Quantum-like model of brain's functioning: Decision making from decoherence

Abstract

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation which in quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics of in the brain; especially roles played by lateral prefrontal cortex or and orbitofrontal cortex.

A Quantum-Like View to a Generalized Two Players Game

“…No matter which was their status at t = 0, its effect simply disappears when t increases. This is clearly a measure of the fact that our model is not really the two-player game proposed in [7], as we have already stressed before, but a slightly different version of that.…”

“…The first essential difference with respect to what is done in [7] is now the way in which these vectors are constructed: we consider two fermionic operators, see Appendix, i.e. two operators b 1 and b 2 , satisfying the following canonical anti-commutation rules (CAR):…”

“…And so on 1 . Now, let us introduce as in [7] four real numbers a, b, c and d satisfying the inequalities c > a > d > b. The payoff of G 1 is a or c if G 2 's choice is 0 2 : 0 1 0 2 corresponds to a payoff a, while 1 1 0 2 corresponds to c. On the other hand, if G 2 chooses 1, 1 2 , G 1 's payoff is b or d: 0 1 1 2 corresponds to b, while 1 1 1 2 corresponds to d. The situation is summarized in the following table, [7]:…”

“…Then, if G 1 and G 2 are rational players, meaning that they are both interested not to get b, they should both choose 1 (1 1 1 2 ). In [7] this problem has been considered using quantum techniques: a mental state vector belonging to some suitable Hilbert space is associated to each possible choice of the players, and it is used to describe the situation. In particular, since we have here only four possible choices, the Hilbert space is four dimensional.…”

Sometimes it does hurt to ask: The constructive role of articulating impressions

“…Other QP approaches to decision making are based on the same core principles of QP theory and, specifically, share the key assumption employed presently, that a decision must involve a corresponding projection of the state vector (e.g., Aerts, 2009;Asano et al, 2011a, Asano et al, 2012Pothos & Busemeyer, 2009;Yukalov & Sornette, 2010). 3 Note that different QP models do somewhat differ in the psychological assumptions which they embody, over and above core quantum principles.…”