Competitive solutions: The strategist's toolkit

Competitive Solutions: The Strategist's Toolkit

Volumn , Issue , 2009, Pages

  McAfee, Preston ^a  

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References (155)

1. Pankaj Ghemawat, Games Businesses Play: Cases and Models (Cambridge and London: MIT Press, 1977), is a partisan for game theory but summarizes both sides well.
2. This delightful insight was first presented, as far as I can tell, in Adam M. Brandenburger and Barry J. Nalebuff, Co-opetition (New York: Doubleday, 1996).
3. The source for this observation, as well as several below, is the entertaining book by Kara Swisher, AOL.COM: How Steve Case Beat Bill Gates, Nailed the Netheads, and Made Millions (New York: Times Books, 1999), p. 97.
4. See "This Is Not Your Father's Prodigy," Wired, December 1993.
5. These ideas are taken from Professor Dale Stahl's "Evolution of Smart-n Players," Games and Economics Behavior 5, no. 4 (October 1993): 604-617.
6. "Pushing Deeper into Services," Business Week, 28 October 1996.
7. Chicago Tribune, 20 January 2001, section 2, p. 1.
8. Harold Hotelling, "Stability in Competition," Economic Journal 39, no. 15 (March 1929): 41-57. Interestingly, this paper contains a much more substantial theory than is usually credited to Hotelling. In particular, the "Hotelling line model" is usually meant to signify competition in location but not in prices; in fact, Hotelling analyzes price competition first.
9. There is no determinate solution to the location problem for three firms. With four firms, one obtains two next to each other one-fourth of the way down the line, and the other two next to each other three-quarters of the way down the line.
10. Poor-quality food combined with good ambiance coexist in some markets like hotels, because there is little opportunity for repeat business.
11. This seems to have been an important insight of Microsoft cofounder William Gates Jr., along with the observation that software could be more valuable than hardware. See, for example, the compelling article by John Heilemann, "The Truth, the Whole Truth, and Nothing but the Truth: The Untold Story of the Microsoft Case," Wired, November 2000.
12. Ghemawat, Games Businesses Play, chap. 5.
13. Quoted in the New York Times, 31 October 1971. Several sources suggest a slightly different quote.
14. Nicole Shepler, "Developing a Hedonic Regression Model for Camcorders in the U.S. CPI," Bureau of Labor Statistics (Washington, D.C.: U.S. Government Printing Office,2000). I have adjusted her numbers to express them in the percentage of base prices rather than logarithms, and I have not reported all categories.
15. Statistical Abstract of the United States, 2000. See http://www.census.gov/statab/www/.
16. Steven Klepper, "Entry, Exit, Growth and Innovation over the Product Life Cycle," American Economic Review 86, no. 3 ( June 1996): 562-583.
17. Statistical Abstract of the United States, 2000. The current boom in patent filings may not indicate increased technological development so much as an increased ability to patent software, business methods, and other formerly unpatentable discoveries.
18. The mathematical derivations are available in R. Preston McAfee, "Production Capacity for Durable Goods," in C. Holsapple, V. Jacob, and H. R. Rao (eds.), Business Modeling: Multidisicplinary Approaches (London: Kluewer Academic, 2002).
19. It is profitable to sell the good if rc < 1; if rc ≥ 1, the good will not be sold.
20. Robert H. Porter, "A Study of Cartel Stability: The Joint Executive Committee, 1880-1886," Bell Journal of Economics 14, no. 2 (Autumn 1983): 301-314.
21. Robert H. Porter, "On the Incidence and Duration of Price Wars," Journal of Industrial Economics 33, no. 4 ( June 1985): 415-426.
22. Timothy Bresnahan, "Competition and Collusion in the American Automobile Industry: The 1955 Price War," Journal of Industrial Economics 35, no. 4 (June 1987): 457-482.
23. Jon Joyce, "Effect of Firm Organizational Structure on Incentives to Engage in Price Fixing," Contemporary Policy Issues 7, no. 4 (October 1989): 19-35.
