"Positional Dominance in Network Games: Equilibrium Conditions for Strategic Abstention from Velocity Competition"

We study a two-player infinite-horizon stochastic game on a capacitated linear distribution network in which one player commits capital to control key nodes — pipelines and storage hubs — while the rival invests in low-latency execution infrastructure. Using Markov Perfect Equilibrium with supply-demand shocks governed by a two-state volatility Markov chain, we establish the existence of a threshold σ* above which the positional player’s equilibrium payoff strictly exceeds that of the velocity-optimizing player. The advantage arises from private inventory signals and flow-redirection optionality that reaction speed cannot replicate in high-volatility regimes. We derive σ* analytically under a quadratic value function approximation, yielding σ* ≈ 0.665, and numerically via value iteration on a calibrated 8×8×8 state grid, yielding σ* ∈ [0.30, 0.36] after accounting for storage optionality and Markov persistence. Under U.S. energy midstream calibration, historical Permian–Cushing volatility of 0.35–0.42 exceeds this interval in approximately 68% of months over 2015–2024. An addendum documents the observation that the calibrated threshold lies near 1/3, a value that recurs across four independently derived operator systems; the recurrence is left as an open conjecture. JEL: C72, D43, L13, Q41 · MSC 2020: 53D10, 91B84, 91G80 · Keywords: network games, Markov perfect equilibrium, positional dominance, velocity competition, strategic abstention, commodity markets, contact geometry