1. Explicit versus Implicit Contracts for Dividing the Benefits of Cooperation Marco Casari and Timothy Cason Purdue University

2. A Partnership Game As in most experimental labor markets, in this game two individuals interact and must cooperate to generate a divisible joint surplus The standard environment (e.g., Fehr & co- authors) is sequential, with payments sometimes before and sometimes after effort By contrast, in our game efforts are simul- taneous, and must be incurred by both parties As in earlier research, however, the relationship is still hierarchical, with one “strong” agent responsible for dividing the surplus –Example: Senior partners at a law firm

3. Parameters and Treatments Baseline: Strong agent selects A & B after effort choices Bonus: Like Baseline, except strong agent makes an unenforceable “promise” of A & B pre-effort (implicit contract) Explicit Commitment: Strong agent announces a committed level of A & B pre-effort (explicit contract) 144 subjects (48 per treatment) Weak Agent Strong Agent 1 (high effort)2 (low effort) 1 (high effort)A, B (A+B=60) 0, 10 2 (low effort)10, 010, 10

4. Design & Predictions Summary 3 preliminary measurements without feedback –lottery choices, ultimatum & trust games (strategy meth) 10 rounds of partnership game, with 1 round paid –perfect strangers re-matching Baseline and Bonus: –low effort equilibrium, but high effort can occur in equilibrium for some distributions of social pref. types Explicit Commitment: –multiple equilibria, including high effort equilibrium (commitment can turn effort choice into a stag hunt)

5. Results: Pooled Effort Choices Summary Panel A: Baseline Weak Agent Strong Agent High Effort Low Effort Totals High Effort 17.9%36.7%54.6% Low Effort 14.6%30.8%45.4% Totals32.5%67.5% 100.0% N=480 Panel B: Bonus Weak Agent Strong Agent High Effort Low Effort Totals High Effort 35.8%36.7%72.5% Low Effort 10.4%17.1%27.5% Totals46.3%53.8% 100.0% N=480 Panel C: Explicit Commitment Weak Agent Strong Agent High Effort Low Effort Totals High Effort 59.6%28.3%87.9% Low Effort 5.0%7.1%12.1% Totals64.6%35.4% 100.0% N=480

6. Time Series of Mutual Cooperation

7. Earnings, Average Bonuses, and Efficiency BaselineBonusExplicit Commitment All Periods Last 3 Periods All Periods Last 3 Periods All Periods Last 3 Periods Overall frequency of high effort choices 43.5%25.0%59.4%47.9%76.3%81.3% Frequency of mutual high effort outcome 17.9%5.6%35.8%25.0%59.6%68.1% Actual bonus paid by strong agents choosing high effort 10.811.921.4 Ave. earnings strong agent13.69.419.815.821.824.5 Ave. earnings weak agent8.49.09.99.718.720.1 Share of earnings of strong agent 61.8%51.1%66.7%62.0%53.8%54.9% Efficiency (possible range from 16.7% to 100%) 36.7%30.7%49.5%42.5%67.5%74.3%

8. Promised and Actual Bonus

9. Implicit and Explicit Bonus Offers to Coordinate Efforts Bonus Treatment Explicit Commitment

10. Measurements of Risk Aversion and Social Preferences A majority (70%) of our subjects appear risk averse on the lottery choices –Most of the others appear risk neutral Average ultimatum offer was 28.2 francs (out of 60), average 27.0 francs demanded 63% of trustors trusted, but 60% of trustees kept all 60 francs and only 26% provided a positive return to the trustor “Fair-minded” strong agents who offered at least 30 francs in the ultimatum game were more trustworthy on average But “Fair-minded” weak agents who demand at least 25 of 60 francs were not less likely to trust

11. Measured Preferences Help Partnership Behavior (stable types across games) Strong agents who are more risk averse tend to exert lower effort In the Bonus treatment, risk-seeking strong agents offer higher bonuses but pay lower actual bonuses Trusting weak agents were more likely to exert high effort in the Baseline and Bonus treatments Untrustworthy strong agents were less likely to exert high effort in the Baseline treatment but more likely to exert high effort in the Explicit Commitment treatment

12. The Last Slide While our results are consistent with some agents having social preferences, explicit contracts—which do not rely on social preferences to achieve efficiency—clearly perform better than implicit contracts in this partnership setting Similar behavior is exhibited by other primates –Non-kin capuchin monkeys choose low effort when dominant member of pair can’t commit to sharing Perhaps implicit contracts in this environment require repeated interaction? Would implicit contracting work better if explicit contracting required costly verification and strong agents had a choice between implicit and explicit contracting?

13. Implicit Contracts and Social Preferences Recent research has documented superior performance of implicit (“bonus”) contracts in some laboratory labor markets –Fehr, Klein & Schmidt (2007) show that principals prefer to offer an unenforceable bonus over an explicit incentive contract that relies on costly verification of agent effort –An efficiency wage “trust” contract does worse, however than an explicit contract Social preferences, such as simple inequity aversion, are consistent with these results How general is this “failure” of contract theory?

14. Equilibrium Predictions (Self-Regarding and Inequity-Averse Preferences) Baseline and Bonus treatments: –Unique equilibrium of low effort for standard, self- interested preferences –For certain type distributions of social preferences (e.g., inequity aversion), high effort outcome can occur in equilibrium –Promised bonus could provide a type signal Explicit Commitment treatment: –Multiple equilibria exist, including both high and low effort equilibria, for self-interested and other-regarding preferences –Commitment can turn effort choice into a stag hunt game

15. Patterns Expected by Different Types of Subjects In Baseline and Bonus treatments, fair-minded strong agents may pay positive bonuses Strong agents have more to gain from cooperation than weak agents, implying higher average effort from strong agents Self-regarding strong agents have more to gain from cooperation than fair-minded strong agents, implying higher effort from them Fair-minded weak agents fear the asymmetric (0, 60) payoffs more than self-regarding weak agents, so they should exert less effort and exhibit less trust