Budget-restricted utility games with ordered strategic decisions

TL;DR

This paper introduces budget games where players select tasks with resource demands, analyzing strategic sharing, ordering effects, equilibrium existence, and convergence complexity, highlighting the computational challenges in such resource allocation scenarios.

Contribution

It presents a new model of budget games with ordered decision effects and analyzes the complexity and equilibrium properties within this framework.

Findings

Optimal solutions are computationally complex.

Equilibria may not always exist or be easy to find.

Convergence to equilibrium can take exponential time.

Abstract

We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to be shared between the tasks. We study strategic budget games, where the budget is shared proportionally. We also consider a variant in which the order of the strategic decisions influences the distribution of the budgets. The complexity of the optimal solution as well as existence, complexity and quality of equilibria are analyzed. Finally, we show that the time an ordered budget game needs to convergence towards an equilibrium may be exponential.