Behavioral eco lect 6: Strategic interaction part 4

Social concerns in the ultimatum, dictator, and trust game

Limited strategic reasoning and fairness

In the guessing game fairness plays hardly any role
→ every deviation from the Nash equilibrium is due to limited
strategic reasoning.

In the ultimatum, dictator, and trust game, limited strategic reasoning plays hardly any role
→ deviations from the subgame-perfect equilibria can now be due to fairness concerns.

Ultimatum game – standard prediction

Ultimatum game

2 players: proposer and responder

• Stage 0: proposer gets sum of money S
• Stage 1: proposer offers x to responder
• Stage 2: responder can accept or reject

Payoffs:

  • if responder accepts: responder gets x, proposer gets S – x
  • if responder rejects: both get 0.

Backward induction:

→ proposer offers lowest possible x>0 if responder rejects offer of 0 proposer offers x=0 if responder accepts offer of 0

Assume that utility depends only on own payoff
→ players aim at maximizing their own payoffs

Stage 2:
if x>0
→ responder gets x > 0 if he accepts and 0 otherwise → responder accepts
if x=0 → responder is indifferent between accept and reject

Stage 1: proposer wants two things: (1) x as low as possible and (2) responder accepts

Ultimatum game – standard prediction

2 subgame-perfect equilibria:

(1) Proposer offers 1 cent &
Responder accepts positive offers and rejects offer of 0

(2) Proposer offers 0 & Responder accepts any offer

Ultimatum game – in practice SLIDE 34-35/57

If responders manage to maximize their own utilities

→ their utilities cannot depend only on their own payoffs

→ their utilities must depend on the payoffs or intentions of others as well

Ultimatum game in practice – interpretation

(1) Proposers manage to maximize their utility given their beliefs – they derive utility only from their own payoffs – they expect responders to reject small positive offers.

(2) Proposers manage to maximize their utility given their beliefs – they derive utility not only from their own payoffs (no matter what they believe about responders).

Dictator game

-Stage 0: proposer gets sum of money S
-Stage 1: proposer offers x to responder

Payoffs: responder gets x, proposer gets S – x

2 players: proposer and responder

Dictator game – standard prediction

• Assume that utility depends only on own payoff
→ players aim at maximizing their own payoffs

• Proposer knows that there is no risk of rejection → x will be as low as possible: x = 0

Dictator game – in practice

Lower offers than in ultimatum game

Offers larger than zero
→ utility depends on more than own payoff.

→ in ultimatum game fear of rejection plays a role

→ in ultimatum game strategic considerations drive the results at least partly

→ difference with ultimatum game is risk of rejection