Small sample properties are of fundamental interest when only limited data is available. Exact inference is limited by constraints imposed by specific nonrandomized tests and of course also by lack of more data. These effects can be separated as we propose to evaluate a test by comparing its...

Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic "times" game such as Matching Pennies. Between matching rounds, individuals sometimes change their strategy after observing a finite sample of other outcomes within their population. Individuals from...