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Expected Worth for 2 × 2 Matrix Games with Variable Grid Sizes

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Abstract

We offer a detailed examination of a broad class of 2 x 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.

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  • Michael R. Powers & Martin Shubik & Wen Wang, 2016. "Expected Worth for 2 × 2 Matrix Games with Variable Grid Sizes," Cowles Foundation Discussion Papers 2039R, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2039r
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384.
    2. Michael R. Powers & Martin Shubik & Wen Wang, 2016. "Expected Worth for 2 × 2 Matrix Games with Variable Grid Sizes," Cowles Foundation Discussion Papers 2039, Cowles Foundation for Research in Economics, Yale University.
    3. Martin Shubik & Gerrit Wolf & Byron Poon, 1974. "Perception of Payoff Structure and Opponent's Behavior in Related Matrix Games," Journal of Conflict Resolution, Peace Science Society (International), vol. 18(4), pages 646-655, December.
    4. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(3), pages 277-286.
    5. anonymous, 1976. "The economy in 1975," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Feb, pages 71-81.
    6. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    Cited by:

    1. Michael R. Powers & Martin Shubik & Wen Wang, 2016. "Expected Worth for 2 × 2 Matrix Games with Variable Grid Sizes," Cowles Foundation Discussion Papers 2039, Cowles Foundation for Research in Economics, Yale University.

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    Keywords

    2 × 2 matrix games; efficiency; coordination; worth of coordination;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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