Game Theory and Prisoner's Dilemma: Determining Payoffs from Decision Making І The Great Courses

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Uploaded by on May 17, 2011

http://www.thegreatcourses.com/gametheory

If you're old enough to remember watching TV before 1971, you probably remember cigarette commercials on TV: "Me and my Winstons"; "Come all the way up to Kool"; "I'd rather fight than switch" (that's for Tareyton); "You've come a long way, baby" (Virginia Slims, the "women's cigarette"); and of course, Chesterfield's 101s, "A silly millimeter longer." I watched way too much TV. The commercials disappeared as a result of negotiations between the federal government and the four major tobacco companies: American Brands, Liggett & Myers, Philip Morris, and Reynolds. In 1964, the surgeon general's report linking smoking to lung cancer came out. So an argument could be made for a desire on the part of the tobacco companies to protect people from cancer.

I'm afraid I'm a bit cynical about this, especially in light of how hard those companies worked to prevent [publicizing] the links [among] cancer, smoking, and addiction in the years before 1964. But then, why would the cigarette companies agree to a ban on advertising? The answer is that it got them out of a prisoner's dilemma.

Before the ban, the decision of whether to advertise or not was really a fourplayer game among the four tobacco companies, but we won't miss any of the salient points if we boil it down to just two companies, say Eagle Tobacco and Dan'l Boone, to keep me out of legal trouble. Why advertise? Yes, it does persuade some nonsmokers to take up the habit, but the biggest payoff is tempting smokers to switch from another brand to yours. We're talking about a big market: In the 1960s, about 40% of all Americans smoked—40%. I've looked for the profit data; in the 2000s, it looks like something like a $3-billion-a-year market for American smokers. I don't know what it might have been in 1971, but the exact figure doesn't matter for this analysis. Let's use the $3 billion figure, and let's keep things simple.

Assume that each company has only two strategies: Advertise on TV or don't. TV ads will cost a company $500 million and will increase the number of smokers by 5%. But the more important part is if you advertise and your opponent doesn't, you'll capture 80% of the market. If you both do the same thing—both advertise or nobody advertises—you split the market evenly.

I have enough information to construct the payoff matrix for profits, and here it is, expressed in millions of dollars of profit per year for the company. You know how to analyze this: Look for dominant strategies. You'll find out that both players have them. Regardless of which choice one makes, the other one is better off advertising. Each player plays the dominant strategy, and the result is that both advertise, making $1.15 billion each. If neither had advertised, they would have each made $1.5 billion.

You can see why I wasn't too worried about the exact size of the payoffs. The truth is that they don't matter. All I need is that the preferences go [as follows]: best, my ads only; then, no ads; then, both ads; then worst, your ads only. These ordinal payoffs generate a prisoner's dilemma again. Both companies would prefer the solution of no ads, but to protect their market shares, they both have to run them.

Now you can see why the cigarette companies were only too happy to agree to the government ban on TV ads. The government removed the other three squares from this matrix, leaving only the lower-right cell. All that was left was the Pareto-optimal solution that the tobacco companies desired anyway but couldn't sustain on their own.

In this particular case, I consider this a win-win-win situation. Both companies make more money, and the size of the market is slightly curbed. Not all legislation has so happy an effect. When we talk about co-opetition, we'll see how some of the federal government's policies—for example, with Medicaid drug pricing—actually raised the prices that they paid.

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