52 research outputs found
Informational Substitutes
We propose definitions of substitutes and complements for pieces of
information ("signals") in the context of a decision or optimization problem,
with game-theoretic and algorithmic applications. In a game-theoretic context,
substitutes capture diminishing marginal value of information to a rational
decision maker. We use the definitions to address the question of how and when
information is aggregated in prediction markets. Substitutes characterize
"best-possible" equilibria with immediate information aggregation, while
complements characterize "worst-possible", delayed aggregation. Game-theoretic
applications also include settings such as crowdsourcing contests and Q\&A
forums. In an algorithmic context, where substitutes capture diminishing
marginal improvement of information to an optimization problem, substitutes
imply efficient approximation algorithms for a very general class of (adaptive)
information acquisition problems.
In tandem with these broad applications, we examine the structure and design
of informational substitutes and complements. They have equivalent, intuitive
definitions from disparate perspectives: submodularity, geometry, and
information theory. We also consider the design of scoring rules or
optimization problems so as to encourage substitutability or complementarity,
with positive and negative results. Taken as a whole, the results give some
evidence that, in parallel with substitutable items, informational substitutes
play a natural conceptual and formal role in game theory and algorithms.Comment: Full version of FOCS 2016 paper. Single-column, 61 pages (48 main
text, 13 references and appendix
Descending Price Optimally Coordinates Search
Investigating potential purchases is often a substantial investment under
uncertainty. Standard market designs, such as simultaneous or English auctions,
compound this with uncertainty about the price a bidder will have to pay in
order to win. As a result they tend to confuse the process of search both by
leading to wasteful information acquisition on goods that have already found a
good purchaser and by discouraging needed investigations of objects,
potentially eliminating all gains from trade. In contrast, we show that the
Dutch auction preserves all of its properties from a standard setting without
information costs because it guarantees, at the time of information
acquisition, a price at which the good can be purchased. Calibrations to
start-up acquisition and timber auctions suggest that in practice the social
losses through poor search coordination in standard formats are an order of
magnitude or two larger than the (negligible) inefficiencies arising from
ex-ante bidder asymmetries.Comment: JEL Classification: D44, D47, D82, D83. 117 pages, of which 74 are
appendi
An Axiomatic Study of Scoring Rule Markets
Prediction markets are well-studied in the case where predictions are probabilities or expectations of future random variables. In 2008, Lambert, et al. proposed a generalization, which we call "scoring rule markets" (SRMs), in which traders predict the value of arbitrary statistics of the random variables, provided these statistics can be elicited by a scoring rule. Surprisingly, despite active recent work on prediction markets, there has not yet been any investigation into more general SRMs. To initiate such a study, we ask the following question: in what sense are SRMs "markets"? We classify SRMs according to several axioms that capture potentially desirable qualities of a market, such as the ability to freely exchange goods (contracts) for money. Not all SRMs satisfy our axioms: once a contract is purchased in any market for prediction the median of some variable, there will not necessarily be any way to sell that contract back, even in a very weak sense. Our main result is a characterization showing that slight generalizations of cost-function-based markets are the only markets to satisfy all of our axioms for finite-outcome random variables. Nonetheless, we find that several SRMs satisfy weaker versions of our axioms, including a novel share-based market mechanism for ratios of expected values
Low-Cost Learning via Active Data Procurement
We design mechanisms for online procurement of data held by strategic agents
for machine learning tasks. The challenge is to use past data to actively price
future data and give learning guarantees even when an agent's cost for
revealing her data may depend arbitrarily on the data itself. We achieve this
goal by showing how to convert a large class of no-regret algorithms into
online posted-price and learning mechanisms. Our results in a sense parallel
classic sample complexity guarantees, but with the key resource being money
rather than quantity of data: With a budget constraint , we give robust risk
(predictive error) bounds on the order of . Because we use an
active approach, we can often guarantee to do significantly better by
leveraging correlations between costs and data.
Our algorithms and analysis go through a model of no-regret learning with
arriving pairs (cost, data) and a budget constraint of . Our regret bounds
for this model are on the order of and we give lower bounds on the
same order.Comment: Full version of EC 2015 paper. Color recommended for figures but
nonessential. 36 pages, of which 12 appendi
Contracts with Information Acquisition, via Scoring Rules
We consider a principal-agent problem where the agent may privately choose to
acquire relevant information prior to taking a hidden action. This model
generalizes two special cases: a classic moral hazard setting, and a more
recently studied problem of incentivizing information acquisition (IA). We show
that all of these problems can be reduced to the design of a proper scoring
rule. Under a limited liability condition, we consider the special cases
separately and then the general problem. We give novel results for the special
case of IA, giving a closed form "pointed polyhedral cone" solution for the
general multidimensional problem. We also describe a geometric, scoring-rules
based solution to the case of the classic contracts problem. Finally, we give
an efficient algorithm for the general problem of Contracts with Information
Acquisition
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