An experimental test of combinatorial information markets

Ledyard, John O.; Hanson, Robin; Ishikida, Takashi

doi:10.1016/j.jebo.2008.04.010

“…A securities market primarily focused on information aggregation is often referred to as a prediction market. The forecasts of prediction markets have proved to be accurate in a variety of domains [8,42,60]. While our work builds on ideas from prediction market design [4,15,49], our framework can be applied to any contingent securities.…”

Section: Introductionmentioning

confidence: 99%

Efficient Market Making via Convex Optimization, and a Connection to Online Learning

Abernethy

¹

,

Chen

²

,

Vaughan

³

2013

ACM Trans. Econ. Comput.

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We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomial-time pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution's bounded budget. Although our framework was designed with the goal of deriving efficient automated market makers for markets with very large outcome spaces, this framework also provides new insights into the relationship between market design and machine learning, and into the complete market setting. Using our framework, we illustrate the mathematical parallels between cost function based markets and online learning and establish a correspondence between cost function based markets and market scoring rules for complete markets.

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“…The logarithmic scoring rule has been applied to a much lesser extent in experiments on education testing (Hambleton et al, 1970;Glein and Wallace, 1974) and information aggregation (Ledyard et al, 2009).…”

Section: Previous Experiments Using Scoring Rules To Elicit Beliefsmentioning

confidence: 99%

On eliciting beliefs in strategic games

Palfrey

¹

,

Wang

²

2009

Journal of Economic Behavior & Organization

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a b s t r a c tSeveral recent studies in experimental economics have tried to measure beliefs of subjects engaged in strategic games with other subjects. Using data from one such study we conduct an experiment where our experienced subjects observe early rounds of strategy choices from that study and are given monetary incentives to report forecasts of choices in later rounds. We elicit beliefs using three different scoring rules: linear, logarithmic, and quadratic. We compare forecasts across the scoring rules and compare the forecasts of our trained observers to forecasts of the actual players in the original experiment. We find significant differences across scoring rules. The improper linear scoring rule produces forecasts closer to 0 and 1 than the proper rules, and these forecasts are poorly calibrated. The two proper scoring rules induce significantly different distributions of forecasts. We find that forecasts by observers under both proper scoring rules are significantly different from the forecasts of the actual players, in terms of accuracy, calibration, and the distribution of forecasts. We also find evidence for belief convergence among the observers.

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“…A securities market primarily focused on information aggregation is often referred to as a prediction market. The forecasts of prediction markets have proved to be accurate in a variety of domains [5,24,32]. While our work builds on ideas from prediction market design [2,10,28], our framework can be applied to any contingent securities.…”

Section: Introductionmentioning

confidence: 99%

An optimization-based framework for automated market-making

Abernethy

¹

,

Chen

²

,

Vaughan

³

2011

Proceedings of the 12th ACM Conference on Electronic Commerce

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We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomial-time pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution's bounded budget.

show abstract

An experimental test of combinatorial information markets

Cited by 42 publications

References 27 publications

Efficient Market Making via Convex Optimization, and a Connection to Online Learning

Efficient Market Making via Convex Optimization, and a Connection to Online Learning

On eliciting beliefs in strategic games

An optimization-based framework for automated market-making

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