Learning transfer in small group coordination

Learning transfer in small group coordination Seth Frey (sethfrey@indiana.edu) Cognitive Science, 1101 E. 10th St., rm. 290B Bloomington, IN 47401 USA Abstract This work tests the adaptation of groups from two generalizations of the multiple-player stag hunt to a difficult third version, the notorious weakest-link game. The two training conditions either encouraged or discouraged the development of stable subgroups. Theories of modularization predict that stable subgroups will facilitate coordination in larger groups by helping them “scale up. ” However, internal structure may also cause “overfitting,” or adaptation to only spurious features of training. In this experiment, experience with internal structure prevented coordination at larger scales, while experience in environments that discourage internal structure led to performance at least as high as in the control environments. I offer the analogy from individual learning transfer, that distracting details from superficially-similar domains may transfer and interfere with coordination. This work has implications for the development and adaptability of small coordinating groups. In particular, it demonstrates that coordination is not a monolith, and experience with one sense may impair performance under others. Keywords: stag hunt; learning transfer; n-player games; coordination games; group structure. Introduction Adaptability and transfer have been a focus of group research since its inception (Bavelas, 1950; Guetzkow & Simon, 1955). The research in “endogenous” groups applies modern experimental methods and game theoretic approaches to understanding adaptability and learning during group formation. Traditional group experiments impose groups by design, and they use careful matching procedures and information conditions to minimize interaction and reputation effects, and to maintain the independence of individual reasoners. Investigations of endogenous group formation encourage interactions and attend to the processes of group formation within an experiment. Endogenous group experiments permit the study of internal (often “network”) structure. In groups, internal structure describes the heterogeneous but systematic pattern of coordinated behavior between subgroups. Internal structure can be measured by observing the behavior of group members over time. As the demands on a group change, these internal patterns should also change. For large networks, group structures can be compared along innumerable dimensions, but for the small groups featured in this study it is possible to meaningfully quantify structure with fewer variables. Ahn, Isaac, & Salmon (2008) documented segregation processes as a result of reputation formation and individual choice. Camerer and Weber elicited unprecedented coordination in the weakest-link game by starting with successful groups of two and “growing” them slowly up to the standard 7-person case (Camerer & Weber, 2008). Their work shows that coordination can be attained if the learning process occurs in parallel with the group formation process. Across a diversity of paradigms, many other experiments have found conditions in which the internal structure created by local information improves group-level outcomes (Ahn, Esarey, & Scholz, 2009; Goldstone, Roberts, Mason, & Gureckis, 2010; Kearns, Suri, & Montfort, 2006; Mullen, Johnson, & Salas, 1991; Mason, Jones, & Goldstone, 2008). There is also conflicting evidence that internal structure interferes with coordination among endogenous groups. Weber & Camerer (2003), complementing their “slow growth” result above, showed that combining two successful medium-sized groups can induce coordination failure in the large merged group. Rick, Weber, & Camerer (2006) hypothesized that decentralization would promote adaptability. After their result failed to materialize, they reframed the experiment in terms of learning transfer (Rick, Weber, & Camerer, 2007). Frey & Goldstone (2010) show the simultaneous emergence of internal structure and coordination failure in a multiple-player stag hunt. Participants in groups of many sizes could coordinate on equilibria that required larger quora for larger payoffs. Despite many trials and large groups, coordination failure was common, and the successes were most typical for the smallest subgroups of pairs and triplets, despite the much larger rewards available with more concentrated groups. There is no theory to reconcile the conflicting effects of group formation on individual outcomes. This experiment explores whether internal structure will help or hinder groups in coordinating at larger scales. The complex experimental designs and large networked groups of most endogenous group experiments make it difficult to carefully distinguish hypotheses. I introduce a 4- player coordination game that elicits three types of coordination, depending on the value of an experimentally manipulated parameter. An experiment with only four players can be represented as a very small network. The design focuses on learning transfer from each of three coordination games. Learning transfer is a growing area of behavioral game theory. Studies suggest that experiences of cooperation or coordination can transfer across very different types of games (Stahl, 2000; Devetag, 2005). In the most ambitious study, Woolley, Chabris, Pentland, & Hashmi (2010) give evidence for a general Collective