Coalitional Games with Priced-Resource Agents

Alternating-time Temporal Logic (ATL) and Coalition Logic (CL) are well-established logical formalisms particularly suitable to model games between dynamic coalitions of agents (like e.g. the system and the environment). Recently, the ATL formalism has been extended in order to take into account boundedness of the resources needed for a task to be performed. The resulting logic is known as Resource-bounded ATL (RB-ATL) and has been presented in quite a variety of scenarios. Model checking RB-ATL in very general setting is usually undecidable. Nevertheless, model checking procedures for semantically or syntactically restricted versions of RB-ATL have been proposed. In this paper, we analyze the problem of coalitions of agents that need to perform complex tasks, by using resources with a variable price. We highlight a certain number of problems and considerations, based on different interpretations of shortage of resources, leading to different scenarios.