A simplicial algorithm approach to Nash equilibria in concave games

Arbeitspapier

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).

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 382

Classification and Topics

• Classification: Wirtschaft
• Subject: Simplicial algorithm ; Nash equilibria ; Strategy labelling

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Haake, Claus-Jochen ; Su, Francis Edward
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2006

Further information

• Handle: http://hdl.handle.net/10419/43829
• URN: urn:nbn:de:hbz:361-9501
• Last update: 10.03.2025, 11:44 AM CET