Enforcing equilibria in multi-agent systems

We introduce and investigate Normative Synthesis: a new class of problems for the equilibrium verification that counters the absence of equilibria by purposely constraining multi-agent systems. We show that norms are powerful enough to ensure a positive answer to every instance of the equilibrium verification problem. Subsequently, we focus on two optimization versions, that aim at providing a solution in compliance with implementation costs. We show that the complexities of our procedures range between 2exptime and 3exptime, thus that the problems are no harder than the corresponding equilibrium verification ones.