Refer to the payoff matrix. Suppose that Speedy Bike and Power Bike are the only two bicycle manufacturing firms serving the market. Both can choose large or small advertising budgets. Is there a Nash equilibrium solution to this game?
There is no possible Nash equilibrium solution.
A Nash equilibrium can occur at either cell B or cell C.
Cell A represents a Nash equilibrium.
Cell D represents a Nash equilibrium.
Cell A represents a Nash equilibrium
In Game theory, there is a concept of solution often referred to as Nash Equilibrium, proposed by John Forbes Nash, is a type of solution concept of a game which involves multiple players, starting from two or more, in which no player has anything to gain by changing only his or her own strategy unilaterally.
Thus, to have Nash Equilibrium the first payoff number, in the payoff pair of the cell, is the maximum of the column of the cell and the second number is the maximum of the row of the cell.
Hence, in this case, the first $20 is the maximum amount of the column of the cell, and at the same time,the second $20 is the maximum amount of the row of the cell.
Yes, cell A which shows a $20 / $20 advertising budget represents a Nash equilibrium.
A Nash equilibrium is a situation where each party's strategy is optimal considering what the other party might do. The Nash equilibrium is best described by the prisoner's dilemma and how both choosing the same alternative solution or action will benefit them both.
In this case, by choosing cell A, both budgets are almost at their lowest possible point, and they are both benefiting from them.
The problem with a Nash equilibrium is that many times the parties involved want to get an extra benefit and try to hurt the other party by doing so (cells B and C). While cell D shows an option that is not optimal because it could be done with less money, and the whole point here is to save money.