Spatial Competition and the Core
Models of spatial competition have proven useful in describing differentiated product markets. A serious problem is the nonexistence of Nash equilibria. This problem is resolved by modelling the price formation process using the core. The equilibrium is the outcome of a two-stage process. In the first stage, two firms choose locations simultaneously. The second stage has prices determined by an allocation in the core of a cooperative subgame allowing for coalitions of buyers and sellers. These prices approach the competitive level as the distance between the firms goes to zero, thus capturing the essence of duopoly rivalry.
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