Cooperation Under the Shadow of the Future

The central result of repeated-game theory: cooperation between self- interested agents is sustainable when interaction is ongoing and its end is unpredictable — and collapses when the end is known or near. In a one-shot or known-finite prisoner’s dilemma, defection dominates. In an indefinitely repeated game, cooperative equilibria exist because today’s defection is punished by tomorrow’s withdrawal of cooperation — the “shadow of the future” disciplines the present.1

This is the formal machinery behind the claim that civilizational glue is an infinite game (in Carse’s sense, Finite and Infinite Games) — play whose point is to continue the play. The “Law of Zeus” framing in the mutual obligation thesis is exactly this: an institution that lets strangers treat encounters as moves in an unbounded game rather than a terminal one.

Axelrod’s lineage

Robert Axelrod’s tournaments (The Evolution of Cooperation, 1984) established the practical shape: Tit-for-Tat — cooperate first, then mirror the partner’s last move — won against far more sophisticated strategies. Its virtues map onto the obligations frame: it is nice (never defects first), retaliatory (defection is answered), forgiving (returns to cooperation immediately), and clear (the partner can predict it). Niceness plus retaliation is enforced reciprocity: obligation honored and obligation demanded.

Experimental evidence

Dal Bó’s experiments with indefinitely repeated prisoner’s dilemmas (random continuation probability standing in for “no known end”) confirm the theory with humans: higher continuation probabilities produce substantially more cooperation, and — critically — cooperation unravels as the known end of a finite game approaches.2 The last-period defection infects backward: if the end is in sight, the whole chain of trust shortens.

Why this matters for the collapse thesis

A civilization whose members expect the game to continue behaves cooperatively even toward strangers. The Homeric fleets pillaging coastal towns on the return from Troy are the finite-game move: each community treated as a terminal interaction. Once that reputation propagates, legitimate resupply becomes impossible — the cycle described in trust-and-social-capital and dramatized via Circe’s rationally justified suspicion of strangers in the Odyssey analysis.

Sources

Footnotes

  1. Stanford Encyclopedia of Philosophy 2021 — Game Theory and Ethics

  2. Pedro Dal Bó 2005 — Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games