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Entropy
Volume 21
Issue 6
10.3390/e21060585
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Article

Betting, Selection, and Luck: A Long-Run Analysis of Repeated Betting Markets

by
Giulio Bottazzi
* and
Daniele Giachini
*
Institute of Economics & Department EMbeDS, Scuola Superiore Sant’Anna, Piazza Martiri della Libertà 33, 56127 Pisa, Italy
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(6), 585; https://doi.org/10.3390/e21060585
Submission received: 15 March 2019 / Revised: 27 May 2019 / Accepted: 11 June 2019 / Published: 13 June 2019
(This article belongs to the Special Issue Information Theory, Social Inquiry, and Economic Analysis: History and Recent Developments)
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Abstract

We consider a repeated betting market populated by two agents who wage on a binary event according to generic betting strategies. We derive new simple criteria, based on the difference of relative entropies, to establish the relative wealth of the two agents in the long-run. Little information about agents’ behavior is needed to apply the criteria: it is sufficient to know the odds traders believe fair and how much they would bet when the odds are equal to the ones the other agent believes fair. Using our criteria, we show that for a large class of betting strategies, it is generically possible that the ultimate winner is only decided by luck. As an example, we apply our conditions to the case of Constant Relative Risk Averse (CRRA) and quantal response betting.
Keywords: bounded rationality; betting strategies; market selection; recurrent processes; luck bounded rationality; betting strategies; market selection; recurrent processes; luck

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MDPI and ACS Style

Bottazzi, G.; Giachini, D. Betting, Selection, and Luck: A Long-Run Analysis of Repeated Betting Markets. Entropy 2019, 21, 585. https://doi.org/10.3390/e21060585

AMA Style

Bottazzi G, Giachini D. Betting, Selection, and Luck: A Long-Run Analysis of Repeated Betting Markets. Entropy. 2019; 21(6):585. https://doi.org/10.3390/e21060585

Chicago/Turabian Style

Bottazzi, Giulio, and Daniele Giachini. 2019. "Betting, Selection, and Luck: A Long-Run Analysis of Repeated Betting Markets" Entropy 21, no. 6: 585. https://doi.org/10.3390/e21060585

APA Style

Bottazzi, G., & Giachini, D. (2019). Betting, Selection, and Luck: A Long-Run Analysis of Repeated Betting Markets. Entropy, 21(6), 585. https://doi.org/10.3390/e21060585

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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