Game theory is the study of conflict and cooperation between intelligent rational decision-makers. Game theory and the famous Prisoner’s Dilemma model explains why, throughout history, OPEC has had only limited success at controlling the supply curve.

In the Prisoner’s Dilemma example, let’s assume there are just two parties, both cannot communicate, and they are separated in two individual rooms. The normal game is shown below:

Here, regardless of what the other decides, each prisoner gets a higher reward by betraying the other (“defecting”). Jack will either cooperate or defect. If Jack cooperates, Jose should defect, because going free is better than serving one year. If Jack defects, Jose should also defect, because serving two years is better than serving three years. So either way, Jose should defect. Parallel reasoning will show that Jack should defect. Game theory shows that the outcome is that Jose will betray Jack. The game is symmetric, so Jack should act the same way. Since both “rationally” decide to defect, each receives a lower reward than if both were to stay quiet. Traditional game theory results in both players being worse off than if each chose to lessen the sentence of his accomplice at the cost of spending more time in jail himself.

Jack and Jose both swore to each other several days before that they’d never rat on each other, but what happens when push comes to shove? It’s every man for himself.

Typically, both men go with their dominant strategy and betray the other. But because both separately decide to confess, they each end up getting two years in prison — a worse outcome than if they had both kept their promise to each other to remain silent. If they had both kept their promise, they each would’ve gone to jail for only one year. The logic of the dominant strategy is so compelling, though, that they each break the agreement and end up going to prison for two years rather than one.

This example of the Prisoner’s Dilemma is set up for just two people, but mathematicians have developed far more advanced models that can analyze the behavior of many participants. These models are invaluable for understanding cartels.

The basic conclusion of these multi-player models is that the dominant strategy is usually to cheat on cartel agreements. This result goes a long way toward explaining why the OPEC oil cartel has a hard time raising oil prices and then holding them there for a lengthy period. Quite simply, cheating on OPEC cartel agreements is a dominant strategy for OPEC member countries. The cheater is better off producing more than its quota because it can sell lots of oil at a higher price if the other countries are obeying their quotas. Overproducing is a dominant strategy and is simply too tempting to resist given the rewards.

Game theory is included in the JEL classification codes as JEL: C7 |

**Game theory** is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, biology and poker. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by the 1944 book *Theory of Games and Economic Behavior*, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. With the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole in 2014, eleven game-theorists have now won the economics Nobel Prize. John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.