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The Supporting Information gives more detail regarding the theoretical model and the way it is simulated. It also gives theoretical results mentioned in the Main Text, with proofs. It is subdivided as follows. <b>The Model.</b> <i>Calculating payoffs. Why these are the average payoffs, if we assume short-run equilibrium. With and without leaving in one setting. Frequencies in the matching pool and in the population as a whole. Histories and strategies. Finite state automata.</i> <b>Simulations.</b> <i>Different mutation procedures. Algorithm for the simulations.</i> <b>Theoretical results.</b> <i>No ESS. No strategy that is RAII. Pure strategies with a trust-building phase</i>. (PDF)