Game Theory Part IV

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

2. APPLICATION 12.2: How is the Price Game Played? • Firms in the same industry often share information with each other at many levels. • A 2000 study of cross-shareholding in the Dutch financial sector showed clear evidence that competition was reduced when firms had financial interests in each other’s profits. • A famous 1914 antitrust case found that a price list published by lumber retailers facilitated higher prices by discouraging wholesalers from selling at retail.

3. Tacit Collusion: Finite Time Horizon • Would the single-period Nash equilibrium in the Bertrand model, PA = PB = c, change if the game were repeated during many periods? • With a finite period, any strategy in which firm A, say, chooses, PA > c in the last period offers B the possibility of earning profits by setting PA > PB > c.

4. Tacit Collusion: Finite Time Horizon • The threat of charging PA > c in the last period is not credible. • A similar argument is applicable for any period before the last period. • The only perfect equilibrium requires firms charge the competitive price in all periods. • Tacit collusion is impossible over a finite period.

5. Tacit Collusion: Infinite Time Horizon • Without a “final” period, there may exist collusive strategies. • One possibility is a “trigger” strategy where each firm sets its price at the monopoly price so long as the other firm adopts a similar price. • If one firm sets a lower price in any period, the other firm sets its price equal to marginal cost in the subsequent period.

6. Tacit Collusion: Infinite Time Horizon • Suppose the firms collude for a time and firm A considers cheating in this period. • Firm B will set PB = PM (the cartel price) • A can set its price slightly lower and capture the entire market. • Firm A will earn (almost) the entire monopoly profit (M) in this period.

7. Tacit Collusion: Infinite Time Horizon • Since the present value of the lost profits is given by (where r is the per period interest rate) • This condition holds for values of r < ½. • Trigger strategies constitute a perfect equilibrium for sufficiently low interest rates.

8. Generalizations and Limitations • Assumptions of the tacit collusion model: • Firm B can easily detect whether firm A has cheated • Firm B responds to cheating by adopting a harsh response that punishes firm A, and condemns itself to zero profit forever. • More general models relax one or both of these assumptions with varying results.

9. APPLICATION 12.3: The Great Electrical Equipment Conspiracy • Manufacturing of electric turbine generators and high voltage switching units provided a very lucrative business to such major producers and General Electric, Westinghouse, and Federal Pacific Corporations after World War II. • However, the prospect of possible monopoly profits proved enticing.

10. APPLICATION 12.3: The Great Electrical Equipment Conspiracy • To collude they had to create a method to coordinate their sealed bids. • This was accomplished through dividing the country into bidding regions and using the lunar calendar to decide who would “win” a bid. • The conspiracy became more difficult as its leaders had to give greater shares to other firms toward the end of the 1950s.

11. APPLICATION 12.3: The Great Electrical Equipment Conspiracy • The conspiracy was exposed when a newspaper reporter discovered that some of the bids on Tennessee Valley Authority projects were similar. • Federal indictments of 52 executives lead to jail time for some and resulted in a chilling effect on the future establishment of other cartels of this type.

12. Entry, Exit, and Strategy • Sunk Costs • Expenditures that once made cannot be recovered include expenditures on unique types of equipment or job-specific training. • These costs are incurred only once as part of the entry process. • Such entry investments mean the firm has a commitment to the market.

13. First-Mover Advantages • The commitment of the first firm into a market may limit the kinds of actions rivals find profitable. • Using the Cournot model of water springs, suppose firm A can move first. • It will take into consideration what firm B will do to maximize profits given what firm A has already done.

14. First-Mover Advantages • Firm A knows fir B’s reaction function which it can use to find its profit maximizing level of output. • Using the previously discussed functions.

15. First-Mover Advantages • Marginal revenue equals zero (revenue andprofits are maximized) when qA = 60. • With firm A’s choice, firm B chooses to produce • Market output equals 90 so spring water sells for $30 increasing A’s revenue by $200 to $1800. • Firm B’s revenue falls by $700 to $900. • This is often called a “Stakelberg equilibrium.”

16. Entry Deterrence • In the previous model, firm A could only deter firm B from entering the market if it produces the full market output of 120 units yielding zero revenue (since P = $0). • With economies of scale, however, it may be possible for a first-mover to limit the scale of operation of a potential entrant and deter all entry into the market.

17. A Numerical Example • One simple way to incorporate economies of scale is to have fixed costs. • Using the previous model, assume each firm has to pay fixed cost of $784. • If firm A produced 60, firm B would earn profits of $116 (= $900 - $784) per period. • If firm A produced 64, firm B would choose to produce 28 [ = (120-64)  2].

18. A Numerical Example • Total output would equal 92 with P = $28. • Firm B’s profits equal zero [profits = TR - TC = ($28·28) - $784 = 0] so it would not enter. • Firm A would choose a price of $56 (= 120 - 64) and earn profits of $2,800 [= ($56·64) - $784]. • Economies of scale along with the chance to be the first mover yield a profitable entry deterrence.