Generating Random Sequences For You: Modeling Subjective Randomness in Competitive Games

Rapoport and Budescu (1992) showed that despite subjects’ failure to generate random sequences under explicit instructions, they were able to generate more random sequences when engaging in competitive games like Matching Pennies. Why people were able to correct their distorted sense of randomness in competitive games remains unclear. Therefore, I explored two probabilistic models to answer this question. The first one is the Coin-Weight Model, which assumes that subjects predict their competitor’s choices by implicitly assuming that their competitors intended to generate binary sequences that simulated the outcome of tossing an unbiased coin. The second one is the Markov model, which assumes that subjects believed that their competitors intended to generate sequences that simulated the outcome of a generating process with transition probability equal to 0.5. I found that both the Coin-Weight Model and Markov Model are able to characterize the calibrated subjective randomness in Dyad condition (playing Matching Pennies), but the Markov Model is better than Coin-Weight Model in explaining the Single condition, in which subjects were paired to play Matching Pennies but needed to specify their choice sequences in advance. The current study suggests that the calibrated subjective randomness in competitive games can be simulated by probabilistic models that combine the on-line evaluation of sequence randomness and Theory-of-Mind reasoning.