# Game Theory

Economists have discovered that game theory is useful for understanding the behavior of oligopolists. **Game theory** looks at the outcomes of decisions made when those decisions depend upon the choices of others. In other words, game theory is a study of interdependent decision-making. One game that is particularly applicable to the study of oligopoly is the prisoner's dilemma.

Two men, Adam and Karl, are picked up by the police on suspicion of burglary. The chief investigator knows that she has little evidence against the men and is counting on a confession from either one or both in order to prosecute them for burglary. Otherwise, she can only prosecute them for unlawful trespass.

Upon entering police headquarters, the men are immediately separated and taken to different rooms for interrogation. The interrogator individually informs Adam and Karl that if one confesses to the crime and implicates his partner while the other remains silent, then the one who confesses will receive a two-year jail sentence while the silent partner will likely serve a ten-year sentence in a notorious prison. If both confess, then they will likely each serve a three-year prison sentence.

What is the best strategy for Adam and Karl? If they could get together and collude, both would probably decide that it would be wise to remain silent and serve a one-year jail term for unlawful trespass. However, they are unable to collude, so they each must consider their options. Adam thinks to himself, “If I confess, then I'll either go to jail for two years or three years. If I'm silent, then I'll spend a year in jail or go to prison for ten years.” Karl thinks exactly the same thing. Because they are separated and have no idea what the other is doing, they both confess in order to avoid a possible tenyear prison sentence. They both end up doing three years in jail. This logical conclusion is referred to as a **dominant strategy**.

Organized crime enjoys much of its success in evading prosecution to a good understanding of game theory. You talk, you die. That completely changes the payoff in the prisoner's dilemma and helps to explain why prosecutors find it difficult to get confessions from members of organized crime.

## Game Theory in Business

Some business decisions follow the same logic. Assume in an isolated small town there are only two gas stations and they are out of direct sight from each other. By law they are only allowed to change their price once a day. Each firm has two pricing options available to them. They can charge a high price or a low price. From past experience they know that when they both charge a high price, they both profit by $1,000. When one charges a high price and the other a low price, then the high-priced station earns $300 in profits while the low-priced station earns $1,200. When they both charge a low price then profits are $750 for each.

If given the chance to collude, which strategy would they both take? Given collusion, both would agree to set a high price for gas and each would earn daily profits of $1,000. What should the gas stations do if they are unable to collude? The thinking goes like this. “If I charge a high price, I'll either earn $1,000 or $300. If I charge a low price, I'll either earn $1200 or $750.” Because the firms are out of sight from each other and have no legal way to know the other's pricing strategy, then their best course of action or dominant strategy is to set a low price, which guarantees at least $750 in profits and as much as $1200. Just like in the prisoner's dilemma, when the players do not have the ability to collude, they select a strategy that results in an outcome that is not necessarily the one that maximizes profits.

Mathematician and game theorist John Nash is the subject of the film **A Beautiful Mind**. John Nash won the Nobel Prize in economics in 1994 for his contributions to the field. A Nash equilibrium is said to exist if a player has no incentive to independently change his course of action in a game.

Unlike the prisoner's dilemma, which is a one-time game, firms compete against each other day after day. Given the chance to play the “game” over and over results in something called **tacit collusion**. By playing a game of tit for tat, the firms can eventually reach a point where they both charge a high price and maximize their profits. How does it work? Assume that on the first day, both gas stations charge a high price. Both earn profits of $1,000. On the second day, one of the stations charges a high price, but the other cheats and charges a low price to earn profits of $1,200. Predictably, the next day the other station retaliates and lowers its price, resulting in profits of $750 for each. Eventually both gas stations come to the realization that if they both set a high price and do not cheat, they both will earn higher profits in the long run. They learn that if they cheat, their additional profit for the next day will not offset the lower profits that will ensue.