Yiling Chen
Nikhil R. Devanur
David M. Pennock
ABSTRACT
We observe that Lambert et al.'s [2008] family of weighted score wagering mechanisms admit arbitrage: participants can extract a guaranteed positive payoff by betting on any prediction within a certain range. In essence, participants leave free money on the table when they ``agree to disagree,'' and as a result, rewards don't necessarily go to the most informed and accurate participants. This observation suggests that when participants have immutable beliefs, it may be possible to design alternative mechanisms in which the center can make a profit by removing this arbitrage opportunity without sacrificing incentive properties such as individual rationality, incentive compatibility, and sybilproofness. We introduce a new family of wagering mechanisms called no-arbitrage wagering mechanisms that retain many of the positive properties of weighted score wagering mechanisms, but with the arbitrage opportunity removed. We show several structural results about the class of mechanisms that satisfy no-arbitrage in conjunction with other properties, and provide examples of no-arbitrage wagering mechanisms with interesting properties.
- ALI, M. M. 1977. Probability and utility estimates for racetrack bettors. Journal of Political Economy 85, 4, 803--816.Google Scholar
Cross Ref
- ALLEN, F. AND GALE, D. 1992. Stock-price manipulation. The Review of Financial Studies 5, 3, 503--529.Google ScholarCross Ref
- BERG, J. E., FORSYTHE, R., NELSON, F. D., AND RIETZ, T. A. 200 Results from a dozen years of election futures markets research. In Handbook of Experimental Economic Results, C. A. Plott and V. Smith, Eds.Google Scholar
- BRIER, G. W. 1950. Verification of forecasts expressed in terms of probability. Monthly Weather Review 78, 1, 1--3.Google ScholarCross Ref
- CHAKRABORTY, A. AND YILMAZ, B. 2004. Manipulation in market order models. Journal of Financial Markets 7, 2, 187--206.Google ScholarCross Ref
- CHEN, Y., CHU, C.-H., MULLEN, T., AND PENNOCK, D. M. 2005. Information markets vs. opinion pools: An empirical comparison. In ACM Conference on Electronic Commerce. ACM, New York, NY, USA, 58--67. Google ScholarDigital Library
- CHEN, Y., DIMITROV, S., SAMI, R., REEVES, D. M., PENNOCK, D. M., HANSON, R. D., FORTNOW, L., AND GONEN, R. 2010. Gaming prediction markets: Equilibrium strategies with a market maker. Algorithmica 58, 4, 930--969. Google ScholarDigital Library
- CHUN, S. AND SHACHTER, R. D. 2011. Strictly proper mechanisms with cooperating players. In UAI'11: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence. 125--134.Google Scholar
- DANI, V., MADANI, O., PENNOCK, D., SANGHAI, S., AND GALEBACH, B. 2006. An empirical comparison of algorithms for aggregating expert predictions. In Conference on Uncertainty in Artificial Intelligence.Google Scholar
- FORSYTHE, R. AND LUNDHOLM, R. J. 1990. Information aggregation in an experimental market. Econometrica 58, 309--347.Google ScholarCross Ref
- FORSYTHE, R., NELSON, F., NEUMANN, G. R., AND WRIGHT, J. 1991. Forecasting elections: A market alternative to polls. In Contemporary Laboratory Experiments in Political Economy, T. R. Palfrey, Ed. University of Michigan Press, Ann Arbor, MI, USA, 69--111.Google Scholar
- GANDAR, J. M., DARE, W. H., BROWN, C. R., AND ZUBER, R. A. 1999. Informed traders and price variations in the betting market for professional basketball games. Journal of Finance LIII, 1, 385--401.Google ScholarCross Ref
- GAO, X. A., ZHANG, J., AND CHEN, Y. 2013. What you jointly know determines how you act: Strategic interactions in prediction markets. In ACM Conference on Electronic Commerce. ACM, New York, NY, USA, 489--506. Google ScholarDigital Library
- GNEITING, T. AND RAFTERY, A. E. 2007. Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102, 477, 359--378.Google ScholarCross Ref
- GOOD, I. J. 1952. Rational decisions. Journal of the Royal Statistical Society, Series B (Method-ological) 14, 1, 107--114.Google ScholarCross Ref
- GROSSMAN, S. J. 1976. On the efficiency of competitive stock markets where traders have diverse information. The Journal of Finance 31, 2, 573--585.Google ScholarCross Ref
- HANSEN, J., SCHMIDT, C., AND STROBEL, M. 2001. Manipulation in political stock markets ' preconditions and evidence. Technical Report.Google Scholar
