Figure 1a: Chairman

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
Two Perspectives

• 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.

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 Doesnt Know Acceptable Proposals Before
  Choosing
• Receiver Knows Proposal Before Choosing
• How are players rewarded based on what they do?
• Proposer Rx if 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)
• Dictators 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 (gt50) Often
  Rejected
• Gender (Andreoni Vesterlund)
• Some Evidence that Men More Self-Interest Women
  More Rawlsian
• Age
• Children More Self-Interested

13
How did you do?

• 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

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 Doesnt 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
How did you do?

• 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

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