Game - Theoretic Modelling of Oligopolistic Competition under Uncertainty

  • Michal Krol

Student thesis: Phd


This thesis reconsiders some of the most widely debated controversies in game theoretic modelling of oligopolistic competition, and proposes modifications of existing models and concepts demonstrating how these controversies can be addressed in the presence of uncertainty.The first part of the discussion is concerned with competition by product design in heterogeneous goods' markets, as captured by the Hotelling framework. The most prominent difficulty here is the model's lack of robustness to changes in the transportation cost specification, and the fact that the only universally tractable quadratic formulation induces an implausible and socially undesirable 'maximum differentiation' outcome. The problem is addressed in Chapter Two, by considering a model with uncertain consumer demand and general linear-quadratic costs. It turns out that, for uncertainty big enough, the presence of a linear component in the cost function no longer rules out an analytical solution to the game. In particular, I characterize a subgame-perfect equilibrium in which the firms' locations converge to the socially efficient ones in the limit as uncertainty increases, regardless of the curvature of the cost function. Thus, the presence of substantial demand uncertainty makes the market more competitive, by reducing the excessive equilibrium product differentiation and the resulting prices.In fact, Chapter Three demonstrates that this also holds when the firms do not know the exact distribution of consumer demand fluctuations, but resolve the resulting ambiguity using the Arrow and Hurwicz alpha-maxmin criterion. This is because firms that are sufficiently pessimistic, in the sense of assigning a large weight to the lowest profit scenario, locate closer together in equilibrium under uncertainty, where it is argued that operating on such a pessimistic premise could become prevalent via strategic commitment, elimination of underperforming firms or as a result of taxation.This discussion is complemented by the second part of the thesis, which is concerned with competition in homogeneous goods' markets. In particular, Chapter Four reconsiders the so far unresolved discrepancy between the Cournot model of quantity competition and the alternative Bertrand price setting specification. To this end, I propose a model evaluation criterion, based on a recent generalization of the von Neumann-Morgenstern stable set concept. In particular, a restriction of the players' strategy sets is said to constitute a stable convention when no one has an incentive to unilaterally violate it, while faced with strategic uncertainty about the counterparts' exact choices within their restricted strategy sets. Applying the criterion to a simultaneous move quantity-price game reveals that Cournot competition is a stable convention when production costs are high relative to the number of firms and difficult to recover for unsold output. In contrast, Bertrand competition is never stable.
Date of Award31 Dec 2011
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorPaul Madden (Supervisor), Igor Evstigneev (Supervisor) & Nicholas Yannelis (Supervisor)

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