Endogenous Randomness from Adversarial Market Learning

We propose a deterministic adversarial market model in which apparent randomness emerges endogenously from the interaction between a market mechanism and a population of predictive traders. Unlike a classical generative adversarial network, the model does not attempt to imitate an external empirical data distribution and does not inject random noise into a generator. The market is represented by a deterministic binary return path, while traders learn predictive strategies from observed in-sample history and trade on an out-of-sample continuation. The market then adapts against the traders by reducing their predictive and trading edge. The central experiment begins with a smooth, highly predictable market path. Traders with multiple lookback windows and multiple holding periods learn to predict future cumulative returns. Initially, these traders earn large out-of-sample profits. After adversarial market adaptation, their out-of-sample profitability collapses toward zero. Importantly, in the final clean specification, no explicit sign-balance, transition-rate, or autocorrelation penalties are imposed. Nevertheless, the out-of-sample return sequence becomes balanced, has transition rate close to one half, has low autocorrelation, and passes block-based distributional diagnostics. In a medium-size experiment with $T_{\mathrm{IS}}=2000$ and $T_{\mathrm{OOS}}=10000$, the out-of-sample positive-return fraction is $0.5010$, the transition rate is $0.4896$, and the maximum absolute autocorrelation is $0.0275$. Binary return blocks transformed into dyadic variables are close to uniform on $[0,1]$, and normalized block sums are broadly consistent with a standard normal law. These results support the hypothesis that market randomness can arise as the endogenous residue of arbitrage pressure rather than from exogenous stochastic shocks.