On the generic nonexistence of pure strategy Nash equilibria in continuous games. (English) Zbl 0641.90094
Summary: S. Srivastava [ibid. 36, 26-35 (1985; Zbl 0602.90141)] states that in the space of continuous games an open and dense subset does not have a pure strategy Nash equilibrium. The purpose of this note is twofold: first, to show that without a connectedness assumption on the strategy sets of the players this statement is false; second, to provide correct proofs of his main results.
MSC:
| 91A10 | Noncooperative games |
Citations:
Zbl 0602.90141References:
| [1] | Hildenbrand, W., Core and Equilibria of a Large Economy (1974), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ · Zbl 0351.90012 |
| [2] | Kannai, Y., Continuity properties of the core of a market, Econometrica, 38, 791-815 (1970) · Zbl 0222.90004 |
| [3] | Le Breton, M., Kannai Topology with Locally Saturated Preferences, (Discussion Paper 8507 (1985), LEME, Université de Rennes I) |
| [4] | Srivastava, S., Pure strategy Nash equilibria with continuous objectives, J. Econ. Theory, 36, 26-35 (1985) · Zbl 0602.90141 |
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