**Appendix B. Definition of the Problem**

In this section we discuss in greater detail the definition of the problem set, P, or, equivalently, the definition of the information vector. Experiments are very helpful for the researcher to define the information vector used in CBL since information is experimentally controlled and limited compared to observed behavior in the 'wild.' Here we describe the decisions we made to define the problem set P in this series of 2 × 2 games.

In contructing a measure of recency we assume that rounds are considered as simple vectors of whole numbers and do not consider additional non-linearities in this information, such as squares or other transformations of the data. Perhaps more difficult in this setting is the definition of opposing player behavior since actions are anonymous in all games of this experiment. The history of the opposing player's action could be incorporated in many ways into the problem. We use a moving average of the past play for all group members encountered by a subject, so as the recent trend of play changes, agents adapt to those trends. Another possibility is that agents use rules that specify the ordering of past play instead of a moving average. We can accommodate this definition in CBL by using binary indicators for the lag in observed play, This would make sense if subjects used strategies similar to Tit-for-Tat or more complex patterns that incorporate how the last three rounds of play occurred. For completeness we estimate CBL under these different information vectors and find small improvements in goodness of fit with more parameters. Table A1 shows the results of different definitions of the problem.

While the use of additional parameters improves the goodness of fit of the model, we choose to use the simpler and possibly more conservative moving average measure in the main models. We argue that our main estimates are more conservative based on fit, but are preferred because the parameters for the weights on the lags are negative in some cases which violate our understanding of the reasonable parameters for this model.


**Table A1.** Information Vector Definitions.

Note: Each lag represents a extra parameter on whether a partner in the past played either Up or Left, depending on the roll of the subject. Abbreviations: MA-3 moving average for past three rounds, MA-5 moving average for past five rounds.
