The usual way of testing probability forecasts in game-theoretic probability is via construction of test martingales. The standard assumption is that all forecasts are output by the same forecaster. In this paper I will discuss possible extensions of this picture to testing probability forecasts output by several forecasters. This corresponds to multiple hypothesis testing in statistics. One interesting phenomenon is that even a slight relaxation of the requirement of family-wise validity leads to a very significant increase in the efficiency of testing procedures. The main goal of this paper is to report results of preliminary simulation studies and list some directions of further research.

翻译：博弈概率中检验概率预测的常规方式是通过构造检验鞅。其标准假设是所有预测均由同一预测者输出。本文将探讨将此图景扩展至检验多个预测者输出的概率预测的可能性，这对应于统计学中的多重假设检验。一个有趣的现象是，即使轻微放宽族系有效性要求，也能显著提升检验程序的效率。本文主要目标是报告初步模拟研究的结果，并列出若干未来研究方向。