In our research, we employ tools from a variety of areas in order to formally analyze scenarios in which multiple agents with possibly conflicting preferences interact. As such, our work can be located at the intersection of mathematics, economics, political science, and computer science. In particular, we focus on axiomatic and computational aspects of social choice theory and game theory, and on the emerging application area of interactive democracy.
Social Choice Theory:
Social choice theory studies how a group of agents can make collective decisions based on the—possibly conflicting—preferences of the members of the group. In the most general setting, there is a set of outcomes over which each group member has preferences. A social choice mechanism aggregates these preferences to social preferences, on the basis of which a collective decision or social choice is made. Social choice theory is an inherently interdisciplinary field that has attracted researchers (and practitioners) from such diverse areas as mathematics, economics, political science, and psychology. The field focusing on computational aspects of social choice theory is known as Computational Social Choice (COMSOC).
Game theory studies strategic interactions of multiple agents in situations where the well-being of a single agent depends not only on his own actions, but also on the actions of all the other agents. The term agent is used to refer to an autonomous decision maker that can be ascribed preferences over different states of the world. For example, an agent can be a person, an institution, or a country. Whereas early developments of the theory were mainly motivated by the analysis of parlor games such as chess and checkers, game theory has developed into an important field at the intersection of economics and mathematics that has numerous applications in the social sciences and beyond.
Y. Shoham and K. Leyton-Brown. Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, 2009.