Stochastic Resonance in Human Cognition: ACT-R Versus Game Theory, Associative Neural Networks, Recursive Neural Networks, Q-Learning, and Humans

Stochastic Resonance in Human Cognition: ACT-R Versus Game Theory, Associative Neural Networks, Recursive Neural Networks, Q-Learning, and Humans Robert L. West ( robert_west@carleton.ca ) 1 , Terrence C. Stewart, ( tcstewar@connect.carleton.ca ) 1 , Christian Lebiere ( clebiere@maad.com ) 2 , Sanjay Chandrasekharan ( schandr2@connect.carleton.ca ) 1 Institute of Cognitive Science, Carleton University, Ottawa, Ontario, Canada, K1S 5B6 Micro Analysis and Design, Inc., 6800 Thomas Blvd, Pittsburgh, PA 15208 USA Abstract We examined the effect of cognitive noise on human game playing abilities. Human subjects played a guessing game against an ACT-R model set at different noise levels. Counter to the normal effect for noise (i.e., to increase randomness) increasing noise over certain ranges increased the win rate in both the ACT-R model and in the humans. We then attempted to model the human results using ACT-R, Q-Learning, neural networks, and Simple Recursive Neural Networks. Overall, ACT-R produced the best match to the data. However, none of these models were able to reproduce a secondary counter intuitive human win rate effect. Noise, or randomness, plays an important role in cognitive modelling. In problem solving it is often necessary to add noise to a model to get it to explore possible solutions rather than freezing onto a single approach. In memory models, noise often plays a role in modelling errors of omission and commission (e.g. Anderson & Lebiere, 1998). Noise is also used to model the ability of humans to purposefully behave stochastically (e.g., Treisman & Faulkner, 1987). In these cases, the role of noise is to create and/or increase randomness in behaviour. However, adding noise to a component within a system can also have the opposite effect. That is, adding noise can, under the right conditions, decrease randomness (i.e. the system’s behaviour moves away from chance). The best-known example of this is stochastic resonance (SR). SR refers to a class of models that produces the effect of reducing randomness by adding noise. Importantly, SR has been implicated in neural functioning (see chapter 22 of Ward, 2002 for a review) and has also been shown to influence decision making in perceptually based tasks (see chapter 21 of Ward, 2002, for a review). However, there is no agreed upon, precise definition of when a system should be classed as SR. For experimental results it is often the case that a result is assumed to be SR if adding noise to a system reduced the level of randomness of the system in some way. This is the sense in which we use the term SR. However, the important point is not the technical definition but whether or not noise can function in this way for the cognitive system, as it is known to do for the neural and perceptual systems. Games, Randomness, and Cognitive Noise In game theory, the ability to behave randomly or pseudo- randomly often plays a central role. This is because increasing the level of randomness in a player’s moves decreases the ability of the opponent to predict these moves. If we assume that increasing noise in a cognitive model will always increase the level of randomness in its behaviour then there is a direct link between cognitive noise levels and the level of randomness in a game. However, if adding noise can, under certain conditions, reduce the level of randomness, then the relationship between cognitive noise and randomness is not so straightforward. We investigated this by looking at the relationship between cognitive noise and the ability to predict your opponent in the game of Paper, Rock, Scissors (henceforth PRS). PRS was chosen for this study because the game theory solution is very simple; just play randomly, 1/3 paper, 1/3 rock, 1/3 scissors. The reason for this is that any deviation from this strategy would leave the player open to exploitation from an opponent who could detect the deviation. The expected outcome for this strategy over time is for both players to play at chance; 1/3 wins, 1/3 losses, and 1/3 ties. If adding noise to the cognitive system of a player increases the randomness of their playing then adding noise should cause the rate of win, losses and ties to move towards the chance rate. In contrast, an SR effect would cause one or both players to move away from the chance rate as more noise is added. Typically, such an effect would occur over only a limited range of the noise parameter. Another reason that PRS is a good choice is that the cognitive processes underlying PRS play have been previously studied. Human PRS play has been successfully modelled using neural networks (West & Lebiere, 2001) and ACT-R (Lebiere & West, 1999). In both cases the basic strategy was the same: to attempt to win through the detection of sequential dependencies. Specifically, each player tries to predict what their opponent will play next by detecting sequential dependencies in past moves. Both the neural network model and the ACT-R model, when compared to human data, indicated that people use their opponent's last two moves to predict the current move. We refer to this as a lag 2 model. Simpler models, which use only the last move, were termed lag 1 models. The effect of cognitive noise on this strategy seems straightforward: as noise is added to the sequential dependency mechanism the player should become less able to predict their opponent's moves. Also, as their moves are increasingly determined by the noise they should become increasingly hard to predict. Eventually the cognitive system will become completely swamped with noise and all the moves will be random. That is, the win/loss/tie rates for both players will converge towards the chance rates. With sufficient noise this outcome is unavoidable. However, if an

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