Simple Budgeting Games

This thesis looks at Nash Equilibria and strategic voting in budgeting games using the Method of Equal Shares (MES), a recently-developed, innovative voting rule for approval-based multiwinner elections and participatory budgeting. I show that, in the general case, it is possible for voters to improve their utilities by voting strategically (i.e. voting for candidates whom they do not truthfully approve). In addition, I demonstrate that it is always possible to find a pure-strategy Nash Equilibrium for these games, no matter the budget of each voter. I also show an important negative result: Under so-called "frugal" best-response dynamics, for voters with small budgets, it is NP-hard to determine reachability of a Nash Equilibrium where a target set of candidates forms a subset of winners. Lastly, I discuss the Justified Representation (JR) family of fairness metrics, and show that in these games, Justified Representation is guaranteed in some cases, but we can do no better.