Model checking coalitional games in shortage resource scenarios

TL;DR

This paper introduces PRBATL, a novel logic for verifying multi-agent systems with shared, dynamically priced resources, providing a semantic approach to model resource evolution and market dynamics.

Contribution

It formalizes resource availability and pricing in MAS verification, proves EXPTIME-hardness of model checking, and compares the approach with previous resource logics.

Findings

PRBATL effectively models resource dynamics in MAS.

Model checking for PRBATL is EXPTIME-hard.

The formalism captures shared and priced resources in real-world scenarios.

Abstract

Verification of multi-agents systems (MAS) has been recently studied taking into account the need of expressing resource bounds. Several logics for specifying properties of MAS have been presented in quite a variety of scenarios with bounded resources. In this paper, we study a different formalism, called Priced Resource-Bounded Alternating-time Temporal Logic (PRBATL), whose main novelty consists in moving the notion of resources from a syntactic level (part of the formula) to a semantic one (part of the model). This allows us to track the evolution of the resource availability along the computations and provides us with a formalisms capable to model a number of real-world scenarios. Two relevant aspects are the notion of global availability of the resources on the market, that are shared by the agents, and the notion of price of resources, depending on their availability. In a previous work of ours, an initial step towards this new formalism was introduced, along with an EXPTIME algorithm for the model checking problem. In this paper we better analyze the features of the proposed formalism, also in comparison with previous approaches. The main technical contribution is the proof of the EXPTIME-hardness of the the model checking problem for PRBATL, based on a reduction from the acceptance problem for Linearly-Bounded Alternating Turing Machines. In particular, since the problem has multiple parameters, we show two fixed-parameter reductions.