Game Theory Part III

1. Chapter 12 Strategy and Game Theory (Part III) © 2004 Thomson Learning/South-Western

2. Cooperation and Repetition • However, A might threaten to use strategy H unless B plays L to increase profits by 5. • If a game is replayed many times, cooperative behavior my be fostered. • Some market are thought to be characterized by “tacit collusion” although firms never meet. • Repetition of the threat game might provide A with the opportunity to punish B for failing to choose L.

3. Many-Period Games • Figure 12.2 repeats the advertising game except that B knows which advertising spending level A has chosen. • The oral around B’s nodes has been eliminated. • B’s strategic choices now must be phrased in a way that takes the added information into account.

4. FIGURE 12.2: The Advertising Game in Sequential Form 7,5 L B H 5,4 L A L 6,4 H B H 6,3

5. Many-Period Games • The four strategies for B are shown in Table 12.6. • For example, the strategy (H, L) indicates that B chooses L if A first chooses H. • The explicit considerations of contingent strategy choices enables the exploration of equilibrium notions in dynamic games.

6. TABLE 12.6: Contingent Strategies in the Advertising Game

7. Credible Threat • The three Nash equilibria in the game shown in Table 12.6 are: • (1) A: L, B: (L, L); • (2) A: L, B: (L, H); and • (3) A: H, B: (H,L). • Pairs (2) and (3) are implausible, however, because they incorporate a noncredible threat that firm B would never carry out.

8. Credible Threat • Consider, for example, A: L, B: (L, H) where B promises to play H if A plays H. • This threat is not credible (empty threats) since, if A has chosen H, B would receive profits of 3 if it chooses H but profits of 4 if it chooses L. • By eliminating strategies that involve noncredible threats, A can conclude that, as before, B would always play L.

9. Credible Threat • The equilibrium A: L, B: (L, L) is the only one that does not involve noncredible threats. • A perfect equilibrium is a Nash equilibrium in which the strategy choices of each player avoid noncredible threats. • That is, no strategy in such an equilibrium requires a player to carry out an action that would not be in its interest at the time.

10. Models of Pricing Behavior: The Bertrand Equilibrium • Assume two firms (A and B) each producing a homogeneous good at constant marginal cost, c. • The demand is such that all sales go to the firm with the lowest price, and sales are evenly split if PA = PB. • All prices where profits are nonnegative, (P  c) are in each firm’s pricing strategy.

11. The Bertrand Equilibrium • The only Nash equilibrium is PA = PB = c. • Even with only two firms, the Nash equilibrium is the competitive equilibrium where price equals marginal cost. • To see why, suppose A chooses PA > c. • B can choose PB < PA and capture the market. • But, A would have an incentive to set PA < PB. • This would only stop when PA = PB = c.

12. Two-Stage Price Games and Cournot Equilibrium • If firms do not have equal costs or they do not produce goods that are perfect substitutes, the competitive equilibrium is not obtained. • Assume that each firm first choose a certain capacity output level for which marginal costs are constant up to that level and infinite thereafter.

13. Two-Stage Price Games and Cournot Equilibrium • A two-stage game where the firms choose capacity first and then price is formally identical to the Cournot analysis. • The quantities chosen in the Cournot equilibrium represent a Nash equilibrium, and the only price that can prevail is that for which total quantity demanded equals the combined capacities of the two firms.

14. Two-Stage Price Games and Cournot Equilibrium • Suppose Cournot capacities are given by • A situation in which is not a Nash equilibrium since total quantity demanded exceeds capacity. • Firm A could increase profits by slightly raising price and still selling its total output.

15. Two-Stage Price Games and Cournot Equilibrium • is not a Nash equilibrium because at least one firm is selling less than its capacity. • The only Nash equilibrium is which is indistinguishable from the Cournot result. • This price will be less than the monopoly price, but will exceed marginal cost.

16. Comparing the Bertrand and Cournot Results • The Bertrand model predicts competitive outcomes in a duopoly situation. • The Cournot model predict monopolylike inefficiencies in which price exceed marginal cost. • The two-stage model suggests that decisions made prior to the final (price setting) stage can have important market impact.

17. APPLICATION 12.2: How is the Price Game Played? • Many factors influence how the pricing “game” is played in imperfectly competitive industries. • Two such factors that have been examined are • Product Availability • Information Sharing

18. APPLICATION 12.2: How is the Price Game Played? • Product availability is an important component of competition in many retail industries. • The impact of movie availability in the video-rental industry was examined in 2001 by James Dana. • His data showed that Blockbuster’s prices were 40% higher than at other stores. • He argued that Blockbuster’s higher price in part stems from its reputation for having movies available and that those prices act as a signal.