4,035 research outputs found
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
Axioms for Constant Function Market Makers
We study axiomatic foundations for different classes of constant-function
automated market makers (CFMMs). We focus particularly on separability and on
different invariance properties under scaling. Our main results are an
axiomatic characterization of a natural generalization of constant product
market makers (CPMMs), popular in decentralized finance, on the one hand, and a
characterization of the Logarithmic Scoring Rule Market Makers (LMSR), popular
in prediction markets, on the other hand. The first class is characterized by
the combination of independence and scale invariance, whereas the second is
characterized by the combination of independence and translation invariance.
The two classes are therefore distinguished by a different invariance property
that is motivated by different interpretations of the num\'eraire in the two
applications.
However, both are pinned down by the same separability property.
Moreover, we characterize the CPMM as an extremal point within the class of
scale invariant, independent, symmetric AMMs with non-concentrated liquidity
provision. Our results add to a formal analysis of mechanisms that are
currently used for decentralized exchanges and connect the most popular class
of DeFi AMMs to the most popular class of prediction market AMMs
Recommended from our members
An Axiomatic Characterization of Continuous-Outcome Market Makers
Most existing market maker mechanisms for prediction markets are designed for events with a finite number of outcomes. All known attempts on designing market makers for forecasting continuous-outcome events resulted in mechanisms with undesirable properties. In this paper, we take an axiomatic approach to study whether it is possible for continuous-outcome market makers to satisfy certain desirable properties simultaneously. We define a general class of continuous-outcome market makers, which allows traders to express their information on any continuous subspace of their choice. We characterize desirable properties of these market makers using formal axioms. Our main result is an impossibility theorem showing that if a market maker offers binary-payoff contracts, either the market maker has unbounded worst case loss or the contract prices will stop being responsive, making future trades no longer profitable. In addition, we analyze a mechanism that does not belong to our framework. This mechanism has a worst case loss linear in the number of submitted orders, but encourages some undesirable strategic behavior.Engineering and Applied Science
Bibliometric indices as a measure of long-term competitive balance in knockout tournaments
We argue for the application of bibliometric indices to quantify long-term
uncertainty of outcome in sports. The Euclidean index is proposed to reward
quality over quantity, while the rectangle index can be an appropriate measure
of core performance. Their differences are highlighted through an axiomatic
analysis and several examples. Our approach also requires a weighting scheme to
compare different achievements. The methodology is illustrated by studying the
knockout stage of the UEFA Champions League in the 16 seasons played between
2003 and 2019: club and country performances as well as three types of
competitive balance are considered. Measuring competition at the level of
national associations is a novelty. All results are remarkably robust
concerning the bibliometric index and the assigned weights. Inequality has not
increased among the elite clubs and between the national associations, however,
it has changed within some countries. Since the performances of national
associations are more stable than the results of individual clubs, it would be
better to build the seeding in the UEFA Champions League group stage upon
association coefficients adjusted for league finishing positions rather than
club coefficients.Comment: 23 pages, 9 figures, 7 table
Equilibrium in Scoring Auctions
This paper studies multi-attribute auctions in which a buyer seeks to procure a complex good and evaluate offers using a quasi-linear scoring rule. Suppliers have private information about their costs, which is summarized by a multi-dimensional type. The scoring rule reduces the multidimensional bids submitted by each supplier to a single dimension, the score, which is used for deciding on the allocation and the resulting contractual obligation. We exploit this idea and obtain two kinds of results. First, we characterize the set of equilibria in quasi-linear scoring auctions with multi-dimensional types. In particular, we show that there exists a mapping between the class of equilibria in these scoring auctions and those in standard single object IPV auctions. Second, we prove a new expected utility equivalence theorem for quasi-linear scoring auctions.Auctions, Procurement
Prediction Markets: Alternative Mechanisms for Complex Environments with Few Traders
Double auction prediction markets have proven successful in large-scale applications such as elections and sporting events. Consequently, several large corporations have adopted these markets for smaller-scale internal applications where information may be complex and the number of traders is small. Using laboratory experiments, we test the performance of the double auction in complex environments with few traders and compare it to three alternative mechanisms. When information is complex we find that an iterated poll (or Delphi method) outperforms the double auction mechanism. We present five behavioral observations that may explain why the poll performs better in these settings
Welfare Maximization and Truthfulness in Mechanism Design with Ordinal Preferences
We study mechanism design problems in the {\em ordinal setting} wherein the
preferences of agents are described by orderings over outcomes, as opposed to
specific numerical values associated with them. This setting is relevant when
agents can compare outcomes, but aren't able to evaluate precise utilities for
them. Such a situation arises in diverse contexts including voting and matching
markets.
