Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game

作者: Dongshuang Hou , Aymeric Lardon , Theo Driessen

DOI:

关键词: Non-cooperative gameMathematical economicsInverse demand functionMarginal costCore (game theory)MicroeconomicsEconomicsBondareva–Shapley theoremOligopolyRepeated gameStackelberg competition

摘要: In this article we consider Stackelberg oligopoly TU-games in gamma-characteristic function form (Chander and Tulkens 1997) which any deviating coalition produces an output at a first period as leader outsiders simultaneously independently play quantity second followers. We assume that the inverse demand is linear firms operate constant but possibly distinct marginal costs. Generally speaking, for TU-game show 1-concavity property of its dual game necessary sufficient condition under core initial non-empty coincides with set imputations. The great interest since it describes contribution followers to join grand by turning leaders. aim provide ensures satisfies property. Moreover, prove depends on heterogeneity firms' costs, i.e., 1-concave if only costs are not too heterogeneous. This last result extends Marini Currarini's non-emptiness (2003) situations.

参考文章(12)
Lardon Aymeric, Cournot oligopoly interval games Research Papers in Economics. ,(2010)
D.A. Dimitrov, S.H. Tijs, R. Brânzei, Shapley-like values for interval bankruptcy games Economics Bulletin. ,vol. 3, pp. 1- 8 ,(2003)
Sergio Currarini, Marco Marini, A Sequential Approach to the Characteristic Function and the Core in Games with Externalities Social Science Research Network. pp. 233- 249 ,(2003) , 10.1007/978-3-662-05611-0_14
Jingang Zhao, A β-Core Existence Result and Its Application to Oligopoly Markets☆ Games and Economic Behavior. ,vol. 27, pp. 153- 168 ,(1999) , 10.1006/GAME.1998.0654
Theo S.H. Driessen, Holger I. Meinhardt, Convexity of oligopoly games without transferable technologies Mathematical Social Sciences. ,vol. 50, pp. 102- 126 ,(2005) , 10.1016/J.MATHSOCSCI.2005.01.003
Aymeric Lardon, The γ-core in Cournot oligopoly TU-games with capacity constraints Theory and Decision. ,vol. 72, pp. 387- 411 ,(2012) , 10.1007/S11238-011-9256-5
Henri Frédéric Bohnenblust, Kenneth Joseph Arrow, Contributions to the theory of games ,(1950)
Parkash Chander, Henry Tulkens, The core of an economy with multilateral environmental externalities International Journal of Game Theory. ,vol. 26, pp. 379- 401 ,(1997) , 10.1007/S001820050041
Jingang Zhao, A necessary and sufficient condition for the convexity in oligopoly games Mathematical Social Sciences. ,vol. 37, pp. 189- 204 ,(1999) , 10.1016/S0165-4896(98)00019-5
Hanif D. Sherali, Allen L. Soyster, Frederic H. Murphy, Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations Operations Research. ,vol. 31, pp. 253- 276 ,(1983) , 10.1287/OPRE.31.2.253