24. Peter Bryant and Woodrow Eckard estimate that the probability of a price-fixing cartel being charged is 15% per year. They study cartels that are eventually caught and acknowledge that there might be some cartels that disband prior to detection, and thus are never caught. Clearly we cannot observe the duration of cartels that are never detected. This is an entertaining example of sample selection bias, a topic discussed in chapter 10. Peter Bryant and Woodrow Eckard, "Price Fixing: The Probability of Being Caught," Review of Economics and Statistics 73, no. 3 (August 1991): 531-536.
25. This is the nature of cartel pricing-the prices are higher than the competitive prices. By definition, competitive prices are the prices at which each firm or country can sell all it wants to sell.
26. Martin Pesendorfer, "A Study of Collusion in First-Price Auctions," Review of Economic Studies 67, no. 3 ( July 2000): 381-411.
27. This discussion is based on R. Preston McAfee and John McMillan, "Bidding Rings," American Economic Review 82, no. 3 ( June 1992): 579-599.
28. Ghemawat, Games Businesses Play, table 2.4, p. 55.
29. W. Kip Viscusi, John M. Vernon, and Joseph E. Harrington Jr., Economics of Regulation and Antitrust (Cambridge and London: MIT Press, 1992);
30. Nancy L. Rose, "The Incidence of Regulation Rents in the Motor Carrier Industry," Rand Journal of Economics 16, no. 3. (autumn 1985): 299-318.
31. A formal analysis of incrementalism is presented in Anat R. Admati and Motty Perry, "Joint Projects without Commitment," Review of Economic Studies 58, no. 2. (April 1991): 259-276.
32. Michael E. Porter, Competitive Advantage: Creating and Sustaining Superior Performance (New York: Free Press, 1985), p. 511.
33. Paul Milgrom and John Roberts, Economics, Organization and Management (Englewood Cliffs, N.J.: Prentice-Hall, 1992).
34. See Marius Schwartz and Earl A. Thompson, "Divisionalization and Entry Deterrence," Quarterly Journal of Economics 101, no. 2 (May 1986): 307-321;
35. and Michael R. Baye, Keith J. Crocker, and Jiandong Ju, "Divisionalization, Franchising, and Divestiture Incentives in Oligopoly," American Economic Review 86, no. 1 (March 1996): 223-236.
36. R. H. Coase, "The Nature of the Firm," Economica (New Series) 4, no. 16 (November 1937): 386-405.
37. See, for example, Oliver Williamson The Economic Institutions of Capitalism: Firms, Markets and Relational Contracting (New York: Free Press, 1985).
38. Paul R. Milgrom, "Employment Contracts, Influence Activities, and Efficient Organizational Design," Journal of Political Economy 96, no. 1 (February 1988): 42-60.
39. Coase, "The Nature of the Firm," pp. 386-405.
40. Martin Weitzman, "Prices versus Quantities," Review of Economic Studies 41, no. 4 (October 1974): 477-491.
41. Business Week, 2 October 2000, p. 78. The numbers provided in this article conflict with Business Week's M.B.A. calculator, described in its article of 22 October 2001, which puts the postgraduation salary increase at the more plausible figure of $40,000. Interestingly, the later article also makes the mistake of suggesting that the candidate maximize the return on investment rather than on the NPV-an error that suggests picking a less expensive school (Rutgers) over Wharton in spite of the latter's higher NPV.
42. William Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," Journal of Finance 19, no. 3 (September 1964): 425-442;
43. and John Lintner, "The Valuation of Risky Assets and the Selection of Risky Investment in Stock Portfolios and Capital Budgets," Review of Economics and Statistics 47, no. 1 (February 1965): 13-37.
44. James A. Brander and Tracy R. Lewis, "Oligopoly and Financial Structure: The Limited Liability Effect," American Economic Review 76, no. 5 (December 1986): 956-970.
45. R. Preston McAfee and John McMillan, "Bidding for Contracts: A Principal-Agent Analysis," Rand Journal of Economics 17, no. 3 (autumn 1986): 326-338.
