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Preprint . 2026
License: CC BY
Data sources: ZENODO
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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No Stationary Strategy Survives: Nash Equilibrium Impossibility and the Counter-Harvest Trap as a Game-Theoretic Solution Concept

Authors: Kleisarchaki, Kalliopi;

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

Abstract

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average