Modeling the Monty Hall Decision Problem with Reaction Kinetics

Abstract

Using the Monty Hall probability problem as a model system, we ask whether simple chemical reaction mechanisms can implement optimal strategies for non-trivial decision making. In this puzzle, a contestant chooses one of three doors (only one hides a prize), the host, knowing the content, opens another door revealing no prize, and finally the contestant must decide whether to stay with the original choice or switch to the remaining closed door. Assigning distinct molecular species to the player, initial choice, reveal step, and final decision, we encode the problem in mass-action kinetics. For pseudo-first-order conditions, tuning a single rate constant shifts the network continuously between "always-stay" (1/3 success) and "always-switch" (2/3 success) regimes. We derive closed-form, time-dependent expressions for the success kinetics, concluding with a brief discussion of proposed DNA strand-displacement implementations and kinetically hard-wired molecular decision-making.