The movie A Beautiful Mind details the life of mathematician John Nash, winner of the 1994 Nobel Prize in economics for his contribution to game theory known as the Nash Equilibrium. Consider the following cola pricing game as described by the matrix below.
|Cut Price||Maintain Price|
|Coca-Cola||Cut Price||50, 50||100, 40|
|Maintain Price||40, 100||80, 80|
Each firm has two strategies: either maintain the current price of their cola, or to cut price. The numbers inside the matrix represent the profits that each firm earns depending on the strategies chosen by each firm. Thus, if Pepsi maintains its price and Coke cuts price, then Coke will earn $100 and Pepsi will earn $40.
What is the Nash Equilibrium for this game? Explain carefully.
Congratulations to Jake Verdoorn for correctly identifying and describing the only Nash Equilibrium in the game above.