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Shapley's "2 by 2" theorem for game forms


  • Nikolai S. Kukushkin

    () (Russian Academy of Sciences, Dorodnicyn Computing Center)


If a finite two person game form has the property that every 2-by-2 fragment is Nash consistent, then no derivative game admits an individual improvement cycle.

Suggested Citation

  • Nikolai S. Kukushkin, 2007. "Shapley's "2 by 2" theorem for game forms," Economics Bulletin, AccessEcon, vol. 3(33), pages 1-5.
  • Handle: RePEc:ebl:ecbull:eb-07c70017

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    References listed on IDEAS

    1. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    2. Kukushkin, Nikolai S., 2002. "Perfect Information and Potential Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 306-317, February.
    3. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    4. repec:ebl:ecbull:v:3:y:2002:i:22:p:1-6 is not listed on IDEAS
    5. Gurvich, Vladimir A. & Libkin, Leonid O., 1990. "Absolutely determined matrices," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 1-18, August.
    6. Tetsuo Yamamori & Satoru Takahashi, 2002. "The pure Nash equilibrium property and the quasi-acyclic condition," Economics Bulletin, AccessEcon, vol. 3(22), pages 1-6.
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    Cited by:

    1. Endre Boros & Khaled Elbassioni & Vladimir Gurvich & Kazuhisa Makino & Vladimir Oudalov, 2016. "Sufficient conditions for the existence of Nash equilibria in bimatrix games in terms of forbidden $$2 \times 2$$ 2 × 2 subgames," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1111-1131, November.

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory


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