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What Is a Solution to a Matrix Game

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Abstract

These notes are provided to describe many of the problems encountered concerning both structure and behavior in specifying what is meant by the solution to a game of strategy in matrix or strategic form. In the short term in particular, it is often reasonable for the individual to accept as given, both the context in which decisions are being made and the formal structure of the rules of the game. A solution is usually considered as a complete set of equations of motion that when applied to the game at hand selects a final outcome. There are many different theories and conjectures about how games of strategy are, or should be played. Several of them are noted below. They are especially relevant to the experimental gaming facility noted in the companion paper.

Suggested Citation

  • Martin Shubik, 2012. "What Is a Solution to a Matrix Game," Cowles Foundation Discussion Papers 1866, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1866
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d18/d1866.pdf
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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, April.
    2. George J. Mailath, 1998. "Corrigenda [Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory]," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 1941-1941, December.
    3. Halpern, Joseph Y., 2003. "A computer scientist looks at game theory," Games and Economic Behavior, Elsevier, vol. 45(1), pages 114-131, October.
    4. George J. Mailath, 1998. "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1347-1374, September.
    5. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
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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.
    2. Leland, Jonathan W. & Schneider, Mark, 2018. "A theory of focal points in 2 × 2 games," Journal of Economic Psychology, Elsevier, vol. 65(C), pages 75-89.

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    More about this item

    Keywords

    Matrix games; Solution concepts; Experimental gaming;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments

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