Please help with number 3 3. Consider that two political parties compete each ot
ID: 1127271 • Letter: P
Question
Please help with number 3
3. Consider that two political parties compete each other by proposing policies respectively, in order to win the national election. Let [In, Imax C R++ be the range of pre-tax income of the households living in this nation state, where Imax represents the maximal (pre-tax) ncome level while Imin represents the min+Imax 2 tion of households in this society is characterized by a cumulative distribution There are two political parties L and R, where L is the Left-wing party and R is the Right-wing party, each of which would propose a policy selected from a policy space X in order to maximize the probability of winning the election given the opponent party's policy proposal. To simplify the argument, let us That is, the range of pre-income distribution also represents the policy space of this society over which the two parties can select their own policy proposals. Note that X-Tmin,,n implies that each policy r E X is the best ideal policy for the households with the income level -r Imax represents the policy which is the best for the richest households. Let each household with an income level i E [Imin, Imax have the utility function ui : X R which is defined as: for any x e X, 2 ideal, and the longer the distance between the policy r and the income level i is, the lower the utility of the households with the income level i is Given the environment X:F": (th),ex), let us define the probability of national election, and R be a policy proposed by R in the national election Then, let 1(zL·IR ) = TL 2TR . Let the percentage of the households who prefer of the environment, P (xL R) is specified as follow:s: Next, n this environment, given a profile of policy proposals, (rL ,rr) E X ×X, let the probability of winning the election for L be denoted by 11 (x1 ,TR ),Explanation / Answer
The dominant strategy equilibrium of this auction game is V3 = $1000
This is because if an individual private value is high than definitely it will help them to achive the dominant strategy of the equilibrium and hence it is been proved in the Nash equilibrium.