The Evolution of Human–AGI Coexistence A Conditionally Cooperative Majority, Visible and Hidden Violations, and Whether the Sum of Risks Converges — An Absorbing Markov–Game Analysis

Abstract Working within the absorbing-barrier framework of [S4], this paper uses four models to analyse a society in which humans and AGI coexist, and obtains five conclusions. People are classified by behavioural types measured in public-goods experiments — paying enforcers, conditional cooperators, and free riders (including antisocial punishers); AGI is classified along three dimensions — capability, whether it violates boundaries, and whether its violations are visible — as within bounds, visibly violating or covertly violating. Together these form nine cells, plus two absorbing states: sudden barrier contact and gradual lock-in. (i) A time-homogeneous coexistence society has a positive risk floor, equal to the cells' exit rates weighted by the quasi-stationary distribution; meeting the summability condition of [S4] means pushing down exactly this weighted sum. (ii) The more effective the governance, the more the remaining failures take the form of quiet lock-in rather than sudden barrier contact, and the more the floor is supplied by the most ordinary cells — the part that comes neither from malice nor from malfunction; these two directions hold in 99.3% and 100% of 2000 random parameter draws. (iii) The majority are conditional cooperators, whose direction depends, with hysteresis, on whether a minority of paying enforcers stays above a collapse point; on networks the hysteresis loop persists but collapse comes earlier than in the mean field, and when enforcers sit at network hubs the shares needed to sustain and to restore cooperation fall to between a quarter and a third of those under random placement. (iv) Governance that reads only visible violations and has no independent audit fails quietly: in the long run all violations become hidden, and the reading and the attention both go to zero; correction strength has an interior optimum beyond which the reading improves while reality worsens; and audit capacity is capped by error correlation. (v) The number of learnable warnings before barrier contact, W = (s_fatal / max(s_felt, κs₀))α − 1, shrinks both with capability growth and with weaker readings; under super-exponential capability growth the calendar time over which these warnings arrive is compressed and the window closes before the singularity; and the stability margin of a race is eaten multiplicatively by (1 + ψ)(1 + χ). The result is a unified reading: the course of a coexistence society is decided not by whether there are more good people than bad, or by whether AGI is good or evil, but by three structural quantities — whether violations are visible, whether the race is stable, whether enforcement is institutionalised — and one temporal condition: whether the sum of risks converges. Nine testable predictions are given at the end.