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In online betting, the bookmaker can update the payoffs it offers on a particular event many times before the event takes place, and the updated payoffs may depend on the bets accumulated thus far. We study the problem of bookmaking with…

Computer Science and Game Theory · Computer Science 2025-01-14 Alankrita Bhatt , Or Ordentlich , Oron Sabag

This paper considers the use of observed and predicted match statistics as inputs to forecasts of the outcomes of football matches. It is shown that, were it possible to know the match statistics in advance, highly informative forecasts of…

Applications · Statistics 2020-01-27 Edward Wheatcroft

Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…

Computer Science and Game Theory · Computer Science 2024-06-10 Zhihuan Huang , Yuqing Kong , Tracy Xiao Liu , Grant Schoenebeck , Shengwei Xu

We consider mechanisms for truthfully eliciting probabilistic predictions from a group of experts. The standard approach -- using a proper scoring rule to separately reward each expert -- is not robust to collusion: experts may collude to…

Computer Science and Game Theory · Computer Science 2021-09-07 Eric Neyman , Tim Roughgarden

Evaluating the accuracies of models for match outcome predictions is nice and well but in the end the real proof is in the money to be made by betting. To evaluate the question whether the models developed by us could be used easily to make…

Applications · Statistics 2017-02-21 Albrecht Zimmermann

Bookmakers' odds consistently provide one of the most accurate methods for predicting the results of professional tennis matches. However, these odds usually only become available shortly before a match takes place, limiting their…

Applications · Statistics 2025-08-25 Matthew J Penn , Jed Michael , Samir Bhatt

As game companies increasingly embrace a service-oriented business model, the need for predictive models of players becomes more pressing. Multiple activities, such as user acquisition, live game operations or game design need to be…

Artificial Intelligence · Computer Science 2022-09-27 Paolo Burelli

Correlated equilibria enable a coordinator to influence the self-interested agents by recommending actions that no player has an incentive to deviate from. However, the effectiveness of this mechanism relies on accurate knowledge of the…

Computer Science and Game Theory · Computer Science 2026-05-18 Jaehan Im , Ufuk Topcu , David Fridovich-Keil

In economy, markets are denoted as efficient when it is impossible to systematically generate profits which outperform the average. In the past years, the concept has been tested in other domains such as the growing sports betting market.…

Physics and Society · Physics 2023-03-30 Ralph Stömmer

We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive values for the goods. The prior distributions on those…

Computer Science and Game Theory · Computer Science 2024-10-22 Jamie Tucker-Foltz , Richard Zeckhauser

The valuation process that economic agents undergo for investments with uncertain payoff typically depends on their statistical views on possible future outcomes, their attitudes toward risk, and, of course, the payoff structure itself.…

Pricing of Securities · Quantitative Finance 2010-01-11 Constantinos Kardaras

In this paper, we deal with the uncertainty of bidding for display advertising. Similar to the financial market trading, real-time bidding (RTB) based display advertising employs an auction mechanism to automate the impression level media…

Computer Science and Game Theory · Computer Science 2017-01-23 Haifeng Zhang , Weinan Zhang , Yifei Rong , Kan Ren , Wenxin Li , Jun Wang

Consumers often face products sold as lotteries rather than fixed outcomes. A prominent case is the loot box in video games, where players pay for randomized rewards. We investigate how presentation formats shape consumer beliefs and…

General Economics · Economics 2025-11-04 Markus Dertwinkel-Kalt , Hans-Theo Normann , Jan-Niklas Tiede , Tobias Werner

We use the fertile ground of betting markets to study the anticipation of major news in financial markets. While there is a considerable body of literature on the accuracy and efficiency of betting markets after important in-match events,…

General Economics · Economics 2025-05-28 David Winkelmann , Christian Deutscher

Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to…

Computer Science and Game Theory · Computer Science 2014-02-17 Liming Pan , Dong Hao , Zhihai Rong , Tao Zhou

We modify the standard model of price competition with horizontally differentiated products, imperfect information, and search frictions by allowing consumers to flexibly acquire information about a product's match value during their…

Theoretical Economics · Economics 2021-04-28 Vasudha Jain , Mark Whitmeyer

We use a logical device called the Dutch Book to establish epistemic confidence, defined as the sense of confidence \emph{in an observed} confidence interval. This epistemic property is unavailable -- or even denied -- in orthodox…

Statistics Theory · Mathematics 2021-06-09 Yudi Pawitan , Hangbin Lee , Youngjo Lee

We study the Online Bookmaking problem, where a bookmaker dynamically updates betting odds on the possible outcomes of an event. In each betting round, the bookmaker can adjust the odds based on the cumulative betting behavior of gamblers,…

Machine Learning · Computer Science 2025-06-23 Hadar Tal , Oron Sabag

Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent…

Trading and Market Microstructure · Quantitative Finance 2021-03-09 Bastien Baldacci , Dylan Possamaï , Mathieu Rosenbaum

This note proposes a procedure for enhancing the quality of probabilistic prediction algorithms via betting against their predictions. It is inspired by the success of the conformal test martingales that have been developed recently.

Machine Learning · Computer Science 2021-05-19 Vladimir Vovk