No Stationary Strategy Survives: Nash Equilibrium Impossibility and the Counter-Harvest Trap as a Game-Theoretic Solution Concept

Paper 1 formalised rival energy-state inference as a Hidden Markov Model (HMM) over a 40-state space and characterised the counter-harvest trap as a detectable phenomenon. That framework assumed rivals behave as stationary processes. This paper breaks that assumption.

We prove three results. Theorem 1: no stationary strategy profile constitutes a Nash equilibrium in the 2026 F1 energy deployment game. The proof uses Fink's (1964) stationarity condition: because ERS depletion makes the action set state-dependent, any stationary policy that responds to energy signals is exploitable by a sufficiently patient rival. Theorem 2: the counter-harvest trap constitutes a sequential equilibrium strategy for the leading car under four explicit conditions — (C-Regen), (C-Deceive), (C-Value), and (C-Continuation) — which we characterise analytically. Theorem 3: rho_c >= rho* is necessary for the trap to be a sequential equilibrium strategy on circuit c, and is sufficient given race-horizon (H > k*), emission-separation, and payoff conditions (each car-specific and empirically verifiable, with rho_c >= rho* as the binding circuit-fixed constraint).

This yields a circuit classification at the central pre-season parameter estimate: the trap is not viable at low-regen circuits (Australia, Monza, Saudi Arabia; rho_c approximately 1.0) and is viable at high-regen circuits (Azerbaijan, Singapore; rho_c approximately 2.2). The pre-season sensitivity of rho* spans the discrete set {0.77, 1.40, 1.92, 2.56}, so circuit classification for intermediate circuits is uncertain until Baum-Welch calibration from Race 2.

We introduce two structural improvements over Paper 1: (i) a circuit-conditioned harvest transition matrix in which ERS recharge transition probabilities scale with rho_c; and (ii) a bivariate Gaussian emission model for the joint observable (delta_v_trap, delta_t_sector) that replaces the conditional independence assumption of Paper 1. Four falsifiable predictions (P3-1 through P3-4) are locked before Race 2 (China). The primary empirical test is Azerbaijan (Race 17), the highest-rho_c circuit on the 2026 calendar.