Elicitation of Strategies in Four Variants of a Round-Robin Tournament: The Case of Goofspiel

Abstract

Goofspiel is a simple two-person zero-sum game for which there exist no known equilibrium strategies. To gain insight into what constitute winning strategies, we conducted a round-robin tournament in which participants were asked to provide computerized programs for playing the game with or without carryover. Each of these two variants was to be played under two quite different objective functions, namely, maximization of the cumulative number of points won across all opponents (as in Axelrod's tournament), and maximization of the probability of winning any given round. Our results show that there are, indeed, inherent differences in the results with respect to the complexity of the game and its objective function, and that winning strategies exhibit a level of sophistication, depth, and balance that are not captured by present models of adaptive learning.