Abstract
Spatial models of two-player competition in spaces with more than one dimension almost never have pure-strategy Nash equilibria, and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to avoid the uniqueness of the equilibrium position. As a result, a “region of equilibrium” appears, which can be located by geometric methods. In this area, the players can move around in an “almost-equilibrium” situation and do not necessarily have to adopt the same position.
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Abellanas, M., López, M.D., Rodrigo, J. et al. Weak equilibrium in a spatial model. Int J Game Theory 40, 449–459 (2011). https://doi.org/10.1007/s00182-010-0241-y
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DOI: https://doi.org/10.1007/s00182-010-0241-y