Model Checking and Strategy Synthesis for Multi-agent Systems for Resource Allocation

Synthesis of Cost-Optimal Multi-Agent Systems for Resource Allocation

“…We have that [23]). We can now immediately conclude that there does not exist a joint winning strategy to achieve Φ.…”

“…In [23] we showed how to encode standard MRA strategy synthesis problems [M, s 0 |= Agt Φ] as propositional logic formulas F such that the following equivalence holds:…”

“…Agt that results in a path π(s 0 , σ α Agt ) where resource r is never allocated by any agent at all time steps until k where k is the latest deadline (shown in [23]). We can conclude that α characterises a strategy that results in a k-bounded path where w s α are the cumulative costs of the resources that are never used, and w u α are the cumulative costs of the resources that are actually used.…”

“…where [ Agt ] encodes that all agents must follow a uniform strategy and adhere to the protocol, [M] encodes the feasible paths of M, and [Φ] restricts the paths to those that satisfy all goals in Φ. In [23] we only considered simple goals, one for each agent and with regard to a single type of resource. Thus, for the more complex goals that we focus on in this work, we introduce the following extended encoding of goals: Definition 20 (Encoding of Goals).…”

“…The corresponding model checking problem is to determine whether such a winning strategy exists or not, and the synthesis problem is to actually build the strategy. In [23] we introduced a SAT-based technique for checking goal-achievability properties of multi-agent systems for resource allocation. The technique does not only decide the model checking problem, it also synthesises a corresponding winning strategy if existent.…”