  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.