- JACOBS, R. 1995. Methods for combining experts' probability assessments. Neural Computation 7, 5, 867--888. Google ScholarDigital Library
- JOHNSTONE, D. J. 2007. The parimutuel Kelly probability scoring rule. Decision Analysis 4, 2, 66--75. Google ScholarDigital Library
- KILGOUR, D. M. AND GERCHAK, Y. 2004. Elicitation of probabilities using competitive scoring rules. Decision Analysis 1, 2, 108--113. Google ScholarDigital Library
- KUMAR, P. AND SEPPI, D. J. 1992. Futures manipulation with 'cash settlement'. Journal of Finance 47, 4, 1485--1502.Google Scholar
- LAMBERT, N., LANGFORD, J., VAUGHAN, J. W., CHEN, Y., REEVES, D. M., SHOHAM, Y., AND PENNOCK, D. M. 2014. An axiomatic characterization of wagering mechanisms. Journal of Economic Theory. (Forthcoming).Google Scholar
- LAMBERT, N., LANGFORD, J., WORTMAN, J., CHEN, Y., REEVES, D. M., SHOHAM, Y., AND PENNOCK, D. M. 2008. Self-financed wagering mechanisms for forecasting. In ACM Conference on Electronic Commerce. ACM, New York, NY, USA, 170--179. Google ScholarDigital Library
- MATHESON, J. E. AND WINKLER, R. L. 1976. Scoring rules for continuous probability distributions. Management Science 22, 10, 1087--1096.Google ScholarDigital Library
- MILGROM, P. AND STOKEY, N. L. 1982. Information, trade and common knowledge. Journal of Economic Theory 26, 1, 17--27.Google ScholarCross Ref
- OSTROVSKY, M. 2012. Information aggregation in dynamic markets with strategic traders. Econometrica 80, 6, 2595--2648.Google ScholarCross Ref
- PAGE, S. 2007. The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies. Princeton University Press, Princeton, New Jersey. Google ScholarDigital Library
- PLOTT, C. R., WIT, J., AND YANG, W. C. 1997. Parimutuel betting markets as information aggregation devices: Experimental results. Tech. Rep. Social Science Working Paper 986, California Institute of Technology. Apr.Google Scholar
- ROLL, R. 1984. Orange juice and weather. The American Economic Review 74, 5, 861--880.Google Scholar
- SAVAGE, L. J. 1971. Elicitation of personal probabilities and expectations. Journal of the American Statistical Association 66, 336, 783--801.Google ScholarCross Ref
- SUROWIECKI, J. 2004. The Wisdom of Crowds. Doubleday. Google ScholarDigital Library
- THALER, R. H. AND ZIEMBA, W. T. 1988. Anomalies: Parimutuel betting markets: Racetracks and lotteries. Journal of Economic Perspectives 2, 2, 161--174.Google ScholarCross Ref
- UNGAR, L., MELLORS, B., SATOPÄÄ, V., BARON, J., TETLOCK, P., RAMOS, J., AND SWIFT, S. 2012. The good judgment project: A large scale test of different methods of combining expert predictions. AAAI Technical Report FS-12-06.Google Scholar
- WINKLER, R. L. 1969. Scoring rules and the evaluation of probability assessors. Journal of the American Statistical Association 64, 327, 1073--1078.Google ScholarCross Ref
- WOLFERS, J. AND ZITZEWITZ, E. 2004. Prediction markets. Journal of Economic Perspective 18, 2, 107--126.Google ScholarCross Ref
Index Terms
- Removing arbitrage from wagering mechanisms
Recommendations
Self-financed wagering mechanisms for forecasting
EC '08: Proceedings of the 9th ACM conference on Electronic commerceWe examine a class of wagering mechanisms designed to elicit truthful predictions from a group of people without requiring any outside subsidy. We propose a number of desirable properties for wagering mechanisms, identifying one mechanism - weighted-...
The Double Clinching Auction for Wagering
EC '17: Proceedings of the 2017 ACM Conference on Economics and ComputationWe develop the first incentive compatible and near-Pareto-optimal wagering mechanism. Wagering mechanisms can be used to elicit predictions from agents who reveal their beliefs by placing bets. Lambert et al. [20, 21] introduced weighted score wagering ...
An Axiomatic View of the Parimutuel Consensus Wagering Mechanism
AAMAS '18: Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent SystemsWe consider an axiomatic view of the Parimutuel Consensus Mechanism defined by Eisengerg and Gale[6]. The parimutuel consensus mechanism can be interpreted as a parimutuel market for wagering with a proxy that bets optimally on behalf of the agents, ...
Comments