Eran Shmaya
Social and Information Sciences Laboratory
California Institute of Technology
You won't harm me if you fool me, with Federico Echenique (2007)
A decision maker faces a new theory of how certain
events unfold over time. The theory matters for choices
she needs to make, but possibly the theory is a
fabrication. We show that there is a test which is guaranteed to
pass a true theory, and which is also conservative:
A false theory will only pass
when adopting it over the decision maker's
initial theory would not cause substantial harm; if the agent is
fooled she will not be harmed.
Many inspections are manipulable (2007)
A self proclaimed expert uses past observations of a stochastic process
to make probabilistic predictions about the process. An inspector
applies a test function to the infinite sequence of predictions
provided by the expert and the observed realization of the process in
order to check the expert's reliability. If the test function is Borel
and the inspection is such that a true expert will always pass it, then
it is also manipulable by an ignorant expert. The proof uses Martin's
theorem about determinacy of Blackwell games.
Under the axiom of choice, there exist non-Borel test functions that
are not manipulable.
Strongly measurable beliefs (2007)
A type space has strongly measurable beliefs if conditional beliefs
about the state of nature are jointly measurable in own type and the
type of the other player. I prove that separable type spaces admit
strongly measurable beliefs and give an example of a type space without
strongly measurable beliefs.
On
behavioral complementarity and its implications, with Christopher P. Chambers
and Federico Echenique
(2007)
We study the behavioral definition of complementary goods: if the price of
one good increases, demand for a complementary good must decrease. We obtain
its full implications for observable demand behavior (its testable
implications), and for the consumer's underlying preferences. We
characterize those data sets which can be generated by rational preferences
exhibiting complementarities. In a model in which income results from
selling an endowment (as in general equilibrium models of exchange
economies), the notion is surprisingly strong and is essentially equivalent
to Leontief preferences. In the model of nominal income, the notion
describes a class of preferences whose extreme cases are Leontief and
Cobb-Douglas respectively.
Foundations
for Bayesian Updating,
with Leeat Yariv
(2007)
We provide a simple characterization of updating rules that can be
rationalized as Bayesian. Namely, we consider a general setting in which an
agent observes finite sequences of signals and reports probabilistic
predictions on the underlying state of the world. We study when such
predictions are consistent with Bayesian updating, i.e., when does there
exist some theory about the signal generation process that would be
consistent with the agent behaving as a Bayesian updater. We show that the
following condition is necessary and sufficient for the agent to appear
Bayesian: the probability distribution that represents the agent's belief
after observing any finite sequence of signals is a convex combination of
the probability distributions that represent her beliefs after observing
sequences of signals that are the possible continuations of the original
sequence.
Quantum probability and rationality,
preliminary version
Based on the introduction I wrote for my PhD dissertation. I intend to
extend it and add references
Signaling
and mediation in Bayesian games, with Ehud Lehrer and Dinah
Rosenberg (2007).
We introduce natural transformations
between information structures and relate them to payoff achievable in
Bayesian games, with various notions of equilibrium.
Signaling
and mediation in games with
common interests, with Ehud
Lehrer and Dinah Rosenberg (2007).
We study analogs of Blackwell's Theorem about comparison of
information structures in the framwerok of two-player common interest
games. We introduce natural transformations between information
structures and relate them to the maximal payoff under various notions
of equilibrium.
Two
remarks on Blackwell's
Theorm, with Ehud
Lehrer (2006).
One concerning an agent that can withdraw from the game and get payoff
0, and another concerning a malevolent nature that picks a state
strategically to minimize the agent's payoff.
Comparison of information
structures and completely positive maps, J.
Phys. A: Math. Gen.38
(2005)
A quantum analog to Blackwell's theorem about comparison of
information structures in classical statistics. Completely positive
maps arise as the quantum counterpart of classical stochastic maps.
Stopping games
Stopping games are multi-player generalization of optimal stopping
problems. They appear in several models in economics and management
sciences, such as optimal equipment replacement, job search, consumer
behavior, research and development and analysis of strategic exist. We
prove that two-player stopping games admit Nash equilibrium. We study
both a deterministic setup and a stochastic setup. (with Eilon Solan
and Nicolas Vieille). The proofs use a stochastic variation of Ramsey's theorem