Nonparametric Strategy Test
This provides a method for analyzing strategic behavior in games, but it is incremental as it adapts existing statistical tests to a specific domain.
The paper tackles the problem of determining if an agent follows a mixed strategy in repeated games by developing a nonparametric statistical test that combines chi-squared and runs tests, applied to human rock-paper-scissors data showing 61% of subjects adhere to a uniform random strategy.
We present a nonparametric statistical test for determining whether an agent is following a given mixed strategy in a repeated strategic-form game given samples of the agent's play. This involves two components: determining whether the agent's frequencies of pure strategies are sufficiently close to the target frequencies, and determining whether the pure strategies selected are independent between different game iterations. Our integrated test involves applying a chi-squared goodness of fit test for the first component and a generalized Wald-Wolfowitz runs test for the second component. The results from both tests are combined using Bonferroni correction to produce a complete test for a given significance level $α.$ We applied the test to publicly available data of human rock-paper-scissors play. The data consists of 50 iterations of play for 500 human players. We test with a null hypothesis that the players are following a uniform random strategy independently at each game iteration. Using a significance level of $α= 0.05$, we conclude that 305 (61%) of the subjects are following the target strategy.