Optimal social laws

Abstract

Social laws have proved to be a powerful and theoretically elegant framework for coordination in multi-agent systems. Most existing models of social laws assume that a designer is attempting to produce a set of constraints on agent behaviour which will ensure that some single overall desirable objective is achieved. However, this represents a gross simplification of the typical situation, where a designer may have multiple (possibly conflicting) objectives, with different priorities. Moreover, social laws, as well as bringing benefits, also have implementation costs: imposing a social law often cannot be done at zero cost. We present a model of social laws that reflects this reality: it takes into account both the fact that the designer of a social law may have multiple differently valued objectives, and that the implementation of a social law is not costneutral. In this setting, designing a social law becomes an optimisation problem, in which a designer must take into account both the benefits and costs of a social law. We investigate the issue of representing a designer's objectives, characterise the complexity of the optimal social law design problem, and consider possible constraints that lead to reductions in computational complexity. We then show how the problem of designing an optimal social law can be formulated as an integer linear program.