Differentiated Entry or “Me-Too” Entry in Bertrand and Cournot Oligopoly

When would an oligopolistic entrant imitate an incumbent’s product (“me-too” entry), rather than horizontally differentiate? We allow an entrant's product choice to vary endogenously with the cost of product differentiation. Such endogenity of product differentiation significantly affects the comparison of Bertrand and Cournot duopoly. We find that if Bertrand entry occurs, products are differentiated, whereas there is a substantial region in which Cournot entry involves a homogenous product. Bertrand prices may be higher than Cournot prices; and, if product differentiation costs are low enough to induce Cournot differentiated entry, then Bertrand industry profit equals or exceeds Cournot industry profit.

Local Stability of Cournot Equilibrium as the Number of Firms Increases

In this paper, a Cournot oligopoly with isoelastic demand function and constant marginal cost is considered. The local stability conditions of the Cournot equilibrium are determined for four models with different decision mechanisms. In the first model, firms adjust their outputs using the best reply response with naive expectations. The second model is a generalization of the first one, where firms have adaptive expectations. Meanwhile, the third and fourth models adopt the bounded rationality and local monopolistic approximation, respectively. The results show that, in the case of identical firms, the Cournot equilibrium is always stable when the firms adopt the local monopolistic approximation mechanism.

Hierarchical model of competition under uncertainty

Oligopoly is a basic concept in the theory of competition. This structure is the central object of research in the economics of markets. There are many mathematical models of the market that are formalized in the form of an oligopoly in economic theory. The Cournot oligopoly is an elementary mathematical model of competition. The principle of equilibrium formalizes the non-cooperative nature of the conflict. Each player chooses the equilibrium strategy of behavior that provides the greatest profit, provided that the other competitors adhere to their equilibrium strategies. The Stackelberg model describes a two-level hierarchical model of firm competition. The top-level player (center, leader) chooses his strategy, assuming reasonable (optimal) decision-making by the lower-level players. Lower-level players (agents, followers) recognize the leadership of the center. They consider the center's strategies known. These players choose their strategies, wanting to maximize their payoff functions. This hierarchical structure is from a game point of view a case of a hierarchical game Gamma1. The indefinite uncontrolled factors (uncertainties) are the values for which only the range of possible values is known in this paper. Recently, studies of game models under uncertainty have been actively conducted. In particular, non-coalitional games under uncertainty are investigated. The concepts of risk and regret are formalized in various ways in the theory of problems with uncertainty. At the same time, the decision-maker takes into account both the expected losses and the possibility of favorable actions of factors beyond his control.\nThis article examines the two-level hierarchical structure of decision-making in the problem of firm competition. A linear-quadratic model with two levels of hierarchy is considered. This model uses the concepts of Cournot and Stackelberg under uncertainty. Uncontrolled factors (uncertainties) are identified with the actions of the importing company. The Wald and Savage principles are used to formalize the solution. According to Wald's maximin criterion, game with nature is seen as a conflict with a player who wants to harm the decision-maker as much as possible.\n\nSavage's minimax regret criterion, when choosing the optimal strategy, focuses not on winning, but on regret. As an optimal strategy, the strategy is chosen in which the amount of regret in the worst conditions is minimal. A new approach to decision-making in the game with nature is formalized. It allows you to combine the positive features of both principles and weaken their negative properties. The concept of U-optimal solution of the problem in terms of risks and regrets is considered.\nThe problems of formalization of some types of optimal solutions for a specific linear-quadratic problem with two levels of hierarchy are solved.

A Few Bad Apples Spoil the Barrel: An Anti-Folk Theorem for Anonymous Repeated Games with Incomplete Information

We study anonymous repeated games where players may be “commitment types” who always take the same action. We establish a stark anti-folk theorem: if the distribution of the number of commitment types satisfies a smoothness condition and the game has a “pairwise dominant” action, this action is almost always taken. This implies that cooperation is impossible in the repeated prisoner's dilemma with anonymous random matching. We also bound equilibrium payoffs for general games. Our bound implies that industry profits converge to zero in linear-demand Cournot oligopoly as the number of firms increases. (JEL C72, C73, D83)