dartmouth.

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EDP-0638 - Economics Discussion Paper EDP-0638 On a...

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