(Election campaigns) A new political party, A, is challenging an established party, B. The race involves three localities of different sizes. Party A can wage a strong campaign in only one locality; B must commit resources to de- fend its position in one of the localities, without knowing which locality A has targeted. If A targets district i and B devotes its resources to some other district then A gains ai votes at the expense of B; let a1 > a2 > a3 > 0. If B devotes resources to the district that A targets then A gains no votes. Each party's prefer- ences are represented by the expected number of votes it gains. (Perhaps seats in a legislature are allocated proportionally to vote shares.) Formulate this situation as a strategic game and find its mixed strategy equilibria.