The paper, authored by Nagwan Alqershi of Universiti Teknologi MARA and Midocean University and Ramayah Thurasamy of Universiti Sains Malaysia, develops a dynamic framework in which markets are modeled as systems of interacting learning processes embedded in endogenous informational environments. Rather than characterizing agents by fixed strategies, the framework represents each participant as an adaptive algorithmic decision system defined by an objective function, a time-varying decision rule, and a learning operator that updates the rule in response to realized outcomes. The approach encompasses a broad class of adaptive procedures, including reinforcement learning, gradient-based updating, and bandit methods, all of which share the essential feature that decision rules evolve as a function of market experience rather than being solved once and for all.

Three structural features distinguish the environments the theory targets from classical models. First, decision rules are continuously updated rather than fixed, so behavior cannot generally be characterized independently of the dynamics governing the rules themselves. Second, information is generated endogenously: the actions algorithms take today shape the data they observe tomorrow, creating recursive loops that link behavior, outcomes, information, and future behavior. Third, feedback effects connect current outcomes to future decisions at very high frequency, often on time scales far shorter than human decision-making. In the formal model, a learning-intensity parameter captures how aggressively decision rules respond to new data, while a feedback-intensity parameter captures how strongly current outcomes propagate into future information and behavior. The interaction of these two parameters, rather than either in isolation, determines the qualitative character of the market.

The first major result is that stability depends jointly on learning responsiveness and feedback strength. When the aggregate learning operator satisfies a local contraction condition and feedback effects remain sufficiently weak, the system converges locally to a unique fixed point, and under stochastic disturbances it can admit a stable invariant distribution. In this regime, standard equilibrium models emerge as limiting benchmark cases: decision rules become approximately stationary, the informational environment behaves as if it were exogenous, and the classical apparatus applies as a special case. The framework does not reject equilibrium theory; it embeds it, treating convergence as a property requiring explicit demonstration rather than a maintained primitive.

The second result is more destabilizing. As learning responsiveness and feedback intensity increase together, the system crosses what the authors call a local instability frontier, identified through a linearized analysis in which the norm of the Jacobian governing local dynamics exceeds a critical threshold. Beyond that frontier, the adaptive process may generate persistent oscillations, bounded fluctuations, endogenous volatility, and outright local failure of convergence. Crucially, instability arises from the interaction between learning and feedback rather than from either force alone. A companion proposition on variance amplification shows that in a locally stable regime, stationary volatility grows with the persistence of the adaptive process, meaning substantial fluctuations can emerge endogenously even when external shocks remain small. Volatility, in other words, need not be imported from outside the system; it can be manufactured inside it.

The framework also yields a result with direct welfare consequences: the adaptation-stability trade-off. Faster learning improves responsiveness and information processing, but because learning and feedback interact multiplicatively, faster adaptation simultaneously amplifies the feedback effects that can destabilize the system. When the welfare benefits of adaptation are concave and the instability costs are convex, an interior optimum exists, and stronger feedback pushes the welfare-maximizing level of responsiveness downward. The relationship between responsiveness and performance is therefore non-monotonic, in sharp contrast to standard equilibrium settings where faster adjustment is unambiguously associated with improved efficiency. Interventions that look efficiency-enhancing in a static model may be actively destabilizing in an adaptive one.

A third strand of the analysis concerns emergent coordination. Because adaptive agents learn from data generated collectively through market interaction, correlated patterns of behavior can arise across participants without any explicit communication. The authors show that under repeated interaction and sufficiently persistent feedback, learning dynamics may synchronize responses to endogenous signals, producing coordinated outcomes that need not correspond to Nash equilibria or classical collusive agreements. This finding connects to experimental and empirical work on algorithmic pricing showing that decentralized learning systems can drift toward supracompetitive prices, and it poses a genuine challenge for competition policy, whose legal tools are built around detecting explicit agreements rather than emergent synchronization in the absence of communication.

To make the mechanisms concrete, the paper presents a stylized quantitative illustration in which a scalar market variable evolves according to a nonlinear adaptive rule whose local persistence depends on the product of learning intensity and feedback strength. Linearizing around the steady state yields a persistence coefficient governed by that interaction, and the model passes through qualitatively distinct regimes as the product crosses one: stable convergence with decaying fluctuations, persistent and oscillatory dynamics, and finally local instability in which small perturbations are amplified over time. The exercise is deliberately parsimonious, but it demonstrates the paper’s central claim that rich, persistent, and disruptive dynamics can arise from relatively simple adaptive systems once feedback loops are present.

The authors also derive testable empirical implications and report an illustrative application to U.S. equity markets using five-minute intraday data from the Trades and Quotes database covering 2015 to 2023. Algorithmic intensity is proxied by message traffic and order activity measures, update speed by the inverse of inter-trade duration, and feedback intensity by short-run order-flow autocorrelation and price-impact persistence. Across specifications with security and time fixed effects and clustered standard errors, realized volatility is positively associated with algorithmic intensity and update speed, and interaction terms between learning and feedback proxies are positive and statistically significant, consistent with the joint-amplification mechanism. Logit estimates likewise link adaptive intensity and feedback to a higher probability of extreme intraday movements exceeding three standard deviations, and specifications with quadratic terms find an inverted-U relationship between responsiveness and measures of market efficiency and liquidity, echoing the adaptation-stability trade-off.

The authors are explicit that these associations are suggestive rather than definitive, since algorithmic activity may itself respond endogenously to volatility, liquidity, and information arrivals, complicating causal inference. Identification, they suggest, will require exogenous variation in algorithm adoption, latency changes, exchange technology upgrades, and market-design reforms. The deeper implications, however, extend to policy design. If stability depends jointly on learning and feedback, regulation must operate on both dimensions at once: throttling update frequencies or imposing execution delays to lower responsiveness, and batching transactions, delaying disclosures, or aggregating signals to weaken amplification. Market design becomes feedback engineering, and policy evaluation shifts from comparing equilibria to assessing entire trajectories of adaptive adjustment. On this view, the rise of algorithmic decision-making is not a marginal extension of existing frameworks but a structural shift in the nature of economic systems, one that places adaptive learning, endogenous information generation, and feedback dynamics at the very center of economic analysis.

Subject of Research: A dynamic theory of how adaptive algorithmic learning and endogenous feedback determine stability and volatility in markets

Article Title: A theory of algorithmic markets

Article References: A theory of algorithmic markets. (n.d.). https://doi.org/10.3389/fcpxs.2026.1819789

Image Credits: AI Generated

DOI: 10.3389/fcpxs.2026.1819789

Keywords: algorithmic markets, adaptive learning, equilibrium, feedback loops, endogenous volatility, high-frequency trading, reinforcement learning, market stability, market design, complex systems, algorithmic pricing, competition policy