New game theory model shows conscious access requires probabilistic competition

A new arXiv paper (2606.11242) from Efthyvoulos Drousiotis, Paul Spirakis, and Sotiris Nikoletseas introduces a game-theoretic model of conscious access in the human brain. The model frames conscious perception as a competition among internal modules (candidate representations) for a single "broadcast slot" that grants conscious awareness. Each module chooses a costly amplification effort to influence the outcome, and access is allocated via a smooth probabilistic rule that interpolates between diffuse selection and winner-take-all competition. The authors establish pure-strategy equilibrium existence under standard convexity and bounded-benefit assumptions, giving sufficient conditions for uniqueness via diagonal strict concavity.

For the two-module case with quadratic costs, they derive a sharp threshold above which capture (dominance by one module) occurs. For strongly convex costs, a precise if-and-only-if capture criterion is provided in terms of cost-adjusted amplification advantage. Under curvature-dominance conditions, they show the unique pure Nash equilibrium of the general M-module contest can be efficiently approximated by projected pseudo-gradient dynamics with logarithmic accuracy dependence. Crucially, an impossibility theorem proves exact winner-take-all efficiency is incompatible with robustness to small score perturbations, structurally motivating the use of smooth probabilistic access rules. These results connect equilibrium analysis, capture dynamics, computational tractability, and mechanism-level limitations under a common formal model of neural competition.