Games with Unawareness: Theory & Applications
Awarded to Burkhard Schipper, National Science Foundation, $111,375
Decision makers in complex situations such as in business, politics or
sciences are not aware of all relevant facts when making decisions.
They face not just uncertainty about which facts obtain but may be also
unable to conceive of all relevant facts. Consequently, large resources
are devoted to explore unmapped terrain, figure out opportunities,
conceive of novelties, and to provide for unanticipated events. Yet, in
economics, decision theory and game theory, it is assumed that decision
makers can conceive of all relevant facts. Indeed, Modica and
Rustichini (1994) and Dekel, Lipman and Rustichini (1998) showed that
it is impossible to model unawareness with standard state-space models
that are widely used to analyze incomplete information. This limits
substantially the application of economic theory, decision theory and
game theory. The project is aimed to overcome the unrealistic
assumption of full awareness, to provide a foundation for game theory
with unawareness, and to explore the implications of asymmetric
unawareness in economics. Based on prior work by Heifetz, Meier and
Schipper (2006), an unawareness belief structure is developed, which
has standard properties of probabilistic beliefs but nevertheless
allows for unawareness. Using unawareness belief structures, Bayesian
games with unawareness are introduced, equilibrium is defined, and the
existence and structure of equilibria is analyzed. Such games are not
necessarily "common knowledge" since players may have asymmetric
awareness of payoff-relevant events, actions or opponents. The project
would prove a "No-Agreement-to-Disagree" Theorem. As an application to
markets, it is shown that speculative trade is possible under
unawareness. Yet, a "No-Trade" Theorem is proved according to which
arbitrary small transaction costs rule out speculation under
unawareness. The project also develops dynamic games with unawareness
including learning of new concepts and making others strategically
aware of issues during the play. Games with unawareness are applied to
incomplete contracts, the design of institutions, multi-issue
bargaining and strategic framing. The broader impact of this project is
to provide tractable tools to the social scientist for analyzing
situations with unanticipated events. These tools should be applicable
to more complex situations ranging from business and finance over
politics up to explorative sciences. The project is a contribution to
formal logic, computer science and artificial intelligence since it
provides a multi-person semantic structure for reasoning about
unawareness and beliefs. Moreover, the project yields also a clear
categorization of knowledge, belief and awareness, which is relevant to
cognitive sciences. Altogether the research is expected to provide a
better understanding of decision making with unanticipated events.
Doctoral Dissertation Research in Political Science: Information, Communication & Political Learning