Supplementary Online Material

Contents 1 A social dilemma with value-behavior inconsistency 2 2 Questions 3 3 Specific evolutionary dynamics with binary values 3 3.1 Well-mixed populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 Regular graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 General evolutionary dynamics with multiple values: Theoretical criteria 9 4.1 Preparations for generalisation . . . . . . . . . . . . . . . . . . . . . . . . 10 4.1.1 The social dilemma with value-behavior inconsistency for multi opinion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.1.2 General evolutionary dynamics . . . . . . . . . . . . . . . . . . . 11 4.1.3 Assumptions for stochastic evolutionary dynamics . . . . . . . . . 12 4.1.4 A lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3.1 Beyond small mutation limit . . . . . . . . . . . . . . . . . . . . . 18 4.3.2 Beyond regular graphs . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3.3 Beyond binary opinions . . . . . . . . . . . . . . . . . . . . . . . 18 4.3.4 Beyond weak selection limit . . . . . . . . . . . . . . . . . . . . . 22 5 Codes 2