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Research
Bounded Reasoning and Higher-Order Uncertainty
Standard models of games with incomplete information assume that players form
beliefs about their opponents' beliefs about their opponents' beliefs and so on,
that is, that players have an infinite depth of reasoning. This paper generalizes
the type spaces introduced by Harsanyi (1967-1968) to allow
players to have a finite depth of reasoning. The innovation is that
players can have a coarse perception of the higher-order beliefs of
other players, which formalizes the small world idea of Savage (1954) in a type space context.
Unlike in other models of finite-order reasoning, players with a finite depth of reasoning can
have nontrivial higher-order beliefs about certain events. Intuitively, some higher-order
events are generated by events of lower orders,
making it possible for players to reason about them, even if they have a finite depth.
Ambiguous Language and Differences in Beliefs (with Joe Halpern). Forthcoming in Proceedings of the 13th
International Conference on Principles of Knowledge Representation and
Reasoning (KR2012).
Standard models of multi-agent modal logic do not capture the fact that
information is often ambiguous, and may be interpreted in different
ways by different agents. We propose a framework that can model this,
and consider different semantics that capture different assumptions
about the agents' beliefs regarding whether or not there is ambiguity.
We consider the impact of ambiguity on a seminal result in
economics: Aumann's result saying that agents with a common prior cannot
agree to disagree. This result does not hold if agents do not have a
common prior. We show that it also does not hold in the presence of
ambiguity. We then consider the tradeoff between assuming a common
interpretation (i.e., no ambiguity) and a common prior (i.e., shared
initial beliefs).
All Types Naive and Canny (with Aviad Heifetz)
This paper develops a universal type space that contains both the standard universal type space of
Mertens and Zamir (1985) and a universal type space of types with a finite depth of reasoning as
belief-closed subsets. We thus provide a framework
in which the robustness of predictions to small deviations of perfect rationality can be studied systematically.
Publications
Robustness of equilibria in anonymous local games, Journal of Economic Theory, 146, pp. 300–325, 2011.
Online appendix.
(Working paper version.)
Inequality and network structure (with Garud Iyengar, Rajiv Sethi and Sam Bowles), Games and Economic Behavior 73, pp. 215–226, 2011.
(Working paper version.)
Learning to be prepared (with Mark Voorneveld),
International Journal of Game Theory 37, pp. 333–352, 2008.
(Working paper version.)
An axiomatization of minimal curb sets (with Mark Voorneveld and Henk Norde),
International Journal of Game Theory 33, pp. 479–490, 2005.
(Working paper version.)
Publications in Other Fields
Random
intersection graphs with a tunable degree distribution and
clustering (with Mia Deijfen), Probability in the Engineering and
Informational Sciences 23, pp. 661–674, 2008.
Zn- and
Cd-induced features at the GaAs(110) and InP(110) surfaces
studied by low-temperature scanning tunneling microscopy (with Randy de Kort, Maurice van der WIelen
Ari van Roij, and Herman van Kempen), Physical Review B 63, 125336, 2001.
A low-temperature scanning tunneling microscopy study
on the Sn- and Zn-doped InP(110) surfaces (with Randy de Kort and Herman van Kempen),
Surface Science 482, pp. 495–500, 2001.
Peer-Reviewed Surveys
Learning with fixed rules: The minority game, Journal of Economic Surveys. Forthcoming.
Free
trade and its enemies (with Paul Tang), De Economist, pp. 152–153, pp. 427–437, 2004.
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