A Constrained Coalitional Approach to Price Formation

Martin C. Byford, University of Colorado at Boulder

Abstract

Pure strategy Bertrand Nash equilibria do not typically exist for a number of simple market structures; two prominent examples are price competition with convex costs and spatial competition with finite buyers. This paper develops an alternative model of price formation. The model examines as a non-transferable utility (NTU) coalitional game the set of outcomes that are feasible in the Bertrand price setting game.

In spatial models with finite buyers the core of this NTU coalitional game is equivalent to the set of outcomes that can be produced by undercut-proof prices.

In a market for a homogeneous good, where sellers face convex costs, the market clearing price is always in the core. Moreover, where at least two sellers compete on the supply side, as buyers become numerous the core collapses to only admit market clearing outcomes.

In some settings the price setting game developed in this paper produces results that contradict the predictions of Bertrand. Where this occurs the core outcomes tend to be more efficient than the corresponding Bertrand-Nash equilibrium. For example, double-marginalisation is never a core outcome in vertically related markets.