An Intro to Game Theory

The scene was a crowded classroom, and the two men standing several paces apart were holding sponges rather than dueling pistols, but Benjamin Polak, professor of economics and management at Yale SOM, wanted the audience to at least pretend this was 19th century Russia rather than 21st century New Haven. “The rules are simple,” he told the group on April 8. “Either throw the sponge or take a step forward.” The duel would go several rounds, with each competitor either throwing the sponge or moving forward until one man had been hit. Polak then added: “Gentlemen never duck.”

This damp duel, inspired by Polak’s readings of Tolstoy and Pushkin, was more than just a reenactment to test the mettle of two professors at the Yale Graduate School of Arts and Sciences. Polak was speaking to the audience as part of the Graduate School’s Dean’s Lecture Series, which brings professors from across Yale to discuss their disciplines. While the imaginary Russian setting may have appealed to the literature students in attendance, Polak staged the duel to make a larger point about business. “Say there are two firms looking to launch similar products,” he said. “What if there’s room in the market only for one product? If a firm launches too late, the rival has gained a powerful foothold. If a firm launches too early, the customer is going to reject the product and the competition will waltz right in.”

This hypothetical product launch is an instance where game theory could be used to help determine the best time to act. Over the course of his lecture, titled “Game Theory for Humanists,” Polak walked the audience through the reasoning behind game theory, using the sponge duel as his example. In the case of two men of known, but varying skill, Polak showed how one could use backward induction to find the spot where each should launch the sponge. Backward induction begins at the end — in this example, where the two men would have advanced until standing nose-to-nose if neither threw their sponge — and moves toward the start date by running through the necessary equations. The technique, he said, can help discover an answer that remains unclear through standard induction.

Such reasoning, Polak said, should result in each player launching the sponge at exactly the right moment each time. But as he’s run the game with undergraduates and MBA students, he’s found that time and again, players throw the sponges too soon and miss, thus dooming themselves. The problem could be overconfidence, a well-known issue to behavioral economists. But Polak suggested something else might be at work — something less universal. “I think Americans have a pro-active bias,” he said. “Americans are bred from age zero to be proactive. If you watch ESPN and they interview an athlete after a loss, he always says, ‘We lost the game but at least we controlled our own destiny.’ Americans are taught that doing things is a virtue in itself. But the lesson of game theory is sometimes it’s better to wait. The point is not to go down swinging. The point is not to go down.”