Abstract
In this paper we propose a general framework of distribution-free models for N-person noncooperative games with uncertain information. In the model, we assume that each player's cost function and/or the opponents' strategies belong to some uncertainty sets, and each player chooses his/her strategy according to the robust optimization policy. Under such assumptions, we define the robust Nash equilibrium for N-person games by extending some existing definitions. We present sufficient conditions for existence and uniqueness of a robust Nash equilibrium. In order to compute robust Nash equilibria, we reformulate certain classes of robust Nash equilibrium problems to second-order cone complementarity problems. We finally show some numerical results to discuss the behavior of robust Nash equilibria.
Original language | English |
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Pages (from-to) | 237-259 |
Number of pages | 23 |
Journal | Pacific Journal of Optimization |
Volume | 5 |
Issue number | 2 |
Publication status | Published - 2009 May 1 |
Externally published | Yes |
Keywords
- Complementarity problem
- Incomplete information
- N-person non-cooperative game
- Robust Nash equilibrium
- Robust optimization
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Applied Mathematics