Strategic Temporal Opacity in Interstellar Interaction: Light-Speed Delay, Outdated Beliefs and Asynchronous Action in a Bayesian Game

Abstract

Interstellar communication is not merely slow. It is strategically stale. A message received across distance reports a sender that may no longer occupy the same strategic state, while replies and irreversible actions are chosen on different local clocks. This paper develops a delayed Bayesian interaction game in which each civilisation’s benign or hostile state evolves as a continuous-time Markov chain. An exact filtering equation separates source-time inference from predictive ageing during light-speed transit. Strategic temporal opacity is defined as the loss of discriminatory power between past benign and hostile states; for the two-state process it equals 1 - exp[-(α + β)a]. The model derives posterior floors and ceilings, a finite assurance horizon beyond which even perfect benign evidence cannot prevent pre-emption, a warning horizon beyond which hostile evidence becomes obsolete, and a signal-specific decision-reversal time. A two-way query is valued exactly with a Markov-modulated hostile hazard and becomes irrational beyond a critical delay. Asynchronous decision clocks generate a closed-form probability of crossed irreversible actions before either side can observe the other’s commitment. Numerical illustrations show that distance can destroy reassurance, erase warning and increase reciprocal commitment even without increasing intrinsic hostility. Cosmic silence and pre-emption are therefore conditional consequences of causal delay, state volatility, offensive feasibility and decision tempo.