Theories of imperfectly competitive markets
The author provides a systematic treatment of some models of imperfect competition relying on published works in the area, including the author's own. The opening chapter on non-cooperative game theory devotes a section on aggregative games, where the sum of the strategies of the other players is the relevant variable in each payoff function, aside from the player's own strategy. Under some regularity conditions, the most prominent of which is a condition that the inverse demand function be concave or ``not too convex'', existence of a unique and stable Nash equilibrium is established. Stability is considered in the context of two types of dynamic models, one in which agents change their strategies in the direction of the best reply strategies (best reply dynamics) and another in which agents increase their strategy if and only if the marginal payoff is positive (gradient dynamics). Aggregative games are not suitable for games of price setting behaviour where strategies of competitors enter separately in payoffs. A separate section is devoted to a similar analysis of this type of games under dominant diagonal type assumptions ensuring stability. A chapter on comparative statics investigates, in the context of both the quantity setting Cournot model as well as the price setting Bertrand model, the effects of changes in the number of players, and in the payoff functions, on the Nash equilibrium strategies and payoffs. Various propositions are established, for example, that the effect of a new entrant is to increase aggregate output and decrease the output and payoffs of the incumbents. Effect of shifts in the payoff functions, both for individual players as well as generalized shifts for all players, are analyzed. It is shown that effects of changes in marginal costs on price is not unambiguously more for imperfectly competitive markets than for competitive ones, but rather depends on the degree of concavity of the inverse demand function. Welfare properties of market allocations are studied using a social welfare function which is the sum of producers and consumers utilities which are taken to be quasi-linear. Typically, market allocations are inefficient. A mechanism for achieving optimal allocations under incomplete information is studied. Welfare properties of Cournot allocation with increase in number of firms as well as with free entry is investigated. It is also shown that Cournot equilibrium is constrained efficient if market demand curve is taken as a natural constraint in view of incentive compatibility on the consumer side. A chapter on monopolistic competition looks at models with product heterogeneity and with free entry of firms. Welfare properties of equilibrium allocations are studied in a representative consumer set up as well as a model with a continuum of consumers with different tastes. A final chapter rounds off the treatise with analysis of some examples of two stage game formulations of oligopoly behaviour, employing the notion of subgame perfect Nash equilibrium. Entry deterrence, limit pricing, contestable markets are amongst the topics treated, along with a couple of interesting sections on pricing by public firms that compete in an oligopolistic market with a private firm and on equilibrium in models where a corporate firm can create independent divisions which compete in the same market. Each chapter ends with a copious set of exercises developing on the main themes introduced in the text and an extensive bibliography. Useful as a text or reference manual for a course on imperfect competition.
scientific article; zbMATH DE number 945669