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The core of a strategic game

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  • Chander Parkash

    (Bennett University, Greater Noida, India)

Abstract

In this paper, I introduce and study the γ $\gamma$-core of a general strategic game. I first show that the γ $\gamma$-core of an arbitrary strategic game is smaller than the conventional α $\alpha$- and β $\beta$- cores. I then consider the partition function form of a general strategic game and show that a prominent class of partition function games admit nonempty γ $\gamma$-cores. Finally, I show that each γ $\gamma$-core payoff vector (a cooperative solution) can be supported as an equilibrium outcome of an intuitive non-cooperative game and the grand coalition is the unique equilibrium outcome if and only if the γ $\gamma$-core is non-empty.

Suggested Citation

  • Chander Parkash, 2019. "The core of a strategic game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(1), pages 1-10, January.
    • Handle: RePEc:bpj:bejtec:v:19:y:2019:i:1:p:10:n:20
    DOI: 10.1515/bejte-2017-0155
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Marini, Marco A. & Currarini, Sergio, 2003. "A sequential approach to the characteristic function and the core in games with externalities," MPRA Paper 1689, University Library of Munich, Germany, revised 2003.
    3. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    4. Carsten Helm, 2001. "On the existence of a cooperative solution for a coalitional game with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 141-146.
    5. Aymeric Lardon, 2012. "The γ-core in Cournot oligopoly TU-games with capacity constraints," Theory and Decision, Springer, vol. 72(3), pages 387-411, March.
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