Efficiently Computing Equilibria in Budget-Aggregation Games

Abstract: Budget aggregation deals with the social choice problem of distributing an exogenously given budget among a set of public projects, given agents' preferences. Taking a game-theoretic perspective, we initialize the study of \emph{budget-aggregation games} where each agent has virtual decision power over some fraction of the budget. This paper investigates the structure and shows efficient computability of Nash equilibria in this setting for various preference models. In particular, we show that Nash equilibria for Leontief utilities can be found in polynomial time, solving an open problem from Brandt et al. [2023].