Backward induction argues rational players defect from the first move of any finite game.

Evidence

In mutual trust, again, the interaction is a finitely iterated exchange or prisoner’s dilemma. According to a standard argument in game theory, one should not cooperate in such a game. The argument begins with the premise that one should treat the final play of a finite series of plays of the game as a one-shot game, in which one should defect. If one should defect on the final play, however, then the penultimate play is de facto a final play in the sense that it can have no effect on anything thereafter, and so one should defect on the penultimate play as well. By tedious induction backward, one should defect already on the first play in the series. — Russell Hardin, Trust and Trustworthiness, 135

Categorization

• DEFINE: Clear statement of the backward induction argument in finitely iterated prisoner’s dilemma games, useful for later reference.
• XREF: Mirrors the Milgrom-Roberts folk theorem material on repeated-game cooperation already in the knowledge base. — connects to: Even a fair trading game ruins a finite player against unlimited resources — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 259