Prisoner's Dilemma, Nash Equilibrium & Oligopoly

The Prisoner's Dilemma

The Prisoner's Dilemma is a concept in game theory based on two assumptions:

1. Each player has an incentive to choose an alternative that benefits them but hurts the other player.
2. When both players act in that way, they end up in a worse situation than if they had chosen different alternatives.

Dominant Strategy

A dominant strategy is the best decision an individual can make, regardless of the decision taken by the other player. Not all games have a dominant strategy; it depends on the game's payoff structure. In the Prisoner's Dilemma, a dominant strategy exists (to confess). As long as the two prisoners cannot agree *not* to confess (something that cannot be maintained while incommunicado), they will both act against each other. Consequently, if each acts rationally, both will confess (whereas if neither had confessed, both would have received shorter sentences). In the Prisoner's Dilemma, each player has a clear incentive to act in a way that harms the other player, but when both make that decision, both are harmed.

Nash Equilibrium

The Nash Equilibrium, also known as the non-cooperative equilibrium, is the outcome of the game when each player chooses the action that maximizes their payoff, taking the decisions of other players as given, and without considering the effects their decision might have on the payoffs of others. A Nash Equilibrium is reached if neither player considers that their decisions are interdependent.

Repeated Games and Strategic Behavior

The Prisoner's Dilemma is a single-round game; both prisoners play only once (they choose once and for all whether to confess or remain silent). However, most games involving oligopolies are not of this type. Instead, they expect to play the same game with the same competitors repeatedly. If the game is repeated, players may behave strategically, sacrificing short-term benefits in exchange for influencing the future behavior of other players.

An oligopolistic sector is expected to continue for many years, and it knows that the decision made today about whether to cheat or not will likely influence the future treatment it receives from other companies. Therefore, an oligopoly does not decide what to do today based solely on short-term profits. Instead, it will consider the effects that present decisions can have on future decisions of the other players, exhibiting *strategic behavior*.

A company engages in strategic behavior when it tries to influence the future decisions of other companies. Under certain conditions, oligopolists behaving strategically make the same decisions they would make if they had a formal collusion agreement. When oligopolists expect to compete among themselves for a long period, each company concludes that it is in its best interest to cooperate with other companies in the industry. Therefore, they restrict their production to increase the profits of other companies, hoping to receive the same favorable treatment. While companies may not reach a formal agreement to reduce output and raise prices, they act *as if* such an agreement existed.

Tacit Collusion

When firms reduce output and raise prices to increase their competitors' profits, even without a formal commitment, it is called tacit collusion. In the repeated game of the Prisoner's Dilemma, the "tit for tat" strategy is a good example of strategic behavior that allows for tacit collusion.

Tit for Tat Strategy

The tit for tat strategy involves cooperating during the first period and, in subsequent periods, doing what the other player did in the previous period. Tit for tat rewards the cooperative play of another player: if you behave cooperatively, so will I. It punishes those who cheat: if you breach, do not expect me to behave properly in the future.

Oligopoly in the Real World

The operation of oligopolies in the real world depends on both the legal framework that sets limits on firms' actions and the capacity of the enterprises themselves in a given industry to cooperate without establishing formal agreements.