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Fig. 2. Games with and without turn-taking opportunities, arranged with R= P. The top row shows alternation games with 2R < S+ T. The bottom row shows synchronization games with 2R > $+ T. The experimental (alternation) games are shown in Fig. 2 (top row). The Battle of the Sexes game (defined by the relations T>.S> R= FP) was introduced by Luce and Raiffa (1957, pp. 90-94). It has Nash equilibria at (C, D) and (D, C), with Player I preferring (D, C) and Player II (C, D). The stripped-down version shown in Fig. 2, with zero payoffs in the non- equilibrium cells, is the simplest possible alternation game, without any distracting features. The Hero game (S>7T>R>P) and Leader game (7 >S>R>P) were first explicitly identified and named by Rapoport (1967), and both have Nash equilibria at (C, D) and (D, C), but in Hero Player I prefers (C, D) and Player II (D, C), whereas in Leader Player I prefers (D, C) and Player II (C, D). Hero is a game in which each player receives the highest possible payoff when the other player is the sole defector, accepting the second-best payoff and in this sense playing the role of hero, whereas Leader is a pre-emption game in which

Figure 2 Games with and without turn-taking opportunities, arranged with R= P. The top row shows alternation games with 2R < S+ T. The bottom row shows synchronization games with 2R > $+ T. The experimental (alternation) games are shown in Fig. 2 (top row). The Battle of the Sexes game (defined by the relations T>.S> R= FP) was introduced by Luce and Raiffa (1957, pp. 90-94). It has Nash equilibria at (C, D) and (D, C), with Player I preferring (D, C) and Player II (C, D). The stripped-down version shown in Fig. 2, with zero payoffs in the non- equilibrium cells, is the simplest possible alternation game, without any distracting features. The Hero game (S>7T>R>P) and Leader game (7 >S>R>P) were first explicitly identified and named by Rapoport (1967), and both have Nash equilibria at (C, D) and (D, C), but in Hero Player I prefers (C, D) and Player II (D, C), whereas in Leader Player I prefers (D, C) and Player II (C, D). Hero is a game in which each player receives the highest possible payoff when the other player is the sole defector, accepting the second-best payoff and in this sense playing the role of hero, whereas Leader is a pre-emption game in which

Related Figures (4)

Fig. 1. Prisoner’s Dilemma game and generic payoff matrix. Left panel: the standard Prisoner’s Dilemma game. Right panel: a generic payoff matrix for any symmetric 2 x 2 game.
Fig. 1. Prisoner’s Dilemma game and generic payoff matrix. Left panel: the standard Prisoner’s Dilemma game. Right panel: a generic payoff matrix for any symmetric 2 x 2 game.
Table 1. Percentages of distinct outcomes and reciprocity indices in generation 2000 of each simulation, averaged across replications Note: Percentages of (C, D) and (D, C) are identical because a (C, D) outcome for one player always corresponds to a (D, C) outcome for the other.
Table 1. Percentages of distinct outcomes and reciprocity indices in generation 2000 of each simulation, averaged across replications Note: Percentages of (C, D) and (D, C) are identical because a (C, D) outcome for one player always corresponds to a (D, C) outcome for the other.
Note: The symbols x and y are variables representing arbitrary values P, R, S or T from Fig. 1 (right panel). Table 2. Prevalence of three-round histories (percentages), averaged across replications of each simulation in generations 1, 100, 1000, and 2000
Note: The symbols x and y are variables representing arbitrary values P, R, S or T from Fig. 1 (right panel). Table 2. Prevalence of three-round histories (percentages), averaged across replications of each simulation in generations 1, 100, 1000, and 2000
Fig. 3. Mean frequencies of three-round histories and in generation 2000 in simulations of six games. Error bars indicate standard errors of the means.
Fig. 3. Mean frequencies of three-round histories and in generation 2000 in simulations of six games. Error bars indicate standard errors of the means.
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