Quenching Speculation in Quantum Markets via Entangled Neural Traders

TL;DR

This work investigates qubit-entangled valuations as an endogenous stabilizing mechanism for speculative markets. By training eight reinforcement-learning agents to trade a single commodity in both classical and entangled-valuation setups, the authors show that quantum correlations stabilize prices and improve traders’ net worth, avoiding bust scenarios that plague classical markets. The analysis connects this stabilization to a quantum version of the $p$-guessing game, where entanglement and phase coherence reshape the strategy landscape, eliminating pure Nash equilibria that trigger crashes and yielding nondegenerate mixed equilibria. These results reveal quantum correlations as a novel mechanism for market stabilization and demonstrate the utility of multi-agent reinforcement learning for uncovering optimal quantum strategies in complex decision problems.

Abstract

Speculative trading can drive pronounced market instabilities, yet existing regulatory and macroprudential tools intervene only after such dynamics emerge. Quantum technologies offer a fundamentally new means of shaping economic behavior by introducing non-classical correlations between decision-makers. Here we demonstrate a prototype quantum stock market in which entanglement between traders' valuations mitigates the runaway devaluation characteristic of speculative busts. Using reinforcement-learning agents trading a single commodity, we show that replacing classical valuations with quantum-correlated qubit-encoded valuations stabilizes prices and increases the AI traders' net worth relative to a classical market, where instead agents rapidly converge to liquidation strategies that collapse the asset value. To explain this behavior, we formulate and analyze a quantized version of the $p$-guessing game, a canonical model of speculative dynamics. Quantum entanglement and phase coherence reshape the strategic landscape, eliminating the pathological pure-strategy Nash equilibrium that drives market collapse in the classical game, while mixed-strategy equilibria remain non-degenerate and avoid bust-type outcomes. These results identify quantum correlations as a novel, endogenous mechanism for market stabilization and, more broadly, demonstrate the utility of multi-agent reinforcement learning algorithms for uncovering optimal strategies in complex decision-making frameworks with quantum degrees of freedom.

Figures (5)

• Figure 1: Schematic of the quantum stock market. Each trader is modeled by a neural network that attempts to maximize its net worth by buying and selling a single commodity. At the beginning of each round, the agent’s cash balance, stock holdings, and the previous round’s stock valuation are provided as inputs to its neural network, which enacts a trading policy. The network outputs a real number: its sign determines whether the agent acts as a buyer or seller, and its absolute value specifies the valuation of one unit of stock. In the classical case, buyers and sellers are matched whenever their valuations agree within a given tolerance, and cash is exchanged for a single unit of stock. In the quantum case, before matching, the raw valuations are entangled by a variational quantum circuit (orange box) where they become adjusted before buyers and sellers are matched and transactions occur.
• Figure 2: Stock prices and traders’ net worth in the classical and quantum stock market. The price of the commodity in the A classical and B quantum stock markets, calculated as the average traded price during a given round. The gray curves are commodity valuations from individual runs with random neural network initializations. The colored curves are mean averages of the gray curves over forty runs; the AI traders were randomly initialized at the beginning of each run. The net worth of each of the eight traders (each color corresponds to a different trader) for a single run in the C classical and D quantum stock markets, at each round of trading. The net worth is calculated for each agent as the current stock holdings multiplied by the current stock valuation plus cash holdings. The net worth of the poorest trader in the quantum market (gray) is greater than the richest trader in the classical market (gray).
• Figure 3: Tuning volatility with entanglement in the quantum stock market. A The average commodity price at each round of trading among eight AI agents. The curves are averaged over forty runs in which each AI agent was randomly initialized. The different shadings indicate commodity price for a quantum stock market with no entanglement $\gamma = 0$ (light blue), moderate entanglement $\gamma = \pi / 4$ (blue) and maximal entanglement $\gamma = \pi/2$ (dark blue). B Average change in the commodity price $\Delta$Price from a value of 10 cash units after 1,000 rounds of trading in the quantum stock market with different levels of entanglement. The bars indicate one standard deviation of $\Delta$Price.
• Figure 4: The Nash equilibrium and the two-player quantum guessing game. A The utility function of player 1 for the entire strategy space of the two-player $p=\frac{2}{3}$-quantum guessing game when the player’s bids are maximally entangled. B The utility functions $u_1$ (blue) and $u_2$ (green) for the maximally entangled two-player $p=\frac{2}{3}$-quantum guessing game as a function of the raw bids $\theta_1$ and $\theta_2$ in the reduced strategy space $(\phi_1, \phi_2 ) = (0, \pi/3)$. The set of optimal responses for Player 1 and Player 2 are represented as red and orange solid lines superimposed to each player's utility function. C Each player’s set of optimal responses $S_i$ from b projected onto the $(\theta_1, \theta_2)$-plane. D The utility functions $u_1$ (blue) and $u_2$ (green) for the maximally entangled two-player $p=\frac{2}{3}$-quantum guessing game as a function of the raw bids $\theta_1$ and $\theta_2$ in the reduced strategy space $(\phi_1, \phi_2) = (0, 0)$. The set of optimal responses for Player 1 and Player 2 are represented as red and orange solid lines superimposed to each player's utility function. As these sets never intersect, there is no pure Nash equilibrium. E Each player’s set of optimal responses $S_i'$ from d projected onto the $(\theta_1, \theta_2)$-plane. The intersection of these sets is a bust Nash equilibrium.
• Figure 5: Mixed strategy Nash equilibria of the quantum $p$-guessing game. Average valuation $\bar{\theta}_i$ of A Player 1 and B Player 2 for the mixed Nash equilibrium (equilibria) of the $k$-discretized quantum $p=\frac{2}{3}$ guessing game when $(\phi_1, \phi_2) = (0, \pi/3)$. When a particular discretization affords more than one mixed Nash equilibrium, the players’ average valuations for each equilibrium point are shown as markers with different shapes, e.g. triangles, squares, circles.