The constrained coalitional price setting game: theory and applications

© 2007 Dr. Martin Charles ByfordIn a number of simple settings there do not exist Nash equilibria, to the Bertrand price setting game, in pure strategies. Two prominent examples where pure strategy solutions do not exist are price competition with convex costs and spatial competition with finite buyers. This thesis develops an alternative model of price formation. The model examines as a non-transferable utility 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. While 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 thesis 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. The existence of solutions in pure strategies allows previously intractable problems in spatial markets to be tackled with relative ease. Two such problems are addressed in this thesis: The first investigates the consequence of replacing the continuum of buyers, with a large but finite set of buyers, in common spatial models. It is shown that the maximum stable mark-ups on both the Hotelling line and circle are halved where the continuum is replaced by an arbitrarily large number of discrete buyers. The difference arises because competition at the margin is more intense where sellers are competing for an atom. The second is to develop a theory of price competition in a market for a homogeneous good, where the option to trade is defined by a buyer-seller network. The necessary and sufficient conditions for a network to behave competitively are characterised, and it is shown that local price distortions can propagate across the network; resulting in supra-competitive pricing