Dictator, Ultimatum, & Trust Games

1. Dictator, Ultimatum, & Trust Games APEC 8205: Applied Game Theory Fall 2007

2. Objectives • Equilibrium Strategies • Dictator Game • Ultimatum Game • Trust Game • Review Experimental Evidence

3. Dictator, Ultimatum, & Trust Games • Simple Rules • Stark Equilibrium Predictions • Limited Support for Equilibrium Play • Provide Clear Information on Individual Incentives

4. Classical Economist Stigler: “when self-interest and ethical values with wide verbal allegiances are in conflict, much of the time, most of the time in fact, self-interest-theory …will win.” Behavioral Economists People are more complex with interests besides self-interest. Self-interest, while important, does not necessarily dominate. We must search for parsimonious explanations of behavior that make testable predictions. Two Perspectives

5. Caution in Interpreting Experimental Results • Logic of Game Theory Versus Logic of Preferences • Failures of Assumptions of Games Theory: • Limited Cognitive Ability • Use of Information to Guide Decisions • Failure of Assumptions on Preferences • Altruism • Socialization/Culture • Fairness

6. The Dictator Game • Who are the players? • Dictator & Peasant • Who can do what when? • First: Dictator Proposes a Division of Peasants Crop • Second: Peasant Accepts the Proposal • Who knows what when? • Dictator Knows the Peasant Must Accept Proposed Division • Peasant Gets to See the Dictators Proposed Division Before Accepting • How are players rewarded based on what they do? • Dictator: Rx where R is the size of the crop and 1≥ x ≥ 0 is the Proposed Division • Peasant: R(1 – x)

7. Is this really a game? • No! • Still, what does economic theory predict the dictator will do? • Choose x = 1! • What do the experimental results say? • Mean offer typically fall in the 20% range. • What can we make of these results?

8. The Ultimatum Game • Who are the players? • Proposer & Receiver • Who can do what when? • First: Proposer Proposes a Division of an Asset • Second: Receiver Accepts or Rejects the Proposal • Who knows what when? • Dictator Doesn’t Know Acceptable Proposals Before Choosing • Receiver Knows Proposal Before Choosing • How are players rewarded based on what they do? • Proposer: Rxif Proposal Accepted & 0 otherwise • Peasant: R(1 – x) if Accept & 0 otherwise

9. Is this really a game? • Yes! • What does economic theory predict the Proposer will do? • Choose x = 1 -  where  is the smallest possible division that can be offer to the receiver! • What do the experimental results say? • Median/Mode offers typically around 40%. • Offers 20% or below are typically rejected. • Offers 40% or above typically accepted. • What can we make of these results? • Evidence of strategic play. • Evidence of altruism/fairness. • How do these results withstand scrutiny?

10. High Stakes • Cameron (1999) • Who & Where: Workers in Indonesia • Stakes: 1 day to 1 months wages • Results: • Offers: 42% for 5K, 45% for 40K, & 42% for 200K • Rejection Rates: below 20% usually rejected & above 40% usually accepted • List & Cherry (2000) • Use Quiz to Determine Stakes For Proposer • Stakes: $20 or $400 • Results: • Offers: 34% for $20 & 32% for $400 • Rejection Rates: • Slightly lower for $400 • 25% still reject $100 offer.

11. Other Variations • Anonymity (Hoffman, McCabe, & Smith) • Dictator’s Choice Not Known to Experimenter • Mean Offer Around 10% • 50% Leave Nothing • Repetition • With regular opponents, not much difference. • With self-interested computer opponents, offers fall as do rejection rates. • Payout Rates (Andreoni & Miller) • Give R(1 – x) & Opponent Gets R(1 – x) where  varied from 1/9 to 9 • Found Three Types of Players • 1/2 are Self-Interested (Max g1) • 1/3 are Rawlsian (Max Min(g1, g2)) • 1/6 are Utilitarian (Max g1 + g2)

12. Other Variations Continued • Culture • Mean Offers Ranging From 26% for the Machiguenga in Peru to 58% for the Lamelara in Indonesia • Interestingly, “hyper-fair” Offers (>50%) Often Rejected • Gender (Andreoni & Vesterlund) • Some Evidence that Men More Self-Interest & Women More Rawlsian • Age • Children More Self-Interested

13. Treatment 1: Roles Randomly Assigned Offers: Average: 61 Max: 80 Min: 50 Acceptance Thresholds: Average: 70 Max: 80 Min: 60 Acceptance Rate: 83% Treatment 2: Assignments Based on Quiz Score Offers: Average: 64 Max: 80 Min: 60 Acceptance Thresholds: Average: 67 Max: 80 Min: 50 Acceptance Rate: 71% How did you do?

14. The Trust Game (Berg, Dickhaut, & McCabe, 1995) • Who are the players? • Investor & Trustee • Who can do what when? • First: Investor Divides X Between Private Account (X – T) & Trustee (T) • Second: Trustee Receives (1 + r)T & then returns Y • Who knows what when? • Investor Doesn’t Know How Much Trustee Will Return • Trustee Knows (1 + r)T Before Choosing Y • How are players rewarded based on what they do? • Investor: (X – T) + (1 + r)T - Y • Trustee: Y

15. What is the subgame perfect Nash equilibrium? • Equilibrium Strategies: • Investor: T = 0 • Trustee: Y = (1 + r)T • What does the experimental evidence say for r = 2? • On Average, about 50% is invested and 95% of the investment is returned. • Lots of variability (half return nothing or token amount). • Culture: • Bulgarians: 70% invested & 150% returned. • Orma Herders in Kenya: 40% invested & 55% repayment. • More indirect repayment or larger group tends to reduce investment. • Social pressure can increase investment & repayment rates.

16. Treatment 1: 3 Investment Growth Investments: Average: 54.2% Max: 100% Min: 0% Percent Investing: 66.7% Return: Average: 100% Max: 150% Min: 0% Treatment 2: 1.5 Investment Growth Investments: Average: 33.3% Max: 100% Min: 0% Percent Investing: 50.0% Return: Average: 85% Max: 150% Min: 0% How did you do?

17. Again, what does all this mean for game theory? What does all this mean in terms of understanding individual preferences?