46. Bengt Holmstrom and Paul Milgrom, "Multi-Task Principal-Agent Analyses: Linear Contracts, Asset Ownership and Job Design," Journal of Law, Economics and Organization (1991): 24-52.
47. A striking example of the difficulty of providing incentives to maintain trucks arose with a particular Domino's Pizza franchise in Jacksonville, Florida, which had over thirty trucks, but never more than four that ran at any given time in the author's experience, well prior to the "thirty minutes or it's free" campaign.
48. B. Douglas Bernheim and Michael D. Whinston, "Common Agency," Econometric 54, no. 4 ( July 1986): 423-442.
49. Edward R. Lazear and Sherwin Rosen, "Rank-Order Tournaments as Optimal Labor Contracts," Journal of Political Economy 89, no. 5 (October 1981): 841-864.
50. See also Joel Sobel, "A Re-Examination of Yardstick Competition," Journal of Economics and Management Strategy 8, no. 1 (spring 1999): 33-60
51. and Richard Fullerton and R. Preston McAfee, "Auctioning Entry into Tournaments," Journal of Political Economy 107, no. 3 (June 1999): 573-605.
52. These fines were instituted in 1974; the original fines were $5000, with a maximum imprisonment of one year.
53. U.S. v. Grinnell Corporation, 1966.
54. Malcolm R. Burns, "Predatory Pricing and the Acquisition Cost of Competitors," Journal of Political Economy 94, no. 2 (April 1986): 266-296.
55. Greg Sandoval, "FTC Says Toysmart Violated Net Privacy Law," CNET Technology News, 21 July 2000.
56. Baseball's exemption was enacted in 1922, and was ended by 1998 legislation. Other sports are not covered. The National Football League has repeatedly been found guilty of antitrust violations associated with restrictions on the free agency of players.
57. The major oil companies known as the "seven sisters" were prohibited from bidding jointly on off-shore oil for many years, but this restriction has been removed.
58. See Preston McAfee, Daniel Vincent, Michael Williams, and Melanie Havens, "Collusive Bidding in Hostile Takeovers," Journal of Economics and Management Strategy (winter 1993): 449-482, and "Collusive Bidding in the Market for Corporate Control," Nebraska Law Review 79 (2000).
59. United States v. Terminal Railroad Association, 224 US 383 (1912).
60. Generally, the guidelines call for the use of the shares of market capacity rather than of production or sales. Thus, potential entrants' capacities might be included, even if the firms had zero sales. McAfee et al., "Collusive Bidding."
61. 2 = 2xy.
62. Jerry Hausmann and Gregory Leonard, "Documents versus Econometrics in Staples," see www.antitrust.org/cases/staples/hausleon.html; and
63. Jonathan B. Baker, "Econometric Analysis in FTC v. Staples," paper presented to the American Bar Association, Antitrust Section, Economies Committee, 18 July 1997.
64. Source: http://www.antitrust.org/cases/mergers.htmpencase.
65. Commissioner Christine Varney, "Vertical Merger Enforcement Challenges at the FTC," speech presented before the 36th Annual Antitrust Institute, San Francisco, California, 17 July 1995.
66. This case was viewed as a pure vertical merger. However, it could have been viewed as a merger of firms selling complementary products. As we observed earlier, such mergers tend to decrease prices-the integrated firm accounts for the external effect of the pricing of the two products-and therefore would be procompetitive.
67. Apparently Mark Twain attributed this statement to Disraeli, but an alternate source says the original involved lies, damned lies, and church statistics.
68. The 0.48 can be calculated from 1 - 0.16 - 0.36, but it also can be calculated because the probability of DR and the probability of RD are each 0.4 x 0.6 x 0.24, and either give one of each.
69. To compute the odds of two Rs and one D, note that there are three distinct ways to produce that outcome-RRD, RDR and DRR, each of which has probability 0.4 x 0.6 x 0.6 x 0.144, or 14.4%.
70. 24.
