Subjective Randomness in a Non-cooperative Game
- Michael Payton, Department of Psychology, University of Wisconsin Madison, Madison, Wisconsin, United States
- Jeffrey Zemla, University of Wisconsin-Madison, Madison, Wisconsin, United States
- Joseph Austerweil, Psychology, University of Wisconsin - Madison, Madison, Wisconsin, United States
AbstractRock, Paper, Scissors (RPS) is a simple non-cooperative game. The game has three possible actions: R (rock), P (paper) and S (scissors). The scoring of the game is also simple: scissors beats paper, rock beats scissors and paper beats rock (all signs stalemate against themselves). The game is notable because over multiple games with the same opponent, optimal play according to a Nash Equilibrium requires subjects to play with genuine randomness. To examine the relationship between randomness judgments in the context of competition, we tested subjects with identical sequences in two conditions: one produced from a dice roll, one from someone playing paper rock scissors. We compared these findings to models of subjective randomness from Falk and Konold (1997) and from Griffiths and Tenenbaum. (2001) which explain assessments of randomness as a function of algorithmic complexity and statistical inference, respectively. In both conditions we see failure of the models to adequately describe subjective randomness judgements of ternary outcomes. We also observe that context influences perceptions of randomness such that some isomorphic sequences produced from intentional play are perceived as less random than dice rolls. We discuss this finding in terms of the relation between patterns and opponent modeling.
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