Nash Equilibrium and Prisoner’s Dilemma

The Nash equilibrium is the stable game state in which players do not gain an advantage by altering their strategies if their rivals also keep their strategies intact. For example, there are two companies, X and Y. Each of them can choose to have high or low prices. If both X and Y chose to install low prices for their products, each of them would receive $5mln. However, if both X and Y decide to go for the low prices, they will receive $3mln. In case X decides to have high prices and Y decides to have low prices, X receives $6mln in comparison with two mln for Y. If both X and Y choose the same strategy, no rival will suffer due to the rival’s deviance from the common optimal strategy.

The prisoner’s dilemma is a paradox that illustrates how two rational players will not always cooperate even if the conditions ask for it. For example, company X decides to decrease the price. While company Y has no choice but to follow the strategy, Y chooses not to do so. This leads to company X may win market share and increasing profits while Y experiences losses.

When the demand is elastic, an increase in price will bring fewer sales revenue. Since the consumers are responsive to price, having a large markup will lead to fewer sales and customers.

The prisoner’s dilemma is not always a Nash equilibrium because there are situations when the players are not cooperating, trying to benefit despite the adverse outcomes for the other player. Moreover, the Nash equilibrium is the solution to the prisoner’s dilemma because, given that the players know about each other’s strategies, they can develop their own accordingly.

The Nash equilibrium of a prisoner’s dilemma is characterized as the choices that benefit both players according to the strategies used by the rival player. The optimal strategy is not always used according to the concept of Nash equilibrium, yet the outcomes are positive for both players.

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