Network cost-sharing games: Equilibrium computation and applications to election modeling

Abstract

We introduce and study a variant of network cost-sharing games with additional non-shareable costs (NCSG+), which is shown to possess a pure Nash equilibrium (PNE). We extend polynomial-time PNE computation results to a class of graphs that generalizes series-parallel graphs when the non-shareable costs are player-independent. Further, an election game model is presented based on an NCSG+ when voter opinions form natural discrete clusters. This model captures several variants of the classic Hotelling-Downs election model, including ones with limited attraction, ability of candidates to enter, change stance positions and exit any time during the campaign or abstain from the race, the restriction on candidates to access certain stance positions, and the operational costs of running a campaign. Finally, we provide a polynomial-time PNE computation for an election game when stance changes are restricted.