THE HIDDEN BEAUTY OF THE QUADRATIC MARKET SCORING RULE: A UNIFORM LIQUIDITY MARKET MAKER, WITH VARIATIONS

2012 ◽  
Vol 1 (2) ◽  
pp. 111-125 ◽  
Author(s):  
Michael Abramovicz
Keyword(s):  
Scoring Rules ◽  
Prediction Markets ◽  
Market Maker ◽  
Scoring Rule ◽  
Market Makers ◽  
Market Participants ◽  
Aggregate Information ◽  
Spectrum Market

For some applications, prediction markets that rely entirely on voluntary transactions between individual participants may provide insufficient liquidity to aggregate information effectively, especially where the number of participants is small. A solution to this problem is to rely on an automated market maker, which allows participants to buy from or sell to the house. Robin Hanson has described a class of automated market makers called market scoring rules. This Article examines a member of this class that has received little attention, the quadratic market scoring rule. Its prime virtue is that it provides uniform liquidity across the probability or prediction spectrum. Market participants will thus have the same incentive to do research that is expected to produce an expected change in the market prediction, regardless of the current prediction. Formulas are provided for implementing the quadratic market scoring rule, as well as variations, for example to implement conditional markets.

Optimizing the liquidity parameter of logarithmic market scoring rules prediction markets

2018 ◽  
Vol 13 (3) ◽  
pp. 736-754
Author(s):  
Suparerk Lekwijit ◽  
Daricha Sutivong
Keyword(s):  
Standard Error ◽  
Market Price ◽  
Simulation Models ◽  
Scoring Rules ◽  
Prediction Markets ◽  
Market Mechanisms ◽  
Content Type ◽  
Market Makers ◽  
True Value ◽  
Price Functions

Purpose Prediction markets are techniques to aggregate dispersed public opinions via market mechanisms to predict uncertain future events’ outcome. Many experiments have shown that prediction markets outperform other traditional forecasting methods in terms of accuracy. Logarithmic market scoring rules (LMSR) is one of the most simple and widely used market mechanisms; however, market makers have to confront crucial design decisions including the setting of the parameter “b” or the “liquidity parameter” in the price functions. As the liquidity parameter has significant effects on the market performance, this paper aims to provide a comprehensive basis for the setting of the parameter. Design/methodology/approach The analyses include the effects of the liquidity parameter on the forecast standard error and the amount of time for the market price to converge to the true value. These experiments use artificial prediction markets, the proposed simulation models that mimic real prediction markets. Findings The simulation results indicate that prediction market’s forecast standard error decreases as the value of the liquidity parameter increases. Moreover, for any given number of traders in the market, there exists an optimal liquidity parameter value that yields appropriate price adaptability and leads to the fastest price convergence. Originality/value Understanding these tradeoffs, the market makers can effectively determine the liquidity parameter value under various objectives on the standard error, the time to convergence and cost.

ON MARKET MAKER FUNCTIONS

2012 ◽  
Vol 3 (1) ◽  
pp. 61-63 ◽  
Author(s):  
Robin Hanson
Keyword(s):  
Scoring Rules ◽  
Double Auction ◽  
Market Maker ◽  
Main Function ◽  
Market Makers ◽  
Continuous Double Auction

Since market scoring rules have become popular as a form of market maker, it seems worth reviewing just what such mechanisms are intended to do.The main function performed by most market makers is to serve as an intermediary between people who prefer to trade at different times.  Traders who have the same favorite times to trade can show up together to an ordinary continuous double auction, and then make and accept offers to trade.  But when traders have different favorite times, a market maker can help them by first making offers that some of them will accept, and then later making opposite offers which others will accept.  By adjusting prices in his favor, a market maker can even profit from providing this service.

A Simple Automated Market Maker for Prediction Markets

2013 ◽  
pp. 541-559
Author(s):  
David Johnstone
Keyword(s):  
Behavioral Finance ◽  
Prediction Markets ◽  
Market Maker ◽  
Price Setting ◽  
Simulation Games ◽  
Prior Beliefs ◽  
Over The Counter ◽  
Market Makers ◽  
Market Simulation ◽  
Betting Markets

There is wide scope for reliance on automated “robot” market makers in prediction markets and market simulation games in experimental economics and behavioral finance. The market maker presented here is an alternative to the well-known but less easily understood Hanson market maker. It has the advantage of being easy to derive and makes a good mathematical introduction to the logic of automated bid and ask price–setting in prediction markets. Its main advantage is that the opening security price can be set arbitrarily between zero and one, so as to match the market maker’s prior beliefs. A weakness of the Hanson market maker is that it opens automatically with a uniform prior distribution. In many real-world applications, this is unrealistic and prone to cause the market maker unnecessary trading losses (on average). Common practice, such as in betting markets and over-the-counter financial markets for binaries, is to set opening prices based on expert subjective probabilities.

scholarly journals Evaluating probabilistic forecasts of football matches: the case against the ranked probability score

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Edward Wheatcroft
Keyword(s):  
Scoring Rules ◽  
Brier Score ◽  
Sporting Events ◽  
Forecast Performance ◽  
Scoring Rule ◽  
Probability Score ◽  
Probabilistic Forecasts ◽  
Non Local ◽  
Evaluating Forecasts ◽  
Non Locality

