Bottazzi Giulio, Giachini Daniele
Institute of Economics & Department EMbeDS, Scuola Superiore Sant'Anna, Piazza Martiri della Libertà 33, 56127 Pisa, Italy.
Entropy (Basel). 2019 Jun 13;21(6):585. doi: 10.3390/e21060585.
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.
我们考虑一个重复博弈的市场，其中有两个参与者，他们根据一般的投注策略就一个二元事件进行投注。我们基于相对熵的差异推导出新的简单标准，以确定长期来看两个参与者的相对财富。应用这些标准几乎不需要关于参与者行为的信息：只需知道交易者认为公平的赔率，以及当赔率等于另一个参与者认为公平的赔率时他们会投注多少。利用我们的标准，我们表明对于一大类投注策略，最终的赢家通常可能仅由运气决定。例如，我们将我们的条件应用于常相对风险厌恶（CRRA）和量子响应投注的情况。
