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Research
Bounded Reasoning and Higher-Order Uncertainty
Online appendix.
The standard framework for analyzing games with incomplete information models
players as if they have an infinite depth of reasoning. This paper generalizes the
type spaces of Harsanyi(1967–1968) so that players can have a finite depth of reasoning.
The innovation is that players can have a coarse perception of the higher-order
beliefs of other players, thus formalizing 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
reason about higher-order events if these events are generated by events of sufficiently low order.
In particular, an event F can be common belief if it is entailed by some public event.
This is true even if players cannot reason about higher-order statements like “Ann believes
that Bob believes that Ann believes... (58 times)... that F” in isolation.
Thus, the usual equivalence between the iterative and the fixed-point account of common belief breaks
down when players
have a finite depth, and common belief is easier to attain than as suggested by the iterative approach.
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). Ray Reiter Best Paper Award
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).
Ranking Friends
(with Yossi Feinberg)
We investigate the scope for cooperation within a community engaged in repeated reciprocal interactions.
Players seek the help of others and approach them sequentially according to some fixed order,
that is, a ranking profile.
We study the ranking profiles that are most effective in sustaining cooperation in equilibrium, that is,
profiles that support full cooperation in equilibrium for the largest set of parameters.
These are the profiles that spread the costs of helping others equally among the members of the community.
We show that, generically, these socially optimal ranking profiles correspond to Latin squares -- profiles
in which each player appears in a given position exactly once in other players' list. In addition, we study
equilibria with bilateral enforcement in which only the victims punish non-cooperating deviators.
We show that the Latin squares in which every two players rank each other at the same position can
sustain cooperation for the widest range of parameters in this case.
All Types Naive and Canny (with Aviad Heifetz)
This paper constructs a type space that contains all types with a finite
depth of reasoning, as well as all types with an infinite depth of reasoning
—in particular those types for whom finite-depth types are conceivable, or
think that finite-depth types are conceivable in the mind of other players,
etcetera. We prove that this type space is universal with respect to the
class of type spaces that include types with a finite or infinite depth of
reasoning. In particular, we show that it contains the standard universal
type space of Mertens and Zamir (1985) as a belief-closed subspace, and
that this subspace is characterized by common belief of infinite-depth
reasoning. This framework allows us to study the robustness of classical
results to small deviations from perfect rationality. As an example, we
demonstrate that in the global games of Carlsson and Van Damme (1993), a
small ‘grain of naiveté’ suffices to overturn the classical uniqueness
results in that literature.
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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