Appendix for “ Optimal Contracts for Experimentation ”

SA.1. Proof of Proposition 1 We prove the result more generally for contracts with lockouts. Fix a contract C = ( ,W0, b, l). The result is trivial if = ;, so assume 6= ;. Let T = max . For any period t 2 with t < T , define the smallest successor period in as (t) = min{t0 : t0 > t, t0 2 }; moreover, let (0) = min . Given any action profile for the agent, the agent’s time-zero expected discounted payoff when his type is ✓ 2 {L,H} and the principal’s time-zero expected discounted payoff only depend upon a contract’s induced vector of discounted transfers, say (⌧t)t2 when success is obtained in period t and on the discounted transfer when there is no success. Hence, it suffices to construct a penalty contract, b C, and bonus contract, e C, that induce the same such vector of transfers as C. To this end, define the penalty contract b C = ( ,c W0,l) as follows: (a) For any t such that t < T and t 2 , lt = lt bt + (t) b (t). (b) lT = lT bT . (c) c W0 = W0 + b (0).