Average Controllability Measures for One-player Games

In this talk, I will discuss several ways to measure the extent to which a player can exert control over a one-player stochastic game, relating them to the existing literature on the “skill vs chance” dichotomy. I will focus on measures that depend only on the rules of the games, and not on how people actually play them. After outlining a set of desirable properties, I will observe that two statistical measures of effect size, known as “percentage of standard deviation explained” and “percentage of absolute deviation explained”, satisfy them but give rise to two different orders between games. Finally, I will present numerical estimates of these measures for several well-known games and a sport. The reason for targeting average controllability, rather than minimum or maximum controllability, stems from the observation that the first may more accurately approximate the behavior of a population of players of various skill levels. After all, min, average, and max are the three canonical points in the spectrum of rationality, with bounded rationality à la Simon and actual human players arguably positioned somewhere between the second and the third point. This talk is based on a paper presented at AAMAS 2016.

Authors

• Marco Faella

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