The central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to a given system level objective. Game theory is beginning to emerge as a valuable set of tools for achieving this goal. A central component of this game theoretic approach is the assignment of utility functions to the individual agents. Here, the goal is to assign utility functions within an “admissible” design space such that the resulting game possesses desirable properties, e.g., existence and efficiency of pure Nash equiibria. Our first set of results focuses on ensuring the existence of pure Nash equilibria. Here, we prove that weighted Shapley values completely characterize the space of "local" utility functions that guarantee the existence of a pure Nash equilibrium. That is, if the agents' utility functions cannot be represented as a weighted Shapley value, then there exists a game for which a pure Nash equilibrium does not exist. One of the interesting consequences of this characterization is that guaranteeing the existence of a pure Nash equilibrium necessitates the use of a game structure termed “potential games”. Building on this characterization, our second set of results will focus on characterizing the utility functions that optimize the efficiency of the resulting pure Nash equilibrium.
Jason Marden is an Associate Professor in the Department of Electrical and Computer Engineering at the University of California, Santa Barbara. Jason received a BS in Mechanical Engineering in 2001 from UCLA, and a PhD in Mechanical Engineering in 2007, also from UCLA, under the supervision of Jeff S. Shamma, where he was awarded the Outstanding Graduating PhD Student in Mechanical Engineering. After graduating from UCLA, he served as a junior fellow in the Social and Information Sciences Laboratory at the California Institute of Technology until 2010 when he joined the University of Colorado. Jason is a recipient of the NSF Career Award (2014), the ONR Young Investigator Award (2015), the AFOSR Young Investigator Award (2012), the American Automatic Control Council Donald P. Eckman Award (2012), and the SIAG/CST Best SICON Paper Prize (2015). Jason's research interests focus on game theoretic methods for the control of distributed multiagent systems.