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How does the theory of moves explain cooperation in the prisoner’s dilemma?
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game theory
Table 1
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.
The Theory of Moves (TOM), proposed by Steven J. Brams, explains cooperation in the prisoner’s dilemma by introducing a nonmyopic perspective where players anticipate the consequences of future moves and countermoves within a matrix.1
Unlike traditional models that often assume static, one-time choices, TOM suggests that cooperation depends on the starting point of the game:1
- Cooperative Start: If play begins at the cooperative outcome, players remain there because they recognize that defecting would trigger a retaliatory defection from the other, leaving both worse off.1
- Win-Lose Start: If one player is in a superior position, they may act magnanimously by moving to the cooperative outcome. They do this because they anticipate that failing to do so will lead their opponent to move to the noncooperative outcome, which would result in a worse payoff for both.1
- Noncooperative Start: If play begins at the noncooperative outcome, players remain stuck, as neither has an incentive to move.1
Ultimately, TOM does not guarantee unconditional cooperation; rather, it demonstrates that far-sighted players can escape the dilemma depending on the game's initial conditions.1