Our paper addresses two issues that arise in ordinal mechanism design. To
design social welfare maximizing mechanisms, one needs to be able to
quantitatively measure the welfare of an outcome which is not clear in the
ordinal setting. Second, since the impossibility results of Gibbard and
Satterthwaite~\cite{Gibbard73,Satterthwaite75} force one to move to randomized
mechanisms, one needs a more nuanced notion of truthfulness.
We propose {\em rank approximation} as a metric for measuring the quality of
an outcome, which allows us to evaluate mechanisms based on worst-case
performance, and {\em lex-truthfulness} as a notion of truthfulness for
randomized ordinal mechanisms. Lex-truthfulness is stronger than notions
studied in the literature, and yet flexible enough to admit a rich class of
mechanisms {\em circumventing classical impossibility results}. We demonstrate
the usefulness of the above notions by devising lex-truthful mechanisms
achieving good rank-approximation factors, both in the general ordinal setting,
as well as structured settings such as {\em (one-sided) matching markets}, and
its generalizations, {\em matroid} and {\em scheduling} markets.Comment: Some typos correcte
Recommended from our members
Information Aggregation Under Ambiguity: Theory and Experimental Evidence
We study information aggregation in a dynamic trading model with partially informed and ambiguity averse traders. We show theoretically that separable securities, introduced by Ostrovsky (2012) in the context of Subjective Expected Utility, no longer
aggregate information if some traders have imprecise beliefs and are ambiguity averse. Moreover, these securities are prone to manipulation, as the degree of information aggregation can be influenced by the initial price, set by the uninformed market maker. These observations are also confirmed in our experiment, using prediction markets. We define a new class of strongly separable securities which are robust to the above considerations, and show that they characterize information aggregation in both strategic and non-strategic environments. We derive several theoretical predictions, which we are able to confirm in the lab
Decentralized Prediction Markets and Sports Books
Prediction markets allow traders to bet on potential future outcomes. These
markets exist for weather, political, sports, and economic forecasting. Within
this work we consider a decentralized framework for prediction markets using
automated market makers (AMMs). Specifically, we construct a liquidity-based
AMM structure for prediction markets that, under reasonable axioms on the
underlying utility function, satisfy meaningful financial properties on the
cost of betting and the resulting pricing oracle. Importantly, we study how
liquidity can be pooled or withdrawn from the AMM and the resulting
implications to the market behavior. In considering this decentralized
framework, we additionally propose financially meaningful fees that can be
collected for trading to compensate the liquidity providers for their vital
market function
Q-Strategy: A Bidding Strategy for Market-Based Allocation of Grid Services
The application of autonomous agents by the provisioning and usage of computational services is an attractive research field. Various methods and technologies in the area of artificial intelligence, statistics and economics are playing together to achieve i) autonomic service provisioning and usage of Grid services, to invent ii) competitive bidding strategies for widely used market mechanisms and to iii) incentivize consumers and providers to use such market-based systems.
The contributions of the paper are threefold. First, we present a bidding agent framework for implementing artificial bidding agents, supporting consumers and providers in technical and economic preference elicitation as well as automated bid generation by the requesting and provisioning of Grid services. Secondly, we introduce a novel consumer-side bidding strategy, which enables a goal-oriented and strategic behavior by the generation and submission of consumer service requests and selection of provider offers. Thirdly, we evaluate and compare the Q-strategy, implemented within the presented framework, against the Truth-Telling bidding strategy in three mechanisms – a centralized CDA, a decentralized on-line machine scheduling and a FIFO-scheduling mechanisms
- …