Can you answer it correctly

a Q. 4. Consider the folloving verson of Hhotelling's model of electoral competition. There are three potential political candidates. Each one of them has to simultaneously decide whether or not to enter a political contest. If a candidate decides to contest, she/he also has to simultaneously choose a policy position, which is modelled as choosing a number in some interval (a, b), whithout knowing what the other candidates have decided. There is a continuum of voters, each of whom as a favourite position; the distribution of favourite position is giving by cumulative probability distribution function F. Interprete F(x) as the proportion of voters whose favourite policy position is less than or equal to x. Assume that F is srictly increasing and continuous. A candidate attracts the votes of those citizen whose favourite positions are closer to her/his position then to the position, they equally split the votes that the position attracts. Each potencial candidate prefers to be the sole winning candidate then to tie for first place whith others, prefers to tie for first place then to stay out of the electoral race, and prefers to stay out of the race then to enter and lose. Formulate this situation as a strategic game or show that there is no Nash equilibrium in pure strategies when when there are three potentioal candidates and F is continuos. icno decision