Modeling the Monty Hall Decision Problem with Reaction Kinetics

TL;DR

This paper models the Monty Hall problem using chemical reaction networks, demonstrating how reaction kinetics can implement optimal decision strategies and exploring potential molecular computing applications.

Contribution

It introduces a novel chemical kinetics framework to simulate decision-making strategies in the Monty Hall problem, linking reaction rates to success probabilities.

Findings

Tuning a rate constant switches success probability between 1/3 and 2/3.

Closed-form expressions for success kinetics are derived.

Discusses DNA strand-displacement implementations for molecular decision-making.

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.