922 research outputs found
I Don't Want to Think About it Now:Decision Theory With Costly Computation
Computation plays a major role in decision making. Even if an agent is
willing to ascribe a probability to all states and a utility to all outcomes,
and maximize expected utility, doing so might present serious computational
problems. Moreover, computing the outcome of a given act might be difficult. In
a companion paper we develop a framework for game theory with costly
computation, where the objects of choice are Turing machines. Here we apply
that framework to decision theory. We show how well-known phenomena like
first-impression-matters biases (i.e., people tend to put more weight on
evidence they hear early on), belief polarization (two people with different
prior beliefs, hearing the same evidence, can end up with diametrically opposed
conclusions), and the status quo bias (people are much more likely to stick
with what they already have) can be easily captured in that framework. Finally,
we use the framework to define some new notions: value of computational
information (a computational variant of value of information) and and
computational value of conversation.Comment: In Conference on Knowledge Representation and Reasoning (KR '10
On the Power of Many One-Bit Provers
We study the class of languages, denoted by \MIP[k, 1-\epsilon, s], which
have -prover games where each prover just sends a \emph{single} bit, with
completeness and soundness error . For the case that
(i.e., for the case of interactive proofs), Goldreich, Vadhan and Wigderson
({\em Computational Complexity'02}) demonstrate that \SZK exactly
characterizes languages having 1-bit proof systems with"non-trivial" soundness
(i.e., ). We demonstrate that for the case that
, 1-bit -prover games exhibit a significantly richer structure:
+ (Folklore) When , \MIP[k, 1-\epsilon, s]
= \BPP;
+ When , \MIP[k,
1-\epsilon, s] = \SZK;
+ When , \AM \subseteq \MIP[k, 1-\epsilon,
s];
+ For and sufficiently large , \MIP[k, 1-\epsilon, s]
\subseteq \EXP;
+ For , \MIP[k, 1, 1-\epsilon, s] = \NEXP.
As such, 1-bit -prover games yield a natural "quantitative" approach to
relating complexity classes such as \BPP,\SZK,\AM, \EXP, and \NEXP.
We leave open the question of whether a more fine-grained hierarchy (between
\AM and \NEXP) can be established for the case when
Voting with Coarse Beliefs
The classic Gibbard-Satterthwaite theorem says that every strategy-proof
voting rule with at least three possible candidates must be dictatorial.
Similar impossibility results hold even if we consider a weaker notion of
strategy-proofness where voters believe that the other voters' preferences are
i.i.d.~(independent and identically distributed). In this paper, we take a
bounded-rationality approach to this problem and consider a setting where
voters have "coarse" beliefs (a notion that has gained popularity in the
behavioral economics literature). In particular, we construct good voting rules
that satisfy a notion of strategy-proofness with respect to coarse
i.i.d.~beliefs, thus circumventing the above impossibility results
Computational Extensive-Form Games
We define solution concepts appropriate for computationally bounded players
playing a fixed finite game. To do so, we need to define what it means for a
\emph{computational game}, which is a sequence of games that get larger in some
appropriate sense, to represent a single finite underlying extensive-form game.
Roughly speaking, we require all the games in the sequence to have essentially
the same structure as the underlying game, except that two histories that are
indistinguishable (i.e., in the same information set) in the underlying game
may correspond to histories that are only computationally indistinguishable in
the computational game. We define a computational version of both Nash
equilibrium and sequential equilibrium for computational games, and show that
every Nash (resp., sequential) equilibrium in the underlying game corresponds
to a computational Nash (resp., sequential) equilibrium in the computational
game. One advantage of our approach is that if a cryptographic protocol
represents an abstract game, then we can analyze its strategic behavior in the
abstract game, and thus separate the cryptographic analysis of the protocol
from the strategic analysis
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