Game theory problem answer all parts Consider the following

Game theory problem, answer all parts

Consider the following game: The Nash Equilibrium for this game, shows that Pizza Planet will always go low and Pizza Inc. will always go high. The equilibrium is then High (PI) Low (PP) with payoffs of 132, 70. Aggregate payoffs are 202. Is there an outcome where aggregate payoffs are higher for both players? If so, which one is it? Why is this not an equilibrium? Suppose that the two stores can reach an enforceable agreement whereby the \"cooperative\" outcome found in b can be reached. The two players bargain over this agreement and Pizza Inc. has 2.5 times as much bargaining power as Pizza Planet. In the resulting agreement, what sum will Pizza Inc. Pay to Pizza Planet? Suppose that both players have the same bargaining power, but the owners of Pizza Inc. are a bit impatient, and value $0.85 now more than $1 tomorrow; whereas Pizza Planet\'s owners are not impatient. If Pizza Inc. were to start negotiations, what proportion of the surplus will it get? What proportion will Pizza Inc. get if Pizza Planet were the one to start the bargaining process? Provide an intuitive explanation for your results

Solution

DEFINITION of \'Nash Equilibrium\'

A concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his or her chosen strategy after considering an opponent\'s choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash equilibrium or none at all.

This concept is named after its inventor John Nash and is incorporated in multiple disciplines (ranging from behavioral ecology to economics). If you want to test for a Nash equilibrium, simply reveal each person\'s strategy to all players. The Nash equilibrium exists if no players change their strategy, despite knowing the actions of their opponents. For example, let\'s examine a game between Tom and Sam. In this simple game both players can choose: A received $1, or B) lose $1

Tom

A=1,1

1,-1

B=-1,1

0,0

                                      Sam

Logically , both players choose strategy A, and receive a payoff of $1 . If we revealed Sam’s strategy to Tom and vice versa, we will see that no player deviates from the original choice, knowing the order player’s move means little, and doesn’t change behavior the outcome A,A represents a Nash equilibrium.

1.A is the High outcome where aggregate payoffs are higher for both players.

2.If Pizza ince has 2.5 times much bargaining power ,he will pay low to pizza planet.

3. If pizza ince has no patient he will be ready to take low .

A=1,1	1,-1
B=-1,1	0,0