Economics can also be used to analyze politics. Suppose two politicalparties are competing for votes

Economics can also be used to analyze politics. Suppose two politicalparties are competing for votes. Each party i chooses a policy positionxi 2 [0; 1], i = 1; 2. Voter preferences uj are uniformly distributed on [0; 1]with uj(xi) = ABS(vj – xi). This means that a voter j will vote for the partywith a policy position closest to vj on the unit interval. Whatever partygets the most votes wins the election. If both parties choose the samepolicy position, the election is tied and each win with probability 0.5.(a) What is the Nash equilibrium of the game? (I.e. what are the equi-librium policy positions for the two parties.)(b) Suppose a third party enters the game. Does a pure strategy Nashequilibrium exist? If yes, find it. If no, show that it cannot exist.

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