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Behavioral eco lect 6: Strategic interaction part 5 (Trust game – standard…
Behavioral eco lect 6: Strategic interaction part 5
Trust game
• Stage 0: proposer gets sum of money S
• Stage 1: proposer sends x to responder
• Stage 2: experimenter increases x to (1+r)x
• Stage 3: responder returns y to proposer
Payoffs:
Proposer: S – x + y
Responder: (1+r)x – y
2 players: proposer and responder
Trust game – standard prediction
• Assume that utility depends only on own payoff
→ players aim at maximizing their own payoffs
Backward induction:
Stage 3:
responder starts with (1+r)x
→ responder should not return anything: y = 0
Stage 1:
proposer knows that y = 0
→ proposer knows that he will not get anything back from what he sends to responder
→ proposer sends x = 0
Payoffs in subgame-perfect equilibrium if utility depends only on own payoff:
Proposer: S
Responder: 0
Tragedy in the trust game:
Imagine they could credibly commit to x = S and y = (1+r)S/2 → payoffs would be
Proposer: (1+r)S/2 > S (assuming 1+r > 2)
Responder: (1+r)S/2 > 0
Trust game – in practice
slide 45/57
Social concerns in the public good game
Public good game
• Stage 1: every player i decides to contribute xi ≤ ei to the public good
• Generated value of the public good: m (x1 + x2 + ... + xn) = m ∑ xi
(Assumption: m < 1)
• Stage 0: every player i has an endowment ei
Payoffs: πi = ei – xi + m ∑ xi
• n players – all have the same role.
Public good game – standard prediction
•
πi = ei – xi + m ∑ xi
→ extra unit of contribution generates extra payoff of (– 1 + m) < 0
→ best not to contribute at all → xi = 0
→ Nash-equilibrium = nobody contributes
→ payoffs in Nash-equilibrium: πi = ei
• Assume that utility depends only on own payoff
→ players aim at maximizing their own payoffs
• Tragedy: if everybody would contribute entire endowment xi = ei → πi = m ∑ ei = m n e > e (if we assume that mn>1)
Public good game – in practice
On average people contribute between 40% and 60% of endowment.