Cournot-Walras equilibrium as a subgame perfect equilibrium
Busetto, Francesca, Codognato, Giulio and Ghosal, Sayantan (2008) Cournot-Walras equilibrium as a subgame perfect equilibrium. Working Paper. Coventry: University of Warwick Economics Department. (Warwick economic research papers).
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In this paper, we investigate the problem of the strategic foundation of the Cournot-Walras equilibrium approach. To this end, we respecify à la Cournot-Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed by Lloyd S. Shapley. We show, through an example, that the set of the Cournot- Walras equilibrium allocations of this respecifcation does not coincide with the set of the Cournot-Nash equilibrium allocations of the mixed version of the original Shapley's model. As the nonequivalence, in a one-stage setting, can be explained by the intrinsic two-stage nature of the Cournot-Walras equilibrium concept, we are led to consider a further reformulation of the Shapley's model as a two-stage game, where the atoms move in the first stage and the atomless sector moves in the second stage. Our main result shows that the set of the Cournot-Walras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this two-stage game, which we call the set of the Pseudo-Markov perfect equilibrium allocations.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HB Economic Theory|
|Divisions:||Faculty of Social Sciences > Economics|
|Library of Congress Subject Headings (LCSH):||Game theory, Noncooperative games (Mathematics), Equilibrium (Economics)|
|Series Name:||Warwick economic research papers|
|Publisher:||University of Warwick Economics Department|
|Place of Publication:||Coventry|
|Number of Pages:||23|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Version or Related Resource:||Busetto, F., Codognato, G. and Ghosal, S. (2008). Cournot-Walras equilibrium as a subgame perfect equilibrium. International Journal of Game Theory, 37(3), pp. 371-386. http://wrap.warwick.ac.uk/id/eprint/29123|
|References:|| Aliprantis C.D., Border K.C. (1999), Infinite dimensional analysis, Springer, New York.  Amir R., Sahi S., Shubik M., Yao S. (1990), "A strategic market game with complete markets," Journal of Economic Theory 51, 126-143.  Aumann R.J. (1965), "Integrals of set valued functions," Journal of Math- ematical Analysis and Applications 12, 1-12.  Aumann R.J. (1966), "Existence of competitive equilibria in markets with a continuum of traders," Econometrica 24.  Bonnisseau J-M., Florig M. (2003), "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory 22, 727-741.  Codognato G. (1995), \Cournot-Walras and Cournot equilibria in mixed markets: a comparison," Economic Theory 5, 361-370.  Codognato G., Gabszewicz J.J. (1991), \Equilibres de Cournot-Walras dans une economie d'echange," Revue Economique 42, 1013-1026. 1-17.  Codognato G., Gabszewicz J.J. (1993), \Cournot-Walras equilibria in markets with a continuum of traders," Economic Theory 3, 453-464.  Codognato G., Ghosal S. (2000a), \Cournot-Nash equilibria in limit ex- change economies with complete markets and consistent prices," Journal of Mathematical Economics 34, 39-53.  Codognato G., Ghosal S. (2000b), \Oligopoly µa la Cournot-Nash in mar- kets with a continuum of traders," Discussion Paper No 2000-5, CEPET (Central European Program in Economic Theory), Institute of Public Economics, Graz University.  d'Aspremont C., Dos Santos Ferreira R., Gerard-Varet L.-A. (1997), \General equilibrium concepts under imperfect competition: a Cournotian approach," Journal of Economic Theory 73, 199-230.  Dierker H., Grodal B. (1986), \Nonexistence of Cournot-Walras equi- librium in a general equilibrium model with two oligopolists," in Hilden- brand W., Mas-Colell A. (eds), Contributions to mathematical economics in honor of Gerard Debreu, North-Holland, Amsterdam.  Dubey P., Shapley L.S. (1994), \Noncooperative general exchange with a continuum of traders: two models, " Journal of Mathematical Economics 23, 253-293.  Dubey P., Shubik M. (1978), \The noncooperative equilibria of a closed trading economy with market supply and bidding strategies," Journal of Economic Theory 17, 1-20.  Fudenberg D., Tirole J. (1991), Game theory, MIT Press, Cambridge Mass..  Gabszewicz J.J., Michel P. (1997), \Oligopoly equilibrium in exchange economies," in Eaton B.C., Harris R. G. (eds), Trade, technology and economics. Essays in honour of Richard G. Lipsey, Edward Elgar, Chel- tenham.  Gabszewicz J.J., Vial J.-P. (1972), \Oligopoly `µa la Cournot-Walras' in a general equilibrium analysis," Journal of Economic Theory 4, 381-400.  Gale D. (1960), The theory of linear economic models, Academic Press, New York.  Lahmandi-Ayed R. (2001), \Oligopoly equilibria in exchange economies: a limit theorem," Economic Theory 17, 665-674.  Mas-Colell A. (1982), \The Cournotian foundations of Walrasian equilibrium theory," in Hildenbrand W. (ed), Advances in economic theory, Cambridge University Press, Cambridge.  Maskin E., Tirole J. (2001), \Markov perfect equilibrium," Journal of Economic Theory 100, 191-219.  Minc H. (1988), Nonnegative matrices, Wiley, New York.  Okuno M., Postlewaite A., Roberts J. (1980), \Oligopoly and competi- tion in large markets," American Economic Review 70, 22-31.  Peck J., Shell K., Spear S.E. (1992), \The market game: existence and structure of equilibrium," Journal of Mathematical Economics 21, 271- 299.  Postlewaite A., Schmeidler D. (1978), \Approximate efficiency of non- Walrasian Nash equilibria," Econometrica 46, 127-137.  Roberts D.J., Sonnenschein H. (1977), \On the foundations of the theory of monopolistic competition," Econometrica 45, 101-114.  Roberts K. (1980), \The limit points of monopolistic competition," Journal of Economic Theory 22, 256-278.  Sahi S., Yao S. (1989), \The noncooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics 18, 325-346.  Shapley L.S., Shubik M. (1977), \Trade using one commodity as a means of payment," Journal of Political Economy 85, 937-968.  Shitovitz B. (1973), \Oligopoly in markets with a continuum of traders," Econometrica 41, 467-501.  Shitovitz B. (1997), \A comparison between the core and the monopoly solutions in a mixed exchange economy," Economic Theory 10, 559-563.|
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