The extensive form game we study has multiple perfect equilibria, but it has a unique limiting logit equilibrium (QRE) and a unique level-k prediction as k approaches infinity. The convergence paths of QRE and level-k are different, but they converge to the same limit point. We analyze whether subjects adapt beliefs when gaining experience, and if so whether they take the QRE or the level-k learning path. We estimate transitions between level-k and QRE belief rules using Markov-switching rule learning models. The analysis reveals that subjects take the level-k learning path and that they advance gradually, switching from level 1 to 2, from level 2 to equilibrium, and reverting to level 1 after observing opponents deviating from equilibrium. The steady state therefore contains a mixture of behavioral rules: levels 0, 1, 2, and equilibrium with weights of 2.9%, 16.6%, 37.9%, and 42.6%, respectively.This network project brings together economists, psychologists, computer and complexity scientists from three leading centres for behavioural social science at Nottingham, Warwick and UEA. This group will lead a research programme with two broad objectives: to develop and test cross-disciplinary models of human behaviour and behaviour change; to draw out their implications for the formulation and evaluation of public policy. Foundational research will focus on three inter-related themes: understanding individual behaviour and behaviour change; understanding social and interactive behaviour; rethinking the foundations of policy analysis. The project will explore implications of the basic science for policy via a series of applied projects connecting naturally with the three themes. These will include: the determinants of consumer credit behaviour; the formation of social values; strategies for evaluation of policies affecting health and safety. The research will integrate theoretical perspectives from multiple disciplines and utilise a wide range of complementary methodologies including:theoretical modeling of individuals, groups and complex systems; conceptual analysis; lab and field experiments; analysis of large data sets. The Network will promote high quality cross-disciplinary research and serve as a policy forum for understanding behaviour and behaviour change.

Four experimental treatments involve a 2×2 design. On the one hand, we vary incentives to individuals to join. This facilitates the identification of belief rules, as it varies the predicted QRE strategies without affecting level-k strategies. On the other hand, we manipulate externalities for other players, which allows us to control for social preferences (social preferences are of potential relevance in all multi-player games). Both our methodology, to use strictly sequential games and Markov-switching models in analyses of rule learning, and our results appear directly applicable to all games with similar relevance of beliefs about rationality. This includes games that are iteratively dominance solvable or constant-sum; it may however plausibly exclude, or anyway be less relevant, for games such as public goods games, trust games or joy-of-destruction games which are non-constant-sum and where social preferences and beliefs about others' social preferences are likely to play more significant roles.