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Respond to the question: Question Find the Nash equilibria?

03/03/2011 04:00 PM by name withheld; Question - Find the Nash equilibria

This question is asking me to find the Nash equilibria given these conditions, but I'm really confused about how to set it up:

Consider a variant of electoral competition on the line that captures features of the US presidential election. Voters are divided between two states. State 1 has more electoral college votes than does state 2. The winner is the candidate who obtains the most electoral college votes.

Denote by mi the median's favorite position among the citizens of state i, for i = 1, 2; assume that m2 < m1. Each of two candidates chooses a single position. Each citizen votes non-strategically for the candidate whose position is closest to her favorite position and randomize 50-50 when indifferent between candidates. The candidate who wins a majority of the votes in a state obtains all the state's electoral votes; if for some state the candidates obtain the same number of votes, they each obtain half of the electoral college votes of that state.

Find all NE of the strategic game modeled here. What does the set of NE imply about the role of small and large states in elections? In your answer assume that there is an even number of electoral votes in each district and that if candidates tie in the electoral college then each wins the election with probability ½. [Manage messages]