71. The third measure of the typical outcome is the mode, which is the most frequent outcome. The mode, while being more frequent than other outcomes, need not be frequent, and for this reason is less common as a measure of the usual outcome.
72. 2).
73. 2 + 0.9999 x 102.
74. 2 = 7,110,393.
75. 2/n, which is the variance. The square root of this formula, with σ ≤1/2, gives the result.
76. The data come from the Educational Testing Service by way of Professor P. B. Stark. Posted on the Web at http://www.stat.Berkeley.edu/users/stark/SticiGui/Text/index.htm.
77. These methods were introduced in 1979 in James Heckman, "Sample Selection Bias as a Specification Error," Econometrica 45 (1979): 153-161. Now, most statistical packages include methods for sample selection bias correction.
78. David Dranove, Daniel Kessler, Mark McClellan, and Mark Satterthwaite, "Information Is Good Except When It Is Not: The Effects of Health Quality Report Cards," Northwestern University, unpublished manuscript.
79. This line of research was initiated by T. R. Gilovich, R. Vallone, and A. Tversky, "The Hot Hand in Basketball: On the Misperception of Random Sequences," Cognitive Psychology 17 (1985): 295-314.
80. 6, or 1 in 64. Thus, the odds of getting five or more heads in a row is seven in sixty-four. The analysis of runs of tails is symmetric. However, the outcomes HHHHHTTTTT and TTTTTHHHHH are counted twice, as they have both a run of heads and a run of tails.
81. I don't mean this to be an explanation-what superficially makes sense, doesn't. As a player improves, the likelihood of a string of successes increases, and the likelihood of a string of failures falls. Thus, if a player's success rate is increased from, say, 40% to 60%, the odds of a string occurring is unchanged. However, it may be that people perceive strings of successes more readily than strings of failures.
82. Judith Chevalier and Glenn Ellison, "Are Some Mutual Fund Managers Better than Others? Cross-sectional Patterns in Behavior and Performance, Journal of Finance 54, no. 3 ( June 1999): 875-899.
83. If a stock is consistently riskier in a way that can't be diversified, the stock will have a higher average return, as compensation to the bearers of risk. This is a pattern that can be seen from past performance. However, future peaks and troughs cannot be detected from past behavior.
84. There are many other terms of the same two broad pricing strategies. Classically direct and indirect price discrimination were known as third- and second-degree price discrimination, respectively, a tortured nomenclature. Direct price discrimination is also known as characteristics based, while indirect is known as menu based or self-selection, terms that are informative concerning the method of price discrimination.
85. Raymond Deneckere and R. Preston McAfee, "Damaged Goods," Journal of Economics and Management Strategy 5 (summer 1996): 149-174.
86. George Stocking and M. Watkins, Cartels in Action: Case Studies in International Diplomacy (New York: Twentieth Century Fund, 1946), pp. 402-405.
87. Wolfgang Pesendorfer, "Design Innovation and Fashion Cycles," American Economic Review 85, no. 4 (September 1995): 771-792.
88. Deneckere and McAfee, "Damaged Goods."
89. Ronald Rudkin and David Sibley, "Optional Two-Part Tariffs: Toward More Effective Price Discounting," Public Utilities Fortnightly, 1 July 1997.
90. Copyright © 1998 Alan H. Hess. Originally printed in Travel Weekly, October 1998. Reproduced by permission of the author.
91. This is the per unit cost of the last few units. Thus, when an additional shift must be instituted to increase production, the marginal cost includes the wages of the additional workers, overtime pay required for existing workers, added wear and tear on equipment, and other charges that arise because of the added shift. The marginal cost would not include fixed costs like factory space unless that space had to be enhanced, and then the incremental cost would reflect the cost of enhancements.
92. The elasticity of demand gives the percentage decrease in quantity associated with a 1% price increase.
93. For example, a diabetes medicine that sells for $46.00 in the United States sells for $6.75 in Mexico. Austin American-Statesman, 19 June 2000, p. 1.
