Search decisions in a game of polynomial root counting

There is increasing interest in having mixed teams of humans and smart machines carry out missions of search, surveillance, and reconnaissance. Understanding the way humans make decisions in such search problems is important to achieve effective cooperation. We report research on search styles we have observed in one dimensional search for real roots of randomly generated polynomials. The objective (solution) of the game is to determine the number of distinct real roots in [-1, 1], given an expression for the polynomial and a tool to sample the polynomial. Each player chooses a sequence of sample points in an attempt to collect sufficient information to estimate the number of roots in the interval. Data on eighteen subject players was collected and analyzed. The subjects were classified on the basis of three different types of player strategies that were identified in the games that the subjects played. A formal definition of indistinguishable players is given. Each of the subjects was modeled by a first-order Markov chain that is constructed using the recorded choices that were made by the subject. Using these Markov models, we have created computer programs that play the game so as to be indistinguishable (with respect to a predefined statistic) from the player that was modeled. Formal definitions of player confidence and boredom are proposed based on the analysis of the game play and resulting Markov model.