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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. Martin Shubik, 2012. "What is a Solution to a Matrix Game," Levine's Working Paper Archive 786969000000000541, David K. Levine.
    2. 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, December.
    3. 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.
    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. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-764, May.
    6. 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.
    7. anonymous, 1976. "The economy in 1975," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Feb, pages 71-81.
    8. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    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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    More about this item

    Keywords

    2 � 2 matrix games; efficiency; coordination; worth of coordination;
    All these keywords.

    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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