Lecture 7: The Prisoners' Dilemma and Other Games with Dominant Strategy

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For thirteen weeks across Econ 50 and 51, we have looked at what economists call the neoclassical model of markets and prices. With a couple of exceptions we have been dealing with price-taking behavior: both consumers and firms take market prices as given, and decide how much of a good to buy or sell.

This is a great model for deciding how much gasoline people buy. They drive by a gas station, see the posted prices, and decide whether to stop or not. If they do stop, they pay the posted price; they don’t walk into the mini mart and start negotiating with the cashier over the cost of a gallon of gas. Furthermore, while the buying decisions of millions of drivers constitute the demand curve for gasoline, the impact any one driver has on the global market for gasoline is infinitesimally small.

However, this isn’t such a great model for looking at the behavior of oil companies. There are only a few major oil companies in the world (Saudi Aramco, ExxonMobil, and Chevron are the biggest). If one of them dramatically increases production, it lowers the price of oil for all of them. If one invests heavily in renewable energy, the others have to decide how to respond: to compete, or to refocus on fossil fuels?

Fundamental to analyzing the behavior of these oil companies is the realization that they are acting strategically: when they make a decision, they’re not just thinking about their customers; they’re also thinking about their competitors. Saudi Aramco thinks about what ExxonMobil and Chevron are doing, and also thinks about how those companies will respond to what Saudi Aramco is doing. We call such an environment a strategic environment; and the study of strategic environments is called game theory.

Why a “game”? Well, think about what a game is. It has players, and it has rules about what those players can do, and what the outcomes are. We can model the strategic interactions between the oil companies by treating each one as a “player.” We can then write down a “game” that describes the things they might do, and describe then the outcome of each possible combination of what they do.

When “playing” such a game, it’s usually not enough to just think about yourself: you have to think about what the other players are doing, and develop a strategy for how you are going to approach the game.

What that strategy might look like depends on the nature of the game being played. Specifically, there are two important dimensions on which games differ:

Timing: In some games, like rock-paper-scissors, players choose their strategies simultaneously, without observing what the other player(s) are choosing. In other games, like chess, players take turns, observing the other players’ actions before taking their own. In still others, players play a simultaneous game repeatedly.
Information. In some games, all relevant information is known to all players – for example, all moves in chess are taken out in the open. But in many games, like poker (in which players are dealt hands that only they see), one or more players has private information.