Consider a variant of the Hotelling's model which capture features of the U.S. presidential

elections. Voters are divided into two states. State 1 has more electoral college votes than

State 2. The winner is the one who obtains the most electoral college votes. Denote by m1

and m2 the median voter's favorite position among the residents of State 1 and State 2,

respectively (the 'median' voter is the one that has the same amount of other voters on

his/her right side and on his/her left side). Assume that m2

simultaneously choose one single position on the political spectrum, represented by the

interval [0,1]. Each voter votes for the candidate who is the closest to his/her favorite

position. The candidate who wins the majority of the vote in one states wins all the electoral

college votes in that state. If for some states the candidates receive the same number of

votes, they each obtain half of the electoral college votes of that state.

Is there a dominant/dominated strategy in this game?

Is there a Nash Equilibrium?