Repeated game

In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of their current action on the future actions of other players; this impact is sometimes called their reputation. Single stage game or single shot game are names for non-repeated games.

For a real-life example of a repeated game, consider two gas stations that are adjacent to one another. They compete by publicly posting pricing, and have the same and constant marginal cost c (the wholesale price of gasoline). Assume that when they both charge p = 10, their joint profit is maximized, resulting in a high profit for everyone. Despite the fact that this is the best outcome for them, they are motivated to deviate. By modestly lowering the price, either can steal all of their competitors' customers, nearly doubling their revenues. P = c, where their profit is zero, is the only price without this profit deviation. In other words, in the pricing competition game, the only Nash equilibrium is inefficient (for gas stations) that both charge p = c. This is more of a rule than an exception: in a staged game, the Nash equilibrium is the only result that an agent can consistently acquire in an interaction, and it is usually inefficient for them. This is because the agents are just concerned with their own personal interests, and do not care about the benefits or costs that their actions bring to competitors. On the other hand, gas stations make a profit even if there is another gas station adjacent. One of the most crucial reasons is that their interaction is not one-off. This condition is portrayed by repeated games, in which two gas stations compete for pricing (stage games) across an indefinite time range t = 0, 1, 2,....