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**AF1605**

**Introduction to Economics**

**Written report of Question 5.5 and 6.1**

*Question5.5*

Mr. Smart designed a reward scheme for Peter and Paul. One is gives oneself $10000 bonus, and the other one is gives another salesman $30000 bonus. Peter and Paul can choose either the first one or the second one.

Part (a) requires us to construct a payoff matrix of Peter and Paul. If both Peter and Paul choose to give oneself $10000 bonus, both of them can get $10000. If Peter chooses to give oneself $10000 bonus, Paul chooses to give another salesman $30000 bonus, Peter can get $40000 and Paul can get $0. If Paul chooses to give oneself $10000 bonus, Peter chooses to give another salesman $30000 bonus, Paul can get $40000 and Peter can get $0. If both Peter and Paul choose to give another salesman $30000 bonus, both of them can get $30000.

For part (b), if they can collude, both of them will give another salesman $30000 because they can get the maximum reward in total.

For part (c), if Paul chooses to cooperate (choose to give another salesman $30000 bonus), Peter will choose to give oneself $10000 bonus in order to maximize his individual reward. If Paul chooses to cheat (choose to give oneself $10000 bonus), Peter will choose to give oneself $10000 bonus, which is the most beneficial option. It is the same for Paul to do so. As a result, collusion fails.

For Part (d), Nash equilibrium is an equilibrium in which each player takes the best possible action given the action of the other player. So, when both of them choose to give oneself $10000 bonus, the Nash equilibrium is attained.

*Question6.1*

In order to find out the profit maximizing output of this...