Abstract A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is ‘sensitive to distance’, that is it takes into account the ordering in the outcomes (a home win is ‘closer’ to a draw than it is to an away win). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the Ignorance score, which is local and insensitive to distance. The Ignorance score outperforms both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.

scholarly journals Characterising scoring rules by their solution in iteratively undominated strategies

2021 ◽  
Author(s):  
Christian Basteck
Keyword(s):  
Monotonicity Property ◽  
Scoring Rules ◽  
The Other ◽  
Approval Voting ◽  
Property A ◽  
Borda Rule ◽  
Scoring Rule ◽  
Direct Mechanism ◽  
Social Choice Correspondence ◽  
Choice Correspondence

AbstractWe characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.

scholarly journals Optimal inventory management and order book modeling

2019 ◽  
Vol 65 ◽  
pp. 145-181 ◽  
Author(s):  
Nicolas Baradel ◽  
Bruno Bouchard ◽  
David Evangelista ◽  
Othmane Mounjid
Keyword(s):  
Inventory Management ◽  
High Frequency ◽  
Limit Order Book ◽  
Order Book ◽  
Value Functions ◽  
Limit Order ◽  
Terminal Wealth ◽  
Market Makers ◽  
Market Participants ◽  
The One

We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [12, 18, 19], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy.

Liquidity Provision and Cross Arbitrage in Continuous Double-Auction Prediction Markets

2014 ◽  
Vol 7 (3) ◽  
pp. 61-86
Author(s):  
Werner Antweiler
Keyword(s):  
Stock Market ◽  
Empirical Analysis ◽  
Double Auction ◽  
Prediction Markets ◽  
Market Maker ◽  
Micro Structure ◽  
Liquidity Provision ◽  
Novel Method ◽  
Continuous Double Auction ◽  
Bid Ask Spreads

Continuous double-auction prediction markets often exhibit low transaction volume due to substantial bid-ask spreads. This paper explores a novel method of providing artificial liquidity in continuous double-auction prediction markets by introducing an automated market maker that engages in zero-profit cross-arbitrage in multi-contract markets. Empirical analysis of observed bid-ask spreads, liquidity, offer acceptance, and order sizes in the 2008 UBC Election Stock Market provides additional new insights into the micro-structure of prediction markets. 

High-Frequency Trading and Conflict in the Financial Markets

2017 ◽  
Vol 32 (3) ◽  
pp. 270-282 ◽  
Author(s):  
Ricky Cooper ◽  
Jonathan Seddon ◽  
Ben Van Vliet
Keyword(s):  
Financial Markets ◽  
High Frequency ◽  
High Frequency Trading ◽  
Market Makers ◽  
Market Participants ◽  
Software Vendor ◽  
Traditional Market ◽  
Recent Developments ◽  
The Way

The last few decades has seen an ever-increasing growth in the way activities are productized and associated with a financial cost. This phenomenon, termed financialization, spans all areas including government, finance, health and manufacturing. Recent developments within finance over that past decade have radically altered the way trading occurs. This paper analyses high-frequency trading (HFT) as a necessary component of the infrastructure that makes financialization possible. Through interviews with HFT firms, a software vendor, regulators and banks, the effects of HFT on market efficiency, and its impact on costs to long-term investors are explored. This paper contributes to the literature by exploring the conflict that exists between HFT and traditional market makers in today's fragmented markets. This paper argues that society should be unconcerned with this conflict and should instead focus on the effects these participants have on the long-term investors, for whom the markets ultimately exist. In order to facilitate the best outcomes, regulation should be simple, aimed at keeping participants’ behavior stable, and the interactions among them transparent and straightforward. Financialization and HFT are inextricably linked, and society is best served by ensuring that the creative energy of these market participants is directed on providing liquidity and removing inefficiencies.

scholarly journals FaRM: Fair Reward Mechanism for Information Aggregation in Spontaneous Localized Settings

2019 ◽  
Author(s):  
Moin Hussain Moti ◽  
Dimitris Chatzopoulos ◽  
Pan Hui ◽  
Sujit Gujar
Keyword(s):  
Prior Knowledge ◽  
Incentive Mechanism ◽  
Information Aggregation ◽  
Prediction Markets ◽  
Consistency Score ◽  
Aggregate Information ◽  
Reliability Score ◽  
Random Pairing ◽  
History Of ◽  
Reward Mechanism

Although peer prediction markets are widely used in crowdsourcing to aggregate information from agents, they often fail to reward the participating agents equitably. Honest agents can be wrongly penalized if randomly paired with dishonest ones. In this work, we introduce selective and cumulative fairness. We characterize a mechanism as fair if it satisfies both notions and present FaRM, a representative mechanism we designed. FaRM is a Nash incentive mechanism that focuses on information aggregation for spontaneous local activities which are accessible to a limited number of agents without assuming any prior knowledge of the event. All the agents in the vicinity observe the same information. FaRM uses (i) a report strength score to remove the risk of random pairing with dishonest reporters, (ii) a consistency score to measure an agent's history of accurate reports and distinguish valuable reports, (iii) a reliability score to estimate the probability of an agent to collude with nearby agents and prevents agents from getting swayed, and (iv) a location robustness score to filter agents who try to participate without being present in the considered setting. Together, report strength, consistency, and reliability represent a fair reward given to agents based on their reports.

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