What is the Nash Equilibrium for this game?

Explanation:

Nash Equilibrium:

Nash Equilibrium is a concept in game theory where the players in a game make decisions while taking into account the decisions of the other players. In a Nash Equilibrium, no player has an incentive to change their strategy unilaterally. It is a stable state of the game where each player is satisfied with their choice given the choices of others.

Application to the Game:

In the game described, the options are whether to advertise or not advertise. The Nash Equilibrium occurs when both bp and the mini-mart choose not to advertise. If bp were to advertise while the mini-mart does not, they may not see a significant increase in profit as the cost of advertising might not be justified by the increase in sales. On the other hand, if the mini-mart were to advertise while bp does not, it could lead to a similar outcome where the cost of advertising may not be beneficial.

Therefore, by both choosing not to advertise, bp and the mini-mart reach a Nash Equilibrium where they both optimize their profits without incurring additional costs related to advertising. This decision results in a stable outcome where neither player has an incentive to unilaterally change their strategy.

In conclusion, the Nash Equilibrium for the game described is when bp and the mini-mart both choose not to advertise, as it results in a mutually optimal outcome for both players.