A simplicial algorithm approach to Nash equilibria in concave games
Haake C-J, Su FE (2006) Working Papers. Institute of Mathematical Economics; 382.
Bielefeld: Universität Bielefeld.
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Haake, Claus-JochenUniBi
;
Su, Francis Edward
Abstract
In this paper we demonstrate a new method for computing approximate Nash equilibria in n-person games. Strategy spaces are assumed to be represented by simplices, while payoff functions are assumed to be concave. Our procedure relies on a simplicial algorithm that traces paths through the set of strategy profiles using a new variant of Sperner's Lemma for labelled triangulations of simplotopes, which we prove in this paper. Our algorithm uses a labelling derived from the satisficing function of Geanakoplos (2003) and can be used to compute approximate Nash equilibria for payoff functions that are not necessarily linear. Finally, in bimatrix games, we can compare our simplicial algorithm to the combinatorial algorithm proposed by Lemke & Howson (1964).
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Haake C-J, Su FE. A simplicial algorithm approach to Nash equilibria in concave games. Working Papers. Institute of Mathematical Economics. Vol 382. Bielefeld: Universität Bielefeld; 2006.
Haake, C. - J., & Su, F. E. (2006). A simplicial algorithm approach to Nash equilibria in concave games (Working Papers. Institute of Mathematical Economics, 382). Bielefeld: Universität Bielefeld.
Haake, C. - J., and Su, F. E. (2006). A simplicial algorithm approach to Nash equilibria in concave games. Working Papers. Institute of Mathematical Economics, 382, Bielefeld: Universität Bielefeld.
Haake, C.-J., & Su, F.E., 2006. A simplicial algorithm approach to Nash equilibria in concave games, Working Papers. Institute of Mathematical Economics, no.382, Bielefeld: Universität Bielefeld.
C.-J. Haake and F.E. Su, A simplicial algorithm approach to Nash equilibria in concave games, Working Papers. Institute of Mathematical Economics, vol. 382, Bielefeld: Universität Bielefeld, 2006.
Haake, C.-J., Su, F.E.: A simplicial algorithm approach to Nash equilibria in concave games. Working Papers. Institute of Mathematical Economics, 382. Universität Bielefeld, Bielefeld (2006).
Haake, Claus-Jochen, and Su, Francis Edward. A simplicial algorithm approach to Nash equilibria in concave games. Bielefeld: Universität Bielefeld, 2006. Working Papers. Institute of Mathematical Economics. 382.
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