TY - JOUR

T1 - A note on payments in the lab for infinite horizon dynamic games with discounting

AU - Chandrasekhar, Arun Gautham

AU - Xandri, Juan Pablo

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - It is common for researchers studying infinite horizon dynamic games in a lab experiment to pay participants in a variety of ways, including but not limited to outcomes in all rounds or for a randomly chosen round. We argue that these payment schemes typically induce different preferences over outcomes than those of the target game, which in turn would typically implement different outcomes for a large class of solution concepts (e.g., subgame perfect equilibria, Markov equilibria, renegotiation-proof equilibria, rationalizability, and non-equilibrium behavior). For instance, paying subjects for all rounds generates strong incentives to behave differently in early periods as these returns are locked in. Relatedly, a compensation scheme that pays subjects for a randomly chosen round induces a time-dependent discounting function. Future periods are discounted more heavily than the discount rate in a way that can change the theoretical predictions both quantitatively and qualitatively. We rigorously characterize the mechanics of the problems induced by these payment methods, developing measures to describe the extent and shape of the distortions. Finally, we prove a uniqueness result: paying participants for the last (randomly occurring) round, is the unique scheme that robustly implements the predicted outcomes for any infinite horizon dynamic game with time separable utility, exponential discounting, and a payoff-invariant solution concept.

AB - It is common for researchers studying infinite horizon dynamic games in a lab experiment to pay participants in a variety of ways, including but not limited to outcomes in all rounds or for a randomly chosen round. We argue that these payment schemes typically induce different preferences over outcomes than those of the target game, which in turn would typically implement different outcomes for a large class of solution concepts (e.g., subgame perfect equilibria, Markov equilibria, renegotiation-proof equilibria, rationalizability, and non-equilibrium behavior). For instance, paying subjects for all rounds generates strong incentives to behave differently in early periods as these returns are locked in. Relatedly, a compensation scheme that pays subjects for a randomly chosen round induces a time-dependent discounting function. Future periods are discounted more heavily than the discount rate in a way that can change the theoretical predictions both quantitatively and qualitatively. We rigorously characterize the mechanics of the problems induced by these payment methods, developing measures to describe the extent and shape of the distortions. Finally, we prove a uniqueness result: paying participants for the last (randomly occurring) round, is the unique scheme that robustly implements the predicted outcomes for any infinite horizon dynamic game with time separable utility, exponential discounting, and a payoff-invariant solution concept.

KW - Dynamic game experiments

KW - Experimental economics

KW - Payment in experiments

KW - Dynamic game experiments

KW - Experimental economics

KW - Payment in experiments

UR - http://www.scopus.com/inward/record.url?scp=85125675651&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/32275be0-5ee5-3601-ae72-3dfd0aa161bd/

U2 - 10.1007/s00199-021-01409-x

DO - 10.1007/s00199-021-01409-x

M3 - Article

AN - SCOPUS:85125675651

SN - 0938-2259

VL - 75

SP - 389

EP - 426

JO - Economic Theory

JF - Economic Theory

IS - 2

ER -