Mixed Nash Game theory Two students are competing in an election with 7 voters. Their possible policies are ordered on a

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Mixed Nash Game theory
Two students are competing in an election with 7 voters.Their possible policies are ordered on a number line andare labeled {1; 2; 3; 4; 5; 6; 7}. Each policy is the favoriteof one
voter. The candidates, GRUMP and SILLARY, announce thepolicies and whoever gets the most votes wins and implementsthe policy she announced.
*(If a voter strictly prefers one candidate,they vote for that candidate. If a voter is indifferent,she/he allocates exactly half a vote to each candidate. Ifthe
candidates tie, they flip a coin, and the winner of the cointoss wins the election and implements the policy announced.)* Thevoters have single peaked preferences and unlike the
Downsian model, the candidates also have single peaked policypreferences. GRUMP'S favorite policy is 1. SILLARY'Sfavorite policy is 7. The
winning candidate will obtain a utility of 5 from winningthe election.
• if Grump wins with a policy of k in {1; 2; 3; 4; 5; 6; 7},then Grump obtains -|1-k | + 5 utility and Sillaryobtains -|7- k | utility
• If Sillary wins with a policy of j in {1; 2; 3; 4; 5; 6;7} then Grumps gets -|1-j| and Sillary obtains-|7-j| + 5 utility
1) If Grumps announces a policy of 4, what is Sillary'sbest response?
2) Is it a Nash equilibrium of this game for each candidate toannounce 4? (Hint. Suppose this is a Nashequilibrium. Find each candidate's payoff  from announcing thepolicy 4, given that the
other player does. Then check whether there are any otherpolicies that lead to a strictly higher payoff  for eithercandidate, holding the other's policy fixed at 4. If yes, this isnot a Nash equilibrium; if no, it is a Nash equilibrium.)
3) Is it a Nash equilibrium for each candidate to announce herfavorite policy? (Hint. As in the previous problem, except assumeeach player announces her ideal point instead of the policy 4.)
4) Do your answers to parts (2) and (3) change if the candidateseach obtain 2 utility from winning the election?