Abstract:
We present techniques for verifying strategic abilities of multi-agent systems via SAT-based
and Max-SAT-based bounded model checking. In our approach we focus on systems of
agents that pursue goals with regard to the allocation of shared resources. One of the
problems to be solved is to determine whether a coalition of agents has a joint strategy
that guarantees the achievement of all resource goals, irrespective of how the opposing
agents in the system act. Our approach does not only decide whether such a winning
strategy exists, but also synthesises the strategy.
Winning strategies are particularly useful in the presence of an opposition because they
guarantee that each agent of the coalition will achieve its individual goal, no matter
how the opposition behaves. However, for the grand coalition consisting of all agents in
the system, following a winning strategy may involve an inefficient use of resources. A
winning strategy will only ensure that each agent will reach its goal at some time. But in
practical resource allocation problems it may be of additional importance that once-off
resource goals will be achieved as early as possible or that repetitive goals will be achieved
as frequent as possible. We present an extended technique that synthesises strategies that
are collectively optimal with regard to such quantitative performance criteria.
A collectively optimal strategy allows to optimise the overall system performance but it
may favour certain agents over others. In competitive scenarios a Nash equilibrium strategy
may be a more adequate solution. It guarantees that no agent can improve its individual
performance by unilaterally deviating from the strategy. We developed an algorithm that
initially generates a collectively optimal strategy and then iteratively alternates this strategy
until the strategy becomes a Nash equilibrium or a cycle of non-equilibrium strategies is
detected.
Our approach is based on a propositional logic encoding of strategy synthesis problems.
We reduce the synthesis of winning strategies to the Boolean satisfiability problem and
the synthesis of optimal and Nash equilibrium strategies to the maximum satisfiability
problem. Hence, efficient SAT- and Max-SAT solvers can be employed to solve the encoded
strategy synthesis problems
