Costly Renegotiation in Repeated Bertrand Games

This paper extends the concept of weak renegotiation-proof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost, there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique pure strategy WRP equilibrium without renegotiation costs, which implies marginal-cost pricing in every period. Moreover, in comparison to the findings of McCutcheon (1997), who states that renegotiation costs have to be substantial to facilitate collusion, this result points to a quite different conclusion.

CONSUMER MISTAKES IN BERTRAND GAMES

The identical agent, identical good Bertrand game is associated with prices at marginal cost — the Bertrand Paradox. If consumers make occasional mistakes I show that the standard Bertrand game gives rise to positive profits and prices above marginal cost. Some firms charge low prices to capture the bulk of the sales while others charge high prices selling to mistaken consumers. Furthermore, with free entry the Diamond Paradox arises; a full measure of the firms choose the monopoly price. As a result, the Diamond Paradox arises in an environment with zero search costs by replacing searching costs with searching errors.

APPLICATION OF GAME THEORY FOR DUOPOLY MARKET ANALYSIS

The paper provides the analysis of game theory models application to identify duopoly market equilibrium (quantities sold and market prices), to evaluate and compare the results of enterprises in a market. The purpose of the analysis is to determine to what extent theoretical models correspond to real life, that is how reliable they are in supporting and estimating decisions of duopoly companies, fortifying market prices and quantities sold, evaluating company's competing positions and possibilities for decision co‐ordination. To describe discrete strategies equilibrium the “Prisoner's Dilemma” model is applied to a hypothetic market entrance game with possible side payments. Further analysis of the market entrance game incorporates mixed strategies based “Matching Pennies” model in case discrete strategies equilibrium does not exist. Continuous strategies are described analyzing hypothetic duopoly by applying Cournot, Stackelberg and Bertrand models. The first and the second mover advantage issues are raised comparing outcomes of dynamic Stackelberg and Bertrand games for a leader and a follower. Stability and utility of cartel agreement for its participants is mathematically supported with the help of a multi‐step repeated Cournot game. Having described, compared and applied the main game theory models to artificial duopoly market situations, the author passes over to the comparative analysis of the models’ weaknesses and problems related to their practical application.