By modestly lowering the price, either can steal all of their competitors' customers, nearly doubling their revenues.
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.
A player may normally choose to act selfishly to increase their own reward rather than play the socially optimum strategy.
There are many results in theorems which deal with how to achieve and maintain a socially optimal equilibrium in repeated games.
An important feature of a repeated game is the way in which a player's preferences may be modelled.
There are many different ways in which a preference relation may be modelled in an infinitely repeated game, but two key ones are : For sufficiently patient players (e.g. those with high enough values of
While a Nash equilibrium must be played in the last round, the presence of multiple equilibria introduces the possibility of reward and punishment strategies that can be used to support deviation from stage game Nash equilibria in earlier rounds.
Because there is only one equilibrium here, there is no mechanism for either player to threaten punishment or promise reward in the game's second round.
Cooperation in iterated games is only possible when the number of rounds is infinite or unknown.
In general, repeated games are easily solved using strategies provided by folk theorems.
Complex repeated games can be solved using various techniques most of which rely heavily on linear algebra and the concepts expressed in fictitious play.
It may be deducted that you can determine the characterization of equilibrium payoffs in infinitely repeated games.