Appendix B for “ The Evolution of Strategic Sophistication ” ( Intended for Online Publication ) Nikolaus Robalino and Arthur Robson

This appendix contains the proof of Theorem 2 which is the main result for the general version of the model presented in Section II of the paper. The numbering here (of equations, result, and definitions, etc.) follows the numbering in the published paper. Assumptions 6-10, which are stated in the paper, are assumed implicitly throughout. A single subscript will be used to denote the number of accumulated iterations of the game (as in the proof of Theorem 1 in Appendix A). For example, instead of writing Hn,t for the period n, iteration t history, Hs will be used, where s is the total number of iterations of the game along the history. The notation s(n) denotes ∑ m<n κ(m) + 1. Notice, in particular, that for each period n = 1, 2, . . . , iteration s = s(n) corresponds to the arrival of the n-th novel outcome.