Budget-Constrained Coalition Strategies with Discounting

TL;DR

This paper introduces a logical system that effectively models and reasons about strategic abilities under budget constraints with discounting, filling a gap in existing logical frameworks.

Contribution

It presents a sound and complete logic for reasoning about strategies with budget constraints that explicitly incorporates discounting into its semantics.

Findings

Developed a formal logical system for discounted budget-constrained strategies.

Proved the logic's soundness and completeness.

Addresses a gap in existing reasoning frameworks for strategic abilities.

Abstract

Discounting future costs and rewards is a common practice in accounting, game theory, and machine learning. In spite of this, existing logics for reasoning about strategies with cost and resource constraints do not account for discounting. The paper proposes a sound and complete logical system for reasoning about budget-constrained strategic abilities that incorporates discounting into its semantics.