Dividing money: Two people have $10 to divide between themselves. They use the following procedure. Each...

Dividing money: Two people have $10 to divide between themselves. They use the following procedure. Each person names a number of dollars (a nonnegative integer), at most equal to 10. If the sum of the amounts that the people names is at most 10, then each person receives the amount of money she named (and the remainder is destroyed). If the sum of the amounts that the people name exceeds 10 and the amounts named are different, then the person who named the smaller amount receives that amount and the other person receives the remaining money. If the sum of the amounts that the people name exceeds 10 and the amounts named are the same, then each person receives 5. Model this scenario as a strategic form game and provide the payoff matrix.

Expert Solution

Let P1 be person one and P2 be person 2

Now, each one of them can choose a number between 0 to 10. Thus, the table below shows the strategic game wherein number outside the bracket is payoff and the number inside the bracket say (x,y) is the amount earned by P1 and P2 respectively, i.e., P1 earns x and P2 earns y and the total payoff is x + y

	P2
P1	0	1	2	3	4	5	6	7	8	9	10
0	0(0,0)	1(0,1)	2(0,2)	3(0,3)	4(0,4)	5(0,5)	6(0,6)	7(0,7)	8(0,8)	9(0,9)	10(0,10)
1	1(1,0)	2(1,1)	3(1,2)	4(1,3)	5(1,4)	6(1,5)	7(1,6)	8(1,7)	9(1,8)	10(1,9)	10 (1,9)
2	2(2,0)	3(2,1)	4(2,2)	5(2,3)	6(2,4)	7(2,5)	8(2,6)	9(2,7)	10(2,8)	10(2,8)	10(2,8)
3	3(3,0)	4(3,1)	5(3,2)	6(3,3)	7(3,4)	8(3,5)	9(3,6)	10(3,7)	10(3,7)	10(3,7)	10(3,7)
4	4(4,0)	5(4,1)	6(4,2)	7(4,3)	8(4,4)	9(4,5)	10(4,6)	10(4,6)	10(4,6)	10(4,6)	10(4,6)
5	5(5,0)	6(5,1)	7(5,2)	8(5,3)	9(4,5)	10(5,5)	10(5,5)	10(5,5)	10(5,5)	10(5,5)	10(5,5)
6	6(6,0)	7(6,1)	8(6,2)	9(6,3)	10(6,4)	10(5,5)	10(5,5)	10(6,4)	10(6,4)	10(6,4)	10(6,4)
7	7(7,0)	8(7,1)	9(7,2)	10(7,3)	10(6,4)	10(5,5)	10(4,6)	10(5,5)	10(7,3)	10(7,3)	10(7,3)
8	8(8,0)	9(8,1)	10(8,2)	10(7,3)	10(6,4)	10(5,5)	10(4,6)	10(3,7)	10(5,5)	10(8,2)	10(8,2)
9	9(9,0)	10(9,1)	10(8,2)	10(7,3)	10(6,4)	10(5,5)	10(4,6)	10(3,7)	10(2,8)	10(5,5)	10(9,1)
10	10(10,0)	10(9,1)	10(8,2)	10(7,3)	10(6,4)	10(5,5)	10(4,6)	10(3,7)	10(2,8)	10(1,9)	10(5,5)

Payoff matrix is as follows:

	P2
P1	0	1	2	3	4	5	6	7	8	9	10
0	0	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10	10
2	2	3	4	5	6	7	8	9	10	10	10
3	3	4	5	6	7	8	9	10	10	10	10
4	4	5	6	7	8	9	10	10	10	10	10
5	5	6	7	8	9	10	10	10	10	10	10
6	6	7	8	9	10	10	10	10	10	10	10
7	7	8	9	10	10	10	10	10	10	10	10
8	8	9	10	10	10	10	10	10	10	10	10
9	9	10	10	10	10	10	10	10	10	10	10
10	10	10	10	10	10	10	10	10	10	10	10

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