Conscious access in the human brain is often described as the outcome of a competition among candidate representations, but this competition is usually left at the level of mechanism or metaphor rather than analyzed as a strategic allocation problem. We introduce an access contest in which internal modules compete for a scarce broadcast slot by choosing a costly amplification effort. Access is allocated by a smooth probabilistic rule, allowing the model to interpolate between diffuse selection and winner-take-all competition. We establish pure-strategy equilibrium existence under standard convexity and bounded-benefit assumptions, and give sufficient conditions for uniqueness using diagonal strict concavity. We then analyze capture in the two-module case, and for quadratic costs, we derive a sharp threshold in the competition intensity above which capture occurs. For strongly convex costs, we prove an if-and-only-if capture criterion in terms of the cost-adjusted amplification advantage of the lower-value module. Under the same curvature-dominance condition that guarantees uniqueness, we show that the unique pure Nash equilibrium of the general \(M\)-module access contest can be approximated efficiently by projected pseudo-gradient dynamics, with logarithmic dependence on the desired accuracy. Finally, we prove an impossibility theorem for single-slot access mechanisms. Exact winner-take-all efficiency is incompatible with robustness to small score perturbations. Thus, smooth probabilistic access rules are not merely analytically convenient, but structurally motivated. These results provide a game-theoretic foundation for studying competition for conscious access, connecting equilibrium analysis, capture, computation, and mechanism-level limitations under a common formal model.

翻译：人类大脑中的意识接入常被描述为候选表征之间的竞争结果，但这种竞争通常停留在机制或隐喻层面，鲜少被作为策略性资源分配问题加以分析。我们提出一种接入竞赛模型，其中内部模块通过选择代价高昂的放大努力来竞争稀缺的广播通道。接入分配采用平滑概率规则，使模型能够弥合分散选择与赢家通吃竞争之间的谱系。我们在标准凸性与有界收益假设下建立了纯策略均衡存在性，并利用对角严格凹性给出了均衡唯一性的充分条件。进而分析双模块情形下的捕获现象：对于二次成本函数，我们推导出捕获发生的竞争强度临界阈值；对于强凸成本函数，我们以低价值模块的成本调整放大优势为基础，证明了充要捕获准则。在确保唯一性的曲率主导条件下，我们证明一般M模块接入竞赛的唯一纯纳什均衡可通过投影伪梯度动力学高效逼近，其精度依赖呈对数增长。最后，我们证明了单通道接入机制的不可能性定理：精确的赢家通吃效率与对微小分数扰动的鲁棒性不可兼得。因此，平滑概率接入规则不仅具有分析便利性，更具备结构合理性。这些结果为研究意识接入竞争提供了博弈论基础，将均衡分析、捕获现象、计算方法和机制层面的局限性统一在共同的形式模型之下。