Two polititians, A and B, competing on an election have to decide were on the le

Question

Two polititians, A and B, competing on an election have to decide were on the left-right spectrum to position themselves. The spectrum goes from 0, the left-most position, to 1, the right-most position, and both polititians freely choose any point {0, 0.1, 0.2, . . . , 0.9, 1} in the spectrum to maximize their share of votes. Let pA and pB be the position of polititian A and B respectively. The share of votes is deter- mined according to the following rule. If A takes a position to the right of B, i.e. pA > pB, A gets a share: sA = 1 ? pA + pB 2 and B gets: sB = pA + pB 2 If B takes a position to the right of A then sA and sB are defined analogous to the previous case. The following figure shows an example for pA > pB. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 pB pA pA+pB 2 sB sA If both politians take the same position, i.e. pA = pB, they split the votes evenly. a. Write down the share of votes for polititian A as a function of pA and pB in all three contin- gencies. (pA > pB, pA < pB and pA = pB).

Explanation / Answer

When pA>pB

sA = 1 - pA + pB 2

When pA<pB

sA = pB + pA 2

When pA = pB

sA = (1 - pA + pA 2 + pA + pA2)/ 2

= 1/2 - pA2

Instead of the missing operation ?, I have assumed (-)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.