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Behavioral eco lect 6: Strategic interaction part 4 (Ultimatum game –…
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
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.
Ultimatum game – standard prediction
Backward induction:
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
→ 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
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
→ 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
Offers larger than zero
→ utility depends on more than own payoff.