  Careful rational synthesis was defined in (Condurache et al. 2021) as a
quantitative extension of Fisman et al.'s rational synthesis (Fisman et al.
2010), as a model of multi-agent systems in which agents are interacting in a
graph arena in a turn-based fashion. There is one common resource, and each
action may decrease or increase the resource. Each agent has a temporal
qualitative objective and wants to maintain the value of the resource positive.
One must find a Nash equilibrium. This problem is decidable.
  In more practical settings, the verification of the critical properties of
multi-agent systems calls for models with many resources. Indeed, agents and
robots consume and produce more than one type of resource: electric energy,
fuel, raw material, manufactured goods, etc. We thus explore the problem of
careful rational synthesis with several resources. We show that the problem is
undecidable. We then propose a variant with bounded resources, motivated by the
observation that in practical settings, the storage of resources is limited. We
show that the problem becomes decidable, and is no harder than controller
synthesis with Linear-time Temporal Logic objectives.
