In the study of reactive systems, qualitative properties are usually easier to model and analyze than quantitative properties. This is especially true in systems where mutually beneficial cooperation between agents is possible, such as multi-agent systems. The large number of possible payoffs available to agents in reactive systems with quantitative properties means that there are many scenarios in which agents deviate from mutually beneficial outcomes in order to gain negligible payoff improvements. This behavior often leads to less desirable outcomes for all agents involved. For this reason we study satisficing goals, derived from a decision-making approach aimed at meeting a good-enough outcome instead of pure optimization. By considering satisficing goals, we are able to employ efficient automata-based algorithms to find pure-strategy Nash equilibria. We then show that these algorithms extend to scenarios in which agents have multiple thresholds, providing an approximation of optimization while still retaining the possibility of mutually beneficial cooperation and efficient automata-based algorithms. Finally, we demonstrate a one-way correspondence between the existence of $\epsilon$-equilibria and the existence of equilibria in games where agents have multiple thresholds.

翻译：在反应式系统研究中，定性属性通常比定量属性更容易建模和分析。在智能体之间可能存在互利合作的系统中（如多智能体系统）尤其如此。由于具有定量属性的反应式系统中智能体可获得的收益数量庞大，导致存在大量场景中智能体会为了获取微不足道的收益提升而偏离互利结果。这种行为往往会使所有相关智能体最终获得更不理想的结果。为此，我们研究源自决策方法的满意目标——该方法旨在达成"足够好"的结果而非纯粹优化。通过考虑满意目标，我们能够采用高效的基于自动机算法寻找纯策略纳什均衡。继而证明这些算法可扩展至智能体具有多个阈值的场景，在保持互利合作可能性及高效自动机算法优势的同时实现优化的近似。最后，我们证明了$\epsilon$-均衡的存在性与多阈值博弈中均衡存在性之间的单向对应关系。