Equilibria in weighted voting games with sidepayments

Coalition formation is modeled as a cooperative games. Each party enters the game endowed with a weight that is a function of the proportion of the votes the party obtained in the elections, and an ideal policy position. Payoffs to parties are a function of the distance of the government's policy position from the party's ideal point, and the number of portfolios that the party receives in the coalition. The game analyzed is a variation on the ‘divide the dollar’ problem. Unlike the divide the dollar game, however, ideological payoffs are also introduced into the analysis. It turns out that the ideological concerns of parties ‘induce’ a core in the ‘divide the dollar’ problem that would, otherwise, have a generally empty core. A comprehensive analysis of the new core concept, the ‘IVCORE’, follows.