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CournotWalras equilibrium as a subgame perfect equilibrium
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Busetto, Francesca, Codognato, Giulio and Ghosal, Sayantan (2008) CournotWalras equilibrium as a subgame perfect equilibrium. Working Paper. Coventry: University of Warwick Economics Department. (Warwick economic research papers).

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Abstract
In this paper, we investigate the problem of the strategic foundation of the CournotWalras equilibrium approach. To this end, we respecify à la CournotWalras 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 CournotNash equilibrium allocations of the mixed version of the original Shapley's model. As the nonequivalence, in a onestage setting, can be explained by the intrinsic twostage nature of the CournotWalras equilibrium concept, we are led to consider a further reformulation of the Shapley's model as a twostage 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 CournotWalras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this twostage game, which we call the set of the PseudoMarkov perfect equilibrium allocations.
Item Type:  Working or Discussion Paper (Working Paper) 

Alternative Title:  
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 
Date:  January 2008 
Number:  No.837 
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Status:  Not Peer Reviewed 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). CournotWalras equilibrium as a subgame perfect equilibrium. International Journal of Game Theory, 37(3), pp. 371386. http://wrap.warwick.ac.uk/id/eprint/29123 
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References:  [1] Aliprantis C.D., Border K.C. (1999), Infinite dimensional analysis, Springer, New York. [2] Amir R., Sahi S., Shubik M., Yao S. (1990), "A strategic market game with complete markets," Journal of Economic Theory 51, 126143. [3] Aumann R.J. (1965), "Integrals of set valued functions," Journal of Math ematical Analysis and Applications 12, 112. [4] Aumann R.J. (1966), "Existence of competitive equilibria in markets with a continuum of traders," Econometrica 24. [5] Bonnisseau JM., Florig M. (2003), "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory 22, 727741. [6] Codognato G. (1995), \CournotWalras and Cournot equilibria in mixed markets: a comparison," Economic Theory 5, 361370. [7] Codognato G., Gabszewicz J.J. (1991), \Equilibres de CournotWalras dans une economie d'echange," Revue Economique 42, 10131026. 117. [8] Codognato G., Gabszewicz J.J. (1993), \CournotWalras equilibria in markets with a continuum of traders," Economic Theory 3, 453464. [9] Codognato G., Ghosal S. (2000a), \CournotNash equilibria in limit ex change economies with complete markets and consistent prices," Journal of Mathematical Economics 34, 3953. [10] Codognato G., Ghosal S. (2000b), \Oligopoly µa la CournotNash in mar kets with a continuum of traders," Discussion Paper No 20005, CEPET (Central European Program in Economic Theory), Institute of Public Economics, Graz University. [11] d'Aspremont C., Dos Santos Ferreira R., GerardVaret L.A. (1997), \General equilibrium concepts under imperfect competition: a Cournotian approach," Journal of Economic Theory 73, 199230. [12] Dierker H., Grodal B. (1986), \Nonexistence of CournotWalras equi librium in a general equilibrium model with two oligopolists," in Hilden brand W., MasColell A. (eds), Contributions to mathematical economics in honor of Gerard Debreu, NorthHolland, Amsterdam. [13] Dubey P., Shapley L.S. (1994), \Noncooperative general exchange with a continuum of traders: two models, " Journal of Mathematical Economics 23, 253293. [14] Dubey P., Shubik M. (1978), \The noncooperative equilibria of a closed trading economy with market supply and bidding strategies," Journal of Economic Theory 17, 120. [15] Fudenberg D., Tirole J. (1991), Game theory, MIT Press, Cambridge Mass.. [16] 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. [17] Gabszewicz J.J., Vial J.P. (1972), \Oligopoly `µa la CournotWalras' in a general equilibrium analysis," Journal of Economic Theory 4, 381400. [18] Gale D. (1960), The theory of linear economic models, Academic Press, New York. [19] LahmandiAyed R. (2001), \Oligopoly equilibria in exchange economies: a limit theorem," Economic Theory 17, 665674. [20] MasColell A. (1982), \The Cournotian foundations of Walrasian equilibrium theory," in Hildenbrand W. (ed), Advances in economic theory, Cambridge University Press, Cambridge. [21] Maskin E., Tirole J. (2001), \Markov perfect equilibrium," Journal of Economic Theory 100, 191219. [22] Minc H. (1988), Nonnegative matrices, Wiley, New York. [23] Okuno M., Postlewaite A., Roberts J. (1980), \Oligopoly and competi tion in large markets," American Economic Review 70, 2231. [24] Peck J., Shell K., Spear S.E. (1992), \The market game: existence and structure of equilibrium," Journal of Mathematical Economics 21, 271 299. [25] Postlewaite A., Schmeidler D. (1978), \Approximate efficiency of non Walrasian Nash equilibria," Econometrica 46, 127137. [26] Roberts D.J., Sonnenschein H. (1977), \On the foundations of the theory of monopolistic competition," Econometrica 45, 101114. [27] Roberts K. (1980), \The limit points of monopolistic competition," Journal of Economic Theory 22, 256278. [28] Sahi S., Yao S. (1989), \The noncooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics 18, 325346. [29] Shapley L.S., Shubik M. (1977), \Trade using one commodity as a means of payment," Journal of Political Economy 85, 937968. [30] Shitovitz B. (1973), \Oligopoly in markets with a continuum of traders," Econometrica 41, 467501. [31] Shitovitz B. (1997), \A comparison between the core and the monopoly solutions in a mixed exchange economy," Economic Theory 10, 559563. 
URI:  http://wrap.warwick.ac.uk/id/eprint/219 
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