 Pure Strategy Nash Equilibrium Points and the Lefschetz Fixed Point TheoremStaff General Research Papers Archive from Iowa State University, Department of Economics Abstract: Using the Lefschetz fixed point theorem, a pure strategy Nash equilibrium existence theorem is established for a class of n-person games with possibly nonacyclic strategy sets. It is argued that the Lefschetz approach to fixed point theorems may ultimately prove to be particularly important in economic and game theory due to the generality of spaces that can be considered and the interesting related questions that can be investigated. For example, the Lefschetz approach to fixed point theorems leads naturally to the concept of a "Nielsen Number" of a map f:Y->Y, a homotopy-invariant lower bound for the number of fixed points of f. The Nielsen number provides a lower bound for the number of Nash equilibria in certain n-person games. Annotated pointers to related work can be accessed here: http://www2.econ.iastate.edu/tesfatsi/vita.htm#Game Keywords: N-person game; Nash equilibrium; Lefschetz fixed point theorem; Nielsen number (search for similar items in EconPapers) Published in International Journal of Game Theory 1983, vol. 12, pp. 181-191 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:isu:genres:11210 Access Statistics for this paper More papers in Staff General Research Papers Archive from Iowa State University, Department of Economics Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070. Contact information at EDIRC. |
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