Cooperating in the Prisoner's Dilemma is irrational and some supporting mechanism is needed to stabilize cooperation. Indirect reciprocity based on reputation is one such mechanism. Assessing an individual's reputation requires first-order information, i.e. knowledge about its previous behavior, as it is utilized under image scoring. But there seems to be an agreement that in order to successfully stabilize cooperation, higher-order information is necessary, i.e. knowledge of others' previous reputations. We show here that such a conclusion might have been premature. Tolerant scoring, a first-order assessment rule with built-in tolerance against single defections, can lead a society to stable cooperation. (author's abstract)

Several experimental studies show that ex post communication mitigates opportunistic behavior in social dilemmas. The source of this effect, especially in a repeated interaction, is nonetheless still obscure. This study provides a novel empirical testbed for two channels by which ex post communication may affect behavior in a repeated public goods game. One is related to strategic signaling. The other involves emotions induced by others' expressed disapproval. The presence of ex post communication strongly fosters pro-social behavior. The data do not support the signaling hypothesis, favouring the emotion-based explanation instead. (author's abstract) / Series: Department of Economics Working Paper Series

Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result.

Fictitious Play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for several classes of games, including weighted potential games, supermodular games with diminishing returns, and 3×3 supermodular games. Extending these results, we establish convergence of Continuous-time Fictitious Play for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3×m and 4×4 quasi-supermodular games.

Indirect reciprocity describes a class of reputation-based mechanisms which may explain the prevalence of cooperation in groups where partners meet only once. The first model for which this has analytically been shown was the binary image scoring mechanism, where one's reputation is only based on one's last action. But this mechanism is known to fail if errors in implementation occur. It has thus been claimed that for indirect reciprocity to stabilize cooperation, reputation assessments must be of higher order, i.e. contingent not only on past actions, but also on the reputations of the targets of these actions. We show here that this need not be the case. A simple image scoring mechanism where more than just one past action is observed provides ample possibilities for stable cooperation to emerge even under substantial rates of implementation errors. (authors' abstract) / Series: Department of Economics Working Paper Series

Indirect reciprocity describes a class of reputation-based mechanisms which may explain the prevalence of cooperation in large groups where partners meet only once. The first model for which this has been demonstrated was the image scoring mechanism. But analytical work on the simplest possible case, the binary scoring model, has shown that even small errors in implementation destabilize any cooperative regime. It has thus been claimed that for indirect reciprocity to stabilize cooperation, assessments of reputation must be based on higher-order information. Is indirect reciprocity relying on frst-order information doomed to fail? We use a simple analytical model of image scoring to show that this need not be the case. Indeed, in the general image scoring model the introduction of implementation errors has just the opposite effect as in the binary scoring model: it may stabilize instead of destabilize cooperation.