An agent, or a coalition of agents, is blameable for an outcome if she had a strategy to prevent it. In this paper we introduce a notion of limited blameworthiness, with a constraint on the amount of sacrifice required to prevent the outcome. The main technical contribution is a sound and complete logical system for reasoning about limited blameworthiness in the strategic game setting.

The paper introduces a notion of a budget-constrained multiagent transition system that associates two financial parameters with each transition: a pre-transition minimal budget requirement and a post-transition profit. The paper also proposes a new modal language for reasoning about such a system. The language uses a modality labeled by agent as well as by budget and profit constraints. The main technical result is a sound and complete logical system that describes all universal properties of this modality. Among these properties is a form of Transitivity axiom that captures the interplay between the budget and profit constraints.