Endogenous information obsolescence and energetic viability in an adaptation game

This is the authors' abstract. We don't add key points for this paper.

We study an adaptation game in which agents observe binary environments at chosen Poisson rates and execute interventions after a fixed delay. Interventions increase the switching rates faced by other agents, useful information raises resource capture, and every cycle consumes energy. For nondecreasing concave interaction laws, we derive the exact present-state correlation and characterize the unique symmetric Nash equilibrium conditional on a fixed active population. With a positive delay and a linear interaction law, the net adaptation benefit has a unique maximum as the common unit cost falls. For a positive maintenance deficit below this maximum, the costs with nonnegative mean energy balance form a bounded interval. At sufficiently low costs, this balance becomes negative even though expenditure on complete observation–intervention cycles tends to zero. For bounded interaction laws, we characterize the limiting balance and show that sufficiently high finite saturation can preserve this loss. The bounded-law equilibrium is also locally stable at sufficiently low costs under a specified quasistatic best-response dynamic. Coordinating a common intervention rate preserves the benefit of lower costs. Numerical calculations and event-driven simulations illustrate the results and verify the correlation formula. The conclusions concern a restricted adaptation game and a mean energy balance; they do not establish survival with finite reserves or a universal thermodynamic principle. Revised preprint following AI-assisted review. Not peer reviewed. The accompanying archive contains LaTeX sources, Python code and synthetic numerical outputs.