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<p>This paper revisits the neoclassical production paradigm by developing a generalized framework that explicitly incorporates input indivisibility and inter-agent complementarity. In contrast to the assumption of perfect substitutability, we argue that agents such as labor, artificial intelligence, and capital, generate value both individually and collectively. Classical valuation models, particularly the Shapley value, are shown to be inadequate for capturing this dual contribution structure. We propose an extended cooperative game-theoretic model that decomposes marginal value into two components: the agents stand-alone contribution and their contribution to group productivity. Leveraging tools from fractional calculus, we further integrate memory effects to account for temporal accumulation and learning-by-doing. The resulting framework yields a convex and increasing production function and introduces a refined valuation metric composed of three entitlements: normal wage, rent of ability, and interest from incremental benefits. Numerical illustrations confirm the divergence between memory-based and standard marginal values, underscoring the significance of dynamic complementarities in modern production systems.</p>

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Complementary Agents in Convex Production Under a New Cooperative Game Framework

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Dipankar Das

摘要

This paper revisits the neoclassical production paradigm by developing a generalized framework that explicitly incorporates input indivisibility and inter-agent complementarity. In contrast to the assumption of perfect substitutability, we argue that agents such as labor, artificial intelligence, and capital, generate value both individually and collectively. Classical valuation models, particularly the Shapley value, are shown to be inadequate for capturing this dual contribution structure. We propose an extended cooperative game-theoretic model that decomposes marginal value into two components: the agents stand-alone contribution and their contribution to group productivity. Leveraging tools from fractional calculus, we further integrate memory effects to account for temporal accumulation and learning-by-doing. The resulting framework yields a convex and increasing production function and introduces a refined valuation metric composed of three entitlements: normal wage, rent of ability, and interest from incremental benefits. Numerical illustrations confirm the divergence between memory-based and standard marginal values, underscoring the significance of dynamic complementarities in modern production systems.