Bargaining and Coalition Formation Dr James Tremewan - - PowerPoint PPT Presentation

Bargaining and Coalition Formation

Dr James Tremewan (james.tremewan@univie.ac.at) Fairness Concerns

Fairness Concerns

Fairness concerns in bargaining

• ”Stylized facts” from Ultimatum Game experiments:
• Virtually no offers above 50%. [1]
• Most offers between 40 and 50%. [2]
• Low offers are frequently rejected. [3]
• Probability of rejection decreases in size of offer. [4]
• [2-4] contradict game theoretic predictions based on the

assumption of selfish preferences.

• Altruism can explain [2] but not [3,4].
• Fehr and Schmidt (1999) propose a simple model of fairness

concerns that explain [1-4] (and a number of experimental results for other games).

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Fairness Concerns

Fehr and Schmidt (1999)

• Fairness modeled as ”self-centered inequity aversion.”
• Inequity aversion: people willing to give up some payoff to move

to more equitable outcome.

• Self-centered: people care only how their payoff compares to
• thers’, not about inequality amongst others.
• Note: Can be interpreted as reduced form for caring about
• thers’ intentions if actions that lead to unfair outcomes are

viewed as indicating bad intentions.

• Note: Third party punishment experiments suggest people do

care about unfair outcomes amongst others (e.g. Fehr and Fischbacher (2004). The model can be easily extended to accommodate this and e.g. different reference points such as average payoff.

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Fairness Concerns

Fehr and Schmidt (1999) - two-player case

• Ui(x) = xi − αi max |xj − xi, 0| − βi max |xi − xj, 0|.
• xi (xj) = own (other’s) monetary payoff.
• αi is sensitivity to unfair outcomes where the other gets more.
• βi is sensitivity to unfair outcomes where other gets less.
• F&S assume β ≤ αi and 0 ≤ βi < 1
• β ≤ αi implies people suffer more from inequality that is to their

disadvantage (evidence for this in Loewenstein, Thompson, and Bazerman (1989).

• 0 ≤ βi rules out status seeking. Such people exist, but have no

impact on equilibrium behaviour in contexts considered in F&S.

• β ≥ 1 implies preference for throwing away money if xi > xj,

which is odd.

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Fairness Concerns

Fairness concerns in the Ultimatum Game

• Proposer/Responder characterised by (α1, β1)/(α2, β2).
• Proposer offers proportion s, Responder accepts or rejects.
• Results for responder:
• Responder accepts any offer s ≥ 0.5
• Responder rejects iff s < s(a2) ≡ α2/(1 + 2α2) < 0.5
• If Proposer knows (α2, β2), offers s∗
• = 0.5 if β1 > 0.5
• ∈ [s(α2), 0.5] if β1 = 0.5
• = s(α2) if β1 > 0.5
• Stylised Fact [1-3] explained.
• Similar results if Proposer knows only that α2 ∼ F(α2).

Heterogeneity in (beliefs about) α2 gives variation in offers and Stylised Fact [4].

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Fairness Concerns

More general model of social preferences: Charness and Rabin (2002)

• UB(πA, πB) = (ρ·r +σ ·s +θ·q)·πA +(1−ρ·r −σ ·s −θ·q)·πB
• r = 1 if πB > πA, and 0 otherwise;
• s = 1 if πB < πA, and 0 otherwise;
• q = 1 if A has ”misbehaved”, and 0 otherwise.
• θ measures reciprocity.
• σ and ρ allow for distributional preferences unrelated to

reciprocity:

• σ ≤ ρ implies competitive preferences.
• σ < 0 < ρ < 1 like Fehr and Schmidt.
• 0 < σ ≤ ρ ≤ 1 incorporates ”social-welfare” concerns.
• Many experiments seek to estimate population and individual

level parameters of this model.

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