Oligopolies & Game Theory 5-26-09 Econ 201 Lecture 8.1c1 Oligopolies & Game Theory 5-26-09

Figure 12.4 Duopoly Equilibrium in a Centralized Cartel

Duopoly What are the strategic options and the payoffs? Form a cartel Forego additional profits from increasing output beyond assigned quota Bilateral monopoly Each firm sets Qs at MR(market) = MC(firm) Price falls below single monopoly/cartel price Compete on price Final equilibrium at competitive market price No monopoly rents (or + economic profits)

Game Theory Game theory is a methodology that can be used to analyze both cooperative and non-cooperative oligopolies. Recognizes the interdependence of the firms’ actions Using a payoff matrix to describe options (strategies) and payoffs Firms are profit maximizers!

Figure 12.7 Xbox and PlayStation 2 Payoff Matrix for Advertising

Determining the Dominate Strategy A dominant strategy occurs when one strategy is best for a player regardless of the rival’s actions. Dominate strategy equilibrium—neither player has reason to change their actions because they are pursuing the strategy that is optimal under all circumstances. Here the dominant strategy is for each firm to advertise

Multiple Equilibria Sometimes there are come cases where there are multiple Nash equilibria. In this case, the outcome is uncertain. Firms will have an incentive to collude. An example: Sony/Microsoft can add one of two new features One feature appeals only to YOUTH market Other feature appeals only to TEEN market Incentive to reach agreement on both firms offering the same new (one only) feature

Payoff Table Figure 12.8 Nash Equilibria

Prisoner's Dilemma A prisoner’s dilemma occurs when the dominate strategy leads all players to an undesired outcome.

Figure 12.9 Prisoners’ Dilemma

Best Outcome Neither confesses But without collusion/agreement – how do you guarantee this outcome? Enforcement issues (price, output, quotas) Law & Order Why we keep suspects separated! Prevent collusive agreements

An Economic Application of Game Theory: the Kinked-Demand Curve Above the kink, demand is relatively elastic because all other firm’s prices remain unchanged. Below the kink, demand is relatively inelastic because all other firms will introduce a similar price cut, eventually leading to a price war. Therefore, the best option for the oligopolist is to produce at point E which is the equilibrium point

Nash Equilibrium If firm facing kinked demand curve tries to raise price: Other firms do not As demand is highly elastic and other firms are “close” substitutes Loses market share and revenues If firm lowers price Competitors match price decreases

Nash Equilibrium If firm facing kinked demand curve tries to raise price: Other firms do not As demand is highly elastic and other firms are “close” substitutes Loses market share and revenues If firm lowers price Competitors match price decreases

Features of a Nash Equilibrium In a non-cooperative oligopoly, each firm has little incentive to change price. This represents a Nash Equilibrium, where each firm’s pricing strategy remains constant given the pricing strategy of the other firms. Firms have no incentive to change their strategy.

Non-Cooperative Cartels Either Some degree of price competition Firms engage in highly competitive pricing Similar outcome as perfect competition Firms have some market power Resembles monopolistic competition Bilateral monopoly with price competition or Stable prices prevail Non-collusive Firms choose not to compete because of kinked demand curve

Non-cooperative Oligopolies Competitive/psuedo-competitive behavior (non-cooperative) Perfect Competition (almost): firms undercut each other’s prices competition between sellers is fierce, with relatively low prices and high production Outcome may be similar to PC or Monopolistic Competition Nash equilibrium Firms avoid “ruinous” price competition by keeping prices stable and avoiding price competition (undercutting each others prices) May lead to product proliferation and/or extensive advertising (non-price competition)

Figure 12.3 U.S. 2003 Advertising-to-Sales Ratio for Selected Products and Industries

Game Theory Models of Oligoploy Stackelberg's duopoly. In this model the firms move sequentially (see Stackelberg competition). Cournot's duopoly. In this model the firms simultaneously choose quantities (see Cournot competition). Bertrand's oligopoly. In this model the firms simultaneously choose prices (see Bertrand competition). Monopolistic competition. A market structure in which several or many sellers each produce similar, but slightly differentiated products. Each producer can set its price and quantity without affecting the marketplace as a whole.