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Two-Player, Two-Strategy Games

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Coordinate Systems for Games

Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

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Abstract

While the analysis in this chapter is straightforward, a considerable amount of new information is developed. Thus, a quick preview will help to pull it together.

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Notes

  1. 1.

    From the mathematical perspective developed Sect. 3.4 and in Chap. 7, \(\mathcal G^N\) is the projection of \(\mathcal G\) into a lower dimensional subspace that contains all of the Nash information. This projection eliminates redundancies for the Nash analysis. The Nash subspace is characterized by the sum of Row’s entries in any column, and the sum of Column’s entries in any row, must equal zero.

  2. 2.

    Similar to the previous footnote, this removal of redundancies is equivalent to a projection of \(\mathcal G^{Averages}\), or \(\mathcal G\), into an appropriate lower dimensional subspace. See Sect. 3.4 and Chap. 7.

  3. 3.

    The \(\mathcal G^N\) and \(\mathcal G^B\) components are well defined from the computational approach. For purposes of exposition, proofs and stronger mathematical descriptions are deferred to Sect. 3.4.2 and Chap. 7.

  4. 4.

    For readers familiar with the term, notice how the set of \(\mathcal G^N\) bimatrices forms an additive group  where the identity is the weak Nash setting with zero terms. The same holds for the \(\mathcal G^B\) and \(\mathcal G^K\) components.

  5. 5.

    This statement supports footnote #3 in Chap. 1.

Author information

Authors and Affiliations

  1. Department of Mathematics, Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA, USA

    Daniel T. Jessie

  2. Department of Economics, Department of Mathematics, Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA, USA

    Donald G. Saari

Authors
  1. Daniel T. Jessie
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  2. Donald G. Saari
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Correspondence to Daniel T. Jessie .

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Jessie, D.T., Saari, D.G. (2019). Two-Player, Two-Strategy Games. In: Coordinate Systems for Games. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-35847-1_2

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