94. According to some recent work by the author, offering two options does quite well in many circumstances; diminishing returns are strong in relation to the number of items in the menu of options. In contrast, the full theory, as presented by Robert Wilson's 1993 classic, Nonlinear Pricing (Oxford: Oxford University Press; in association with the Electric Power Research Institute, 1993), requires massive computing effort.
95. There is a corresponding theory of optimal taxation-the theory seeks to minimize the distortion of taxation subject to a revenue constraint-that posits a menu of taxes with taxpayers choosing at the beginning of the year which category they fall into, and paying a fixed amount to reduce their marginal tax rate. Such schemes create problems of bankruptcy in a world with uncertainty and hence tend to be fatally flawed for taxation, while quite successful for pricing, where bankruptcy created by the pricing scheme is rarely an issue.
96. An interesting piece of evidence for the claim that brand-name drugs do not compete directly with generics is that when generics come into existence, the price of the branded drug rises on average. This makes sense from a price-discrimination perspective. Prior to the introduction of generics, the brand name served both the high-value and lowvalue markets, with a corresponding intermediate price. After the generic is introduced, the brand name serves only the highest-value, most inelastic customers, with a correspondingly high price.
97. Product branding has many functions other than price discrimination including signaling quality and commitment to uniformity.
98. ABC Morning News 11 July 2000.
99. In some cases, it is desirable to charge a premium for the bundle. Arbitrage is a major problem because consumers can simply make two independent purchases. Arbitrage may be preventable in services, where it is possible to observe who buys what products. However, charging more for the bundle is an invitation to competitors to skim off the best customers by offering lower single-good prices.
100. This logic was discovered by R. Preston McAfee, John McMillan, and Michael D. Whinston, "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," Quarterly Journal of Economics 104, no. 2 (May 1989): 371-383.
101. Business Week, 16 October 2000, p. 60.
102. This analysis is based on Philip Pfeifer, "The Airline Discount Fare Allocation Problem," Decision Sciences 20, no. 1 (1989): 149-157.
103. R. B. Childs, "Home Video," in J. E. Squire (ed.), The Movie Business Book, 2d Fireside ed. (New York: Simon and Schuster, 1992); reported by Ashutosh Prasad's Ph.D. dissertation, University of Texas, 1999, which is the source for other information about the timing of video release.
104. Indeed, as Adam Brandenburger and Barry Nalebuff eloquently argue, doing the opposite is the most desirable way to insure cooperation and soften price competition, a theme expanded above. See Brandenburger and Nalebuff, Co-opetition.
105. The current version of Microsoft Word is also cheaper for users of past versions of Word, for precisely the same reason-earlier versions of Microsoft Word are competitors to the current version.
106. Daily Telegraph, 27 June 1994.
107. This is based a true story. A court-mandated seal prohibits revealing the identities of the franchiser, so the numbers have been changed to disguise the company. The courts prohibited the company from decertifying the suppliers without a quality-based reason.
108. Paul Joskow presents a fascinating and comprehensive study of these solutions. See Paul L. Joskow, "Contract Duration and Relationship-specific Investments: Empirical Evidence from Coal Markets," American Economic Review 77, no. 1 (March 1987): 168-185.
109. The text oversimplifies a bit; in reality, the complementarities are more complex. Some capture cards are bundled with software products of three or more different firms and include software that coordinates all of the software products. Some software products are also designed to work together as well.
110. Value refers to willingness to pay for the particular item. Thus, a bidder may have a use value of $10,000 for a computer, but be willing to pay only $2000 for a particular computer because of the existence of substitute computers. The value of the particular computer is $2000; at any price over $2000, the buyer will substitute another computer.
111. The price will not generally equal the second-highest value, because of bid increments- the minimum increase permitted by the auctioneer. It is a remarkable fact that bid increments have little substantive effect even at high levels. For example, a 10% bid incre-ment, which seems like a lot, typically has less than a 1% effect on the efficiency of the process. The reason is that the likelihood the increment matters to the outcome is approximately the value of the increment, and the amount that it matters is, on average, half the increment. Thus, the effect of a 10% increment tends to be 10% of 5%, or 0.5%.
