 Equilibrium Selection and Robust Governance in the Agentic Economy: Human AI Delegation in Strategic and Incomplete Market ModelsDavit Gondauri EconStor Preprints from ZBW - Leibniz Information Centre for Economics Abstract: The emergence of the agentic economy-an economic environment in which autonomous artificial intelligence agents increasingly undertake transactions, negotiate contractual terms, allocate resources, and execute decisions on behalf of human and institutional principals-introduces a fundamental challenge to economic theory: individual algorithmic rationality does not necessarily imply collective efficiency, equilibrium stability, or the protection of human welfare. As autonomous decision-making becomes increasingly embedded in economic institutions, the central question extends beyond whether AI agents can optimize delegated objectives. It concerns whether their strategic interactions generate economically desirable outcomes, under what conditions delegated decisions diverge from human interests, and whether governance mechanisms can provide mathematically verifiable guarantees against welfare deterioration. This study develops a comprehensive theoretical-computational framework for equilibrium selection, welfare alignment, and robust governance in the agentic economy. Integrating noncooperative game theory, strategic complementarities, Bayesian and regularized market responses, convex optimization, quasilinear exchange, and incomplete financial markets, the research establishes a structured collection of analytical results, counterexamples, computational algorithms, and verifiable certificates, designated AE1-AE30. Principal Scientific Contributions 1. Equilibrium rationality does not guarantee human-welfare protection. The analysis establishes that individually rational strategies of autonomous AI delegates may generate multiple Nash equilibria with materially different consequences for human principals. Consequently, governance policies evaluated exclusively against a favorable equilibrium may fail to protect human interests under alternative strategically consistent outcomes. For a specified class of finite games with nonnegative additive strategic complementarities and nondecreasing human loss, the research derives conditions under which the greatest pure-strategy equilibrium provides a valid upper bound on human loss across all mixed Nash equilibria (AE9). This result converts a potentially complex equilibrium-safety assessment into a mathematically tractable certificate within the declared game class. 2. Cost-minimizing safe governance may fail to attain an optimum. The study identifies an explicit two-instrument governance mechanism in which autonomy incentives and assurance interventions jointly influence strategic behavior and human exposure. Within this model, the requirement to protect human welfare against every Nash equilibrium generates a nonclosed safety region. An exact analytical construction (AE7-AE8) demonstrates that the governance-cost infimum can remain unattained, even though feasible policies can approach it arbitrarily closely. The result reveals a fundamental distinction between approaching the lowest possible governance cost and possessing an implementable, cost-minimizing safe policy. 3. A common AI valuation bias can be economically neutral, while heterogeneous biases generate welfare losses. The research distinguishes common additive distortions in delegated valuations from cross-agent differences in those distortions. Under explicitly specified quasilinear exchange conditions, a common additive score shift can be absorbed into supporting market prices without changing equilibrium resource allocations or aggregate human welfare. By contrast, heterogeneous distortions alter relative allocation incentives and can generate measurable human-welfare losses. The resulting decomposition (AE24) provides an economic explanation of why the dispersion of delegated objectives-not merely the magnitude of a common algorithmic bias-can be decisive for welfare alignment. 4. Mathematically certified bounds on AI-induced welfare deterioration and safe governance. A central contribution is the derivation of a sharp welfare-loss bound for delegated exchange under uniform curvature assumptions and fixed convex feasibility constraints (AE27). The analysis connects the dispersion of AI-delegate valuation distortions to an explicit upper bound on human-welfare regret, including settings with active portfolio restrictions and incomplete security spanning. Building on this result, AE27-AE29 establish a computable, sufficient safety certificate for governance policies. When delegated score distortions depend affinely on policy instruments, the certificate generates a convex inner approximation of the safe-policy region. This provides a rigorous foundation for identifying governance interventions whose compliance with a prescribed welfare-loss threshold can be mathematically verified under the model's assumptions. 5. Reproducible computational verification and independent numerical benchmarking. The theoretical results are supported by a structured computational research program incorporating exact rational calculations, interval-certified numerical bounds, projected optimization methods, and independent solver comparisons. The computational analysis includes: 100 synthetic nonlinear policy-shock economies, including 50 cases with active joint portfolio constraints. Successful reconstruction of all 100 constructed equilibrium allocations, with certified rational coordinate-error bounds below (10^{-9}). 16 independently checked logit fixed-point certificates, using rigorous exponential enclosures with error bounds below (10^{-13}). 33 additional instances generated independently of preselected equilibrium solutions, covering heterogeneous populations of 4-128 agents and multiple portfolio-constraint regimes. Active portfolio restrictions in 22 of the 33 additional instances. Successful numerical solution of all 33 additional instances using projected-gradient optimization and an independent SLSQP reference solver, with a maximum absolute objective-value difference of approximately (5.433\times10^{-9}). These experiments evaluate numerical consistency, scalability across the examined population sizes, and the robustness of the computational implementation under different feasibility constraints. The results are accompanied by documented computational procedures and replication materials. Originality and Contribution to Economic Science The study's principal scientific contribution is not the invention of a universal equilibrium-existence theorem or a new foundation for convex optimization. Rather, it develops new conditional economic-mathematical results for explicitly specified human-AI delegation mechanisms, drawing on established mathematical tools while extending their application to agentic economic governance. Its distinctive contribution lies in the integration of three analytically connected problems: The relationship between strategic equilibrium selection and the safety of delegated economic decisions. The distinction between common valuation distortions and economically consequential heterogeneity across autonomous delegates. The construction of computable welfare-loss bounds and sufficient governance certificates for protecting human economic interests. Together, these results clarify the difference between optimizing the objectives of AI agents and safeguarding the welfare of the humans and institutions they represent. Scientific Significance and Scope The findings offer a mathematical foundation for further research into human-aligned AI markets, delegated financial decisions, algorithmic market coordination, equilibrium-sensitive regulation, and welfare-constrained autonomous economic systems. The framework provides theoretical guidance for designing assurance mechanisms, reviewing portfolio restrictions, and evaluating governance policies against explicitly defined welfare objectives. The investigation is theoretical-computational. Its mathematical conclusions apply under the stated assumptions, and its numerical results are derived from constructed or independently sampled synthetic economies. The study does not claim causal identification of governance effects in observed AI markets, empirical validation of deployed autonomous agents, or universal safety guarantees across all economic environments. Its broader significance is the demonstration that the economic governance of autonomous AI requires more than algorithmic efficiency: it requires explicit alignment between delegated objectives and human welfare, rigorous treatment of equilibrium multiplicity, and verifiable mathematical conditions under which governance interventions can limit economic harm. By connecting equilibrium theory, incomplete-market allocation, welfare analysis, and reproducible computation, this research contributes to the theoretical foundations of the emerging agentic economy and establishes a platform for subsequent empirical validation and institutional application. Keywords: agentic economy; human AI delegation; equilibrium selection; robust governance; incomplete markets; welfare alignment; exact computation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:zbw:esprep:344185 Access Statistics for this paper More papers in EconStor Preprints from ZBW - Leibniz Information Centre for Economics Contact information at EDIRC. |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.