Learning requires recognizing the similarity between the current instance of a situation and past instances. Game theory is a useful way to identify strategic similarities between situations. When placed in a sequence of strategically similar games, do people recognize and exploit these similarities to learn to coordinate on a way to play?

The experiment reported below uses a random sequence of scrambled payoff perturbed 2×2 bargaining games to discover if subjects learn to use a deductive bargaining concept to solve their coordination problem. All games have the following strategic properties: two efficient strict equilibria one of which is selected by a Utilitarian criterion (select the equilibrium with the largest payoff sum) and the other is selected by a Rawlsian criterion (select the equilibrium that maximizes the welfare of the worst off player); no other outcomes are contained in the set of efficient outcomes; security varies so that risk dominance selects the Utilitarian equilibrium half the time and the Rawlsian equilibrium half the time.

Subjects interact using an evolutionary protocol. Repeated interaction allows subjects to learn to use a principle of justice to select an equilibrium if subjects fail to bring one into the laboratory that is sufficiently flexible to solve the posed asymmetric bargaining problems. The principle would have to be more sophisticated than equal division, since equal division is not a feasible outcome ex post.

Action labels and player roles are also scrambled to prevent players from using non-strategic details to solve their coordination problem. Hence, the only meaningful way to distinguish between actions is by using a deductive principle and it is always possible to label one action Utilitarian, the U-action, and the other action Rawlsian, the R-action. Do subjects behave as if they recognize the map between the current action labels and an abstract description of the game using U-action and R-action labels? If so, which role contingent convention is more likely to emerge: the U-convention or the R-convention?

Of course, this design can not resolve a normative dispute between Harsanyi (1977) and Rawls (1971). Rather, it may demonstrate that subjects can learn to recognize either deductive principle in an environment that eliminates distracting and competing selection principles and coordinate their behavior on one of the two competing principles in small laboratory communities. Will a convention in which subjects use a deductive principle emerge?

The widely documented fact that naive subjects use equal division to solve simple bargaining problems does not appear to reflect any deeper widely shared understanding of general principles of justice. Initial behavior was not ex post mutually consistent. However, conventions based on deductive principles emerge after 70 periods in 5 of 26 eight person cohorts. In four cohorts the U-convention emerged and in one cohort the R-convention emerged.

It is common to make generalizations based on the sex ratio of a group. Observing that behavior in dictator games varied systematically by gender classification, Andreoni and Vesterlund (2001, p307) conclude that "researchers would be wise to assure that their experimental findings are the result of economic incentives and not of varying sex compositions of their control and treatment groups." The experiment reported below varies the sex ratio. All male, all female, and mixed cohorts are used. Does the likelihood of observing a convention vary with the sex ratio? We found no economically significant differences between all male and all female cohorts.

Initially players are particularly reluctant to conform to the Utilitarian convention when doing so gives them a small share and, given their role, requires them to use their least secure action. This economically and statistically significant difference in behavior is predicted by probabilistic choice models and remains an important characteristic of the data through out the convergence process.

Conventions based on the strategic similarities between the games do sometimes emerge. In 5 of 26 cohorts the same convention emerged for all of the similar games within the 70 periods of the evolutionary game. Given convergence in both types of games, the Utilitarian convention emerged 4 times as often as the Rawlsian convention. We never observed the most interesting case, which would have been a Rawlsian convention in games in which risk dominance selects the Rawlsian equilibrium and the Utilitarian convention in games in which risk dominance selects the Utilitarian equilibrium, that is, a convention based on the deductive principle of risk dominance.

Our experiment reveals no evidence of economically significant gender differences in bargaining behavior. The difference in mean earnings between all male and all female cohorts was 3 cents and the difference in standard deviation was 2 cents.

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