112. With major projects and significant variation in expected values, a deeper analysis is appropriate. In addition to adjusting for the winner's curse (discussed below), winning bids usually won't be proportional to value, and may depend on factors other than just the value estimate. These other factors can be handled by using a multivariate regression with a heteroskedasticity correction. While such an analysis requires a much more complex and detailed statistical and economic analysis, the logic of the analysis is the same as the present discussion.
113. The standard deviation can be indirectly estimated by the variation in the bids, using the formula for computing the standard deviation shown in chapter 10.
114. Other reasons for the winner's curse correction to vary include nonnormality or skewness in the distribution, compactness or a finite variance of the true value (the corrections sent the variance of the true value to infinity), and a mixture of common and private value aspects of the auction environment. The model presented sets the estimates to be v ε, where the true value is v and errors are independently distributed.
115. The statistical mechanics of updating projections is akin to updating actuarial tables for new information. Imagine calculating life expectancy for a forty-year-old male, and finding it is seventy-five years. When you learn the male is not a smoker, life expectancy rises to eighty years. Add a history of heart trouble, and it falls. Updating bids is analogous-high bids by others reflect high estimates, which can be deduced approximately by removing winner's curse corrections, which leads to recovery of a floor for their underlying estimates. That floor can be folded into one's own estimates.
116. See, for example, the references in R. Preston McAfee and John McMillan, "Auctions and Bidding," Journal of Economic Literature 25, no. 2 ( June 1987): 699-738.
117. This result and several others used in this section were developed in the remarkable paper by Paul R. Milgrom and Robert J. Weber, "A General Theory of Auctions and Bidding," Econometrica 50, no. 5 (September 1982): 1089-1122.
118. R. Preston McAfee and John McMillan, Incentives in Government Contracting (Toronto: University of Toronto Press, 1988).
119. R. Preston McAfee and Daniel Vincent, "The Declining Price Anomaly," Journal of Economic Theory 60, no. 1 ( June 1993): 191-212.
120. This auction was developed by Paul Milgrom, Robert Wilson, and R. Preston McAfee.
121. See John McMillan, "Selling Spectrum Rights," Journal of Economic Perspectives 8, no. 3 (summer 1994): 145-162.
122. See Jeremy Bulow and Paul Klemperer's intriguing article, "Auctions vs. Negotiations," American Economic Review 86, no. 1 (March 1996): 180-194.
123. This feature of auctions is emphasized by Alejandro M. Manelli and Daniel R. Vincent, "Optimal Procurement Mechanisms," Econometrica 63, no. 3 (May 1995): 591-620.
124. Ralph Blumenthal, New York Times, 22 April 2000.
125. The theory of signaling was pioneered by Michael Spence in his Harvard dissertation, with a portion published as "Job Market Signaling" (Quarterly Journal of Economics 87, no. 3 [August 1973]: 355-374), with the education application.
126. Cited in the Journal of the American Bar Association (August 2000): 70.
127. Business Week, 26 February 2001, p. 33.
128. Business Week, 19 March 2001.
129. This is an example of a more general phenomenon of signaling commitment by investing in "specific assets," which are assets that are useful only in a particular relationship. Thus, by investing in assets useful for one business but not for others, one signals a commitment to that business.
130. See the wonderful survey by Tamara Kaplan, "The Tylenol Crisis: How Effective Public Relations Saved Johnson & Johnson," on which this section is based, in Scott Cutlip, Allen Center, and Glen Broom, Effective Public Relations (Englewood Cliffs, N.J.: Prentice- Hall, 1994).
131. "Circuit Flaw Causes Pentium Chip to Miscalculate, Intel Admits," New York Times, 24 November 1994.
