Finding all pure strategy Nash equilibria in a planar location game

Finding all pure strategy Nash equilibria in a planar location game

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Article ID: iaor20116366
Volume: 214
Issue: 1
Start Page Number: 91
End Page Number: 98
Publication Date: Oct 2011
Journal: European Journal of Operational Research
Authors: , , , ,
Keywords: game theory
Abstract:

In this paper, we deal with a planar location‐price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served. We present characterizations of local and global Nash equilibria. Then an algorithm is shown in order to find all possible Nash equilibrium pairs of locations. The minimization of the social cost leads to a Nash equilibrium. An example shows that there may exist multiple Nash equilibria which are not minimizers of the social cost.

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