There are various problems that people (firms/individuals) face when cooperation is desirable but difficult. Game theory is the study of how people behave in strategic situations.
By "Strategic" in Micro-economics we mean a situation in which each person, in deciding what actions to take, must consider how others might respond to that action.
A particularly important "game" is called the prisoner's dilemma. This game provides insight into the difficulty of maintaining cooperation. Many times in life, people fail to cooperate with one another even when cooperation would make them all better off.
The story of the prisoner's dilemma, is a story about two criminals who have been captured by the police.
Let's call them Bonnie and Clyde. The police have enough evidence to convict Bonnie and Clyde of the minor crime of carrying an unregistered gun, so that each would spend a year in jail.
The police also suspect that the two criminals have committed a bank robbery together, but they lack hard evidence to convict them of this major crime.
The police question Bonnie and Clyde in separate rooms, and they offer each of them the following deal:
"Right now, we can lock you up for 1 year. If you confess to the bank robbery and implicate your partner, however, we'll give you immunity, and you can go free. Your partner will get 20 years in jail. But if you both confess to the crime, we won't need your testimony and we can avoid the cost of a trial, so you will each get an intermediate sentence of 8 years."
If Bonnie and Clyde, bank robbers that they are, care only about their own sentences, what would you expect them to do? Would they confess or remain silent? Each prisoner has two strategies: confess or remain silent. The sentence each prisoner gets depends on the strategy he or she chooses and the strategy chosen by his or her partner in crime.
Consider first Bonnie's decision. She reasons as follows: "I don't know what Clyde is going to do. If he remains silent, my best strategy is to confess, since then I'll go free rather than spending a year in jail. If he confesses, my best strategy is still to confess, since then I'll spend 8 years in jail rather than 20.
So, regardless of what Clyde does, I am better off confessing."
In the language of game theory, a strategy is called a dominant strategy, if it's the best strategy for a player to follow regardless of the strategies pursued by other players.
In this case, confessing is a dominant strategy for Bonnie. xx