132. Mark Mowrey, "Do Expiries Matter?" The Standard, 10 April 2000.
133. The issue of the informational content of willingness to trade was pioneered by George Akerlof, "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism," Quarterly Journal of Economics 84, no. 3 (August 1970): 488-500. The ultimate expression of this work is presented in Paul Milgrom and Nancy Stokey, "Information, Trade and Common Knowledge," Journal of Economic Theory 26, no. 1 (February 1982): 17-27.
134. Further Reading: Upside Magazine, May 2001.
135. To be fair, this is a line in the Rolling Stones's song, "Start Me Up," used to introduce Windows 95.
136. Stefanie Olsen, Staff Writer, CNET News.com 8 April 2000.
137. This issue has a long confused history in the economics literature. The main source of the confusion will become clear in the analysis-signaling doesn't work in all circumstances. The confusion was resolved by Paul Milgrom and John Roberts, "Limit Pricing and Entry under Incomplete Information: An Equilibrium Analysis," Econometrica 50, no. 2 (March 1982): 443-460.
138. See Benjamin Hermalin, "Toward an Economic Theory of Leadership: Leading by Example," American Economic Review 85, no. 5 (December 1998): 1188-1206.
139. David Kreps and Robert Wilson, "Reputation and Imperfect Information," Journal of Economic Theory 27 (1982): 253-279.
140. In the author's experience, the coffee itself provided a means of price discrimination. The coffee was enjoyable for locals and vile to Westerners, so it is a major accomplishment for a Westerner to sit and drink the coffee for hours on end.
141. Vaporware is also the name of a real company that sells real software for Amiga computers.
142. Mark Mehler, "From the Vaporware Hall of Fame," ZDNet, 18 May 1998, 8:30 A.M., EST.
143. Mary Ellen O'Toole, "The School Shooter: A Threat Assessment," Federal Bureau of Investigation, September 2000 (Washington, D.C.: U. S. Government Printing Office).
144. This analysis is based wholly on the much deeper analysis of Ariel Rubinstein, "Perfect Equilibrium in a Bargaining Model," Econometrica 50, No. 1 ( January 1982): 97-110.
145. 2 = 2c, which is 20% for c = 10%. This gives an expected duration of five years. For any event that happens with probability x per period, the expected time until the event happens is 1/x periods.
146. New York Times, 23 July 2000.
147. "Settlement Escrows," Journal of Legal Studies 24, no. 1 ( January 1995): 87-122.
148. Ghemewat P., Games Businesses Play.
149. Thomas Schelling, The Strategy of Conflict (Cambridge: Harvard University Press, 1960).
150. The downside of Wal-Mart's legal tactics, besides litigating cases it is likely to lose, is that it angers judges. See Business Week, 16 July 2001, pp. 58-59.
151. See Aaron Edlin and Stefan Reichelstein, "Holdups, Standard Breach Remedies, and Optimal Investment," American Economic Review 86, no. 3 ( June 1996): 478-501;
152. and Aaron Edlin, "Breach Remedies," National Bureau of Economic Research, October 1997. Expectation damages include two forms: compensatory damages, which reimburse the breached party for its loss, and consequential damages, which reimburse the breached party for its added costs of carrying out the contract with another party.
153. The concept of strategic ambiguity of contracts was pioneered by Douglas Bernheim and Michael Whinston, "Incomplete Contracts and Strategic Ambiguity," American Economic Review 88, no. 4 (September 1998): 902-932.
154. Alvin Roth and Xiaolin Xing, "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review 84, no. 4 (September 1994): 992-1044. This fascinating paper documents the phenomenon of offers made and accepted earlier than optimal, largely for the reason given-a less desirable partner makes an early offer to obtain agreement of a more desirable partner. What is perhaps the earliest example of an offer made and accepted occurs in the Arunta, a Stone Age aborginal tribe of Australia. Shortly after the births of a girl and a boy, the infant girl's prospective daughter is betrothed to the infant boy. That is, an infant girl becomes the planned mother-in-law of the infant boy.
155. Lars Stole and Jeffrey Zwiebel, "Organizational Design and Technology Choice under Intrafirm Bargaining," American Economic Review 86, no. 1 (March 1996): 195-222.