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 defend 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 preferences are represented by the expected number of votes it gains. Formulate this situation as

a strategic game and find its mixed strategy equilibria.