Game theory at war: Battle of the Bismarck Sea

In late February 1943, Japanese commander Rear-Admiral Kimura had assembled a convoy of sixteen transport ships and destroyers at the port of Rabaul. Admiral Kimura’s mission was to bring the convoy to Lae, on the mainland of New Guinea. American Lieutenant-General Kenney, commander of Allied Air Forces in the area, was ordered to intercept and destroy the Japanese convoy.

Admiral Kimura had to choose between sailing along a northern route through the Bismarck Sea and a southern route. Meteorologists forecast that there would be rain on the northern route, which would reduce visibility. Weather on the southern route, however, would be fine.

General Kenney had to decide the direction in which to concentrate his reconnaissance aircraft. Once his aircraft spotted the Japanese convoy, Kenney would dispatch his bombers. The dilemma for Kenney was that his best decision depended on what he believed Kimura would do.

Table 10.2 represents the Battle of the Bismarck Sea in strategic form. In each cell, the first entry represents the number of days of bombing that Kenney could inflict on the Japanese, while the second entry represents the number of days of bombing that Kimura would suffer.

Using the arrow technique, we can solve the Nash equilibrium, which is for Kenney to fly north and Kimura to sail north. Indeed, on February 28, Admiral Kimura set out on the northern route. General Kenney’s reconnaissance planes discovered the Japanese convoy on March 2. In two days of massive aerial raids, Kenney’s bombers destroyed the Japanese convoy.

Sources: O. G. Haywood, “Military Decision and Game Theory,” Journal of the Operations Research Society of America 2, no. 4 (November 1954): pp. 365-85; and J. Rohwer and G. Hummelchen, Chronology of the War at Sea, 1939-45, vol. 2, trans. Derek Masters (London: Ian Allan, 1974), p. 306.

OPEC: dilemma of an oil cartel

The Organisation of Petroleum Exporting Countries (OPEC) includes major oil producers Saudi Arabia, Iran, Kuwait, and Venezuela. Like any other cartel, OPEC suffers from the problem that individual members prefer to exceed their quotas. From a short-term perspective, no matter what others do, each member’s best strategy is to cheat.

In November 1994, OPEC members met to decide production quotas for the following year. Iran’s oil minister Gholamreza Aqazadeh remarked, “it will be very good for the market . . . I hope everybody will agree to the quota without violations”. Twelve months later, it was estimated that Venezuela had exceeded its 2.359 million barrel per day (bpd) quota by 300,000 bpd.

Besides cheaters within the cartel, OPEC had also to contend with high output from non-member countries. In June 1998, OPEC agreed that its members would reduce production by 2.6 million bpd, and non-members Mexico, Norway, Oman, and Russia by 500,000 bpd. Saudi oil minister Ali Ibrahim Naimi was cautiously optimistic: “I don’t think that anybody expects 100% compliance. . . . Is three million bpd going to be pulled out of the market? Probably not. But is 2.5 million? That is still good.”

Predictions of the impending demise of the OPEC cartel or its continued importance abound. As late as 2001, OPEC was referred to as a “historically doomed organization” but the subsequent rise in oil prices to record levels has led many to question this prediction. Oil production data indicate that OPEC production (April 2006) was 27.94 mbd, almost equal the total OPEC quota target of 28 mbd, although 6 of the 10 OPEC members (excluding Iraq) were exceeding their individual quotas. A recent assessment of the future of OPEC states that “Large price swings reveal errors in forecasting and execution, not a lack of power to move the price.”

Sources: “Producers Maintain Oil Output Ceilings,” South China Morning Post, November 23, 1994, Business Post, p. 14; “OPEC Fears Quota Cheats May Hurt Price,” South China Morning Post, November 23, 1995, Business Post, p. 9; “Saudi Minister Expects Nations to Cheat on New Oil-output pact,” Asian Wall Street Journal, June 26-27, 1998, p. 27; Matt Taibbi, “The Motherland Arises,” the exile, #130, November 29, 2001; Platts OPEC Guide, April 2006 (www.platts.com); Theodore W. Boll, “OPEC and the High Price of Oil,” A Joint Economic Committee Study, US Congress, November 2005.

American Football: how a cartel controls cheating

The National Football League (NFL) is the most successful sports league in the U.S., with revenues of about $6 billion per year and labor costs which have only grown by 9% a year since 1990 (compared with 12-16% annual growth in the other major sports leagues: baseball, basketball, and hockey). This, “one of the world’s most effective cartels,” can be attributed to a number of structural factors, as well as good management and good luck. Team owners share roughly 70% of their revenues, negotiate television contracts as a single entity, and has an effective salary cap, all of which transform the incentives from individual profits to maximizing cartel profits.

“The trouble with revenue sharing, however, is that it can encourage free-riders.” An example is the Cincinnati franchise which was the NFL’s fifth most profitable during the 1990s, but which won the fewest number of games. “The team simply skimped on avoidable costs, such as talent scouts, and raked in revenues from the rest of the league.” This is the NFL’s version of cartel cheating.

The NFL limits this problem by allowing individual teams to keep all revenue from a few high-growth segments, such as luxury boxes. Owners have incentives to build new stadiums – 17 of which have been newly constructed or overhauled since 1989. These incentives have also been bolstered by the league leaving at least one major city without a franchise. The threat of teams moving to such cities has been effective at getting cities to provide money and tax breaks for construction of new stadiums. Such incentives provide a counterbalance to incentives by individual teams to free ride on the investments made by other teams.

Source: “In a league of its own,” The Economist, April 29th, 2006, pp. 63-64.

Price promotions: randomization in retailing

For retailers such as supermarkets, a major competitive challenge is how to attract price-sensitive customers without sacrificing profit from the less price-sensitive segment. The typical retailer has two alternative pure strategies: maintain a high price or offer a discount price.

Consider the high-price strategy. This may extract the buyer surplus of the less price-sensitive customers but fails to attract the price-sensitive customers. By contrast, if the retailer chooses the alternative discount-price strategy, it will attract price-sensitive customers but must forgo the full buyer surplus of the less price-sensitive customers.

There is an intermediate alternative: randomize between the high price and the discount price. When a retailer adopts a randomized pricing strategy, its pricing will not be predictable. It then will be more difficult for competitors to take away potential customers. In retailing, a strategy of randomization is an effective way of mitigating the intensity of competition.

Note that the retailer should discount its price at random and not in a predictable way. Suppose, for instance, that Safeway Supermarket announces that it will cut the price of Huggies diapers by 10% in the first week of every month. Competing stores can then respond with even lower prices in the first week of each month, thus, undermining Safeway’s discount. This example shows that price discounts must be random and not predictable.