Conditional Coordination Games on Cyclic Social Influence Networks

Coordinated decision making is one of the fundamental attributes of intelligent behavior, and game theory has long served as a framework within which to model interactive decision making, especially for scenarios where decision makers are motivated to compete for the distribution of scarce resources. It is not obvious, however, that the standard game-theoretic framework is appropriate for complex social scenarios where agents are influenced by the attitudes and opinions of others and, consequently, the opportunity exists to make coordinated decisions in the pursuit of coherent group behavior. Noncooperative game theory is founded on the premise that choices ought to be strategically rational-agents make best-replies to the expected actions of others. However, when modeling groups whose members are responsive to social influence, a relevant notion of behavior is for them to coordinate rather than compete. The combination of conditional game theory and Bayesian network theory provides a framework within which to formalize a theory of coordinated decision making under social influence. As originally developed, however, conditional game theory applies only to acyclical networks involving unilateral influence propagation. This paper extends the theory to account for networks with cycles, where agents are able to exert multilateral influence on each other. The Markov convergence theorem establishes conditions for convergence to steady-state coordinated decisions, and demonstrates its use with a bilateral collaboration scenario. In addition, this paper provides a mathematical analysis of several canonical network topologies.