Reciprocal cooperation can be studied in the Centipede game, in which two players alternate in choosing between a cooperative GO move and a non-cooperative STOP move. GO sustains the interaction and increases the player pair's total payoff while incurring a small personal cost; STOP terminates the interaction with a favorable payoff to the defector. We investigated cooperation in four Centipede games differing in their payoffs at the game's end (positive versus zero) and payoff difference between players (moderate versus high difference). The games shared the same game-theoretic solution, therefore they should have elicited identical decision patterns, according to orthodox game theory. Nevertheless, both zero-end payoffs and high payoff inequality were found to reduce cooperation significantly. Contrary to previous predictions, combining these two factors in one game resulted in a slight weakening of their independent deterrent effects. These findings show that small changes in the payoff function have large and significant effects on cooperation, and that the effects do not combine synergistically.
centipede game backward induction take-it-or-leave-it game end-game effects cooperation reciprocity