Fehr and Schmidt - Theory of Fairness, Competition and Cooperation

Question 1

What is the main concept proposed by Fehr and Schmidt?

Answer 1

Self centered inequity aversion - where individuals are willing to sacrafice some of their own material payoff so to achieve more equitable outcomes.

Question 2

What is the basic assumption behind Fehr and Schmidt’s hypothesis?

Answer 2

That in addition to purely self-interested participants, there is a fraction of people who are also motivated by fairness considerations

Question 3

What “puzzles” did Fehr and Schmidt aim to explain?

Answer 3

1) Why people exploit bargaining power in competitive markets but not in bilateral bargaining, and

2) Why freeriding occurs in some cooperative games while stable cooperation emerges when punishment is not possible

Question 4

How does Fehr and Schmidt’s approach differ from learning models?

Answer 4

They explain behavioural anomalies without relaxing the rationality assumption (which is what typically occurs in learning models where beliefs and heuristics build over time)

Question 5

What is Ferh and Schmidt’s utility function for inequity aversion?

Answer 5

Question 6

What does the alpha parameter represent in the utility function?

Answer 6

It represents the utility loss from disadvantageous inequality (when others have more than you - envy)

Question 7

What does the Beta parameter represent in the utility function?

Answer 7

It represents the utility loss from advantageous inequality (when you have more than others - guilt)

Question 8

What is the key assumption about the relationship between alpha and beta?

Answer 8

That alpha is larger than beta, meaning that individuals place more weight on being disadvantaged (“being the sucker”) than on having an advantage over others.

Question 9

Why is the assumption that alpha is larger than beta psychologically plausible?

Answer 9

Reflects that individuals are loss averse in social comparisons, which is suppored by evidence by Loewenstein, Thompson and Bazerman (1989)

Question 10

What types of economic scenarios did Fehr and Schmidt apply their model to?

Answer 10

Bilateral bargaining games (ultimatum, gift exchange, and trust games), competitive market environments, and public goods games (with and without punishment).

Question 11

What is the standard prediction for the ultimatum game, and how does it differ from actual results?

Answer 11

Standard prediction: proposer offers s=0, responder accepts. Actual results: 60-80% of offers fall within [0.4, 0.5] and low offers are frequently rejected

Question 12

According to Fehr and Schmidt, when will a responder reject an offer in the ultimatum game?

Answer 12

When the offer falls below their acceptance threshold s < α_i/(1+2α_i), where α_i is their aversion to disadvantageous inequality

Question 13

What is the key result regarding market games with proposer competition?

Answer 13

Despite inequity aversion, there is a unique subgame perfect equilibrium where at least two proposers make an offer of one that is accepted, and the responder reaps all gains from trade.

Question 14

How does responder competition affect outcomes according to Fehr and Schmidt?

Answer 14

With sufficient responder competition, even inequity-averse players will accept very low offers, and the share s converges to zero as the number of responders increases.

Question 15

What condition must be met for the proposer to offer s=0 in the market game with responder competition?

Answer 15

What condition must be met for the proposer to offer s=0 in the market game with responder competition?

Question 16

What is the standard prediction for contributions in a one-stage public goods game?

Answer 16

Each player contributes nothing (g_i = 0) because free-riding is the dominant strategy.

Question 17

Under what condition will players cooperate in a one-stage public goods game according to Fehr and Schmidt?

Answer 17

Cooperation is an equilibrium if both players meet the condition α + β ≥ 1

Question 18

What happens in public goods games with punishment opportunities?

Answer 18

A large fraction (approximately 80%) of players cooperate fully, contradicting the standard model of self-interest.

Question 19

What makes punishment of free-riders credible in the two-stage public goods game?

Answer 19

Cooperators are willing to punish defectors even though it’s costly to themselves because it reduces their payoff disadvantage.

Question 20

What is a “conditionally cooperative enforcer” in Fehr and Schmidt’s model?

Answer 20

A player who is sufficiently concerned about inequality that they will cooperate if others cooperate and will punish free-riders even at a cost to themselves.

Question 21

What temporal limitation does Fehr and Schmidt’s model have?

Answer 21

It cannot explain the evolution of play over time or the time path of play in experiments.

Question 22

What criticism did Binmore and Shaked (2020) levy against Fehr and Schmidt?

Answer 22

They accused Fehr and Schmidt of using tactics that portray their theory more favorably without proper disclosure, including selecting experimental designs that produce outcomes supporting their model

Question 23

How might the linear form of inequity aversion be problematic?

Answer 23

It’s a simplification that likely doesn’t capture the full complexity of human fairness preferences.

Question 24

What aspect of fairness does the Fehr-Schmidt model not capture?

Answer 24

The model disregards procedural justice or intentions behind actions, focusing only on payoff inequity.

Question 25

When could fairness considerations feature in the face of competition?

Answer 25

If the competing players can punish the monopolist by destroying some of the surplus and enforce a more equirable outcome e.g. labour markets where you can vary effort, expering a direct impact on the relative material payoff of the employer.

Question 26

What is the average % of subjects that choose g_i = 0 in studies of public good games without punishment?

Answer 26

73%

Question 27

On average, how many people cooperate in the game with punishment?

Answer 27

80% - as established in Fehr and Gachter, defectors do not gain from free riding because they are being punished.

Question 28

What game is a special case of the public good game without punishment for n=2, and how does it apply to Fehr and Schmidt findings?

Answer 28

Simultaneous PD.

Question 29

Using the preference distribution given, what is the probability they give for the randomly drawn group of 4 players to meet conditions for cooperation.

Answer 29

Probability is 61.1 percet - which is roughly consistent with the experimental evidence of Fehr and Gachter.

Question 30

How do they explain the difference between their model prediction and the experimental evidence for the Dictator Game?

Answer 30

That they haven't modelled for non linear equity aversion. If they allow for a utility function that is concave in the amount of advantageous inequality, then can generate optimal offers that are in the interior of [0, 0.5]

Question 31

What is a potential limitation that is raise with respect to time paths?

Answer 31

A model examining eqm behaviour cannot explain the time path of play and cannot explain the short run impact of equity considerations (which the empirical evidence shows to have important SR effects)

Question 32

What approach did Rabin take versus the model proposed to Fehr and Schmidt?

Answer 32

Rabin's model rests on the idea that people are willing to reward fair intentions and to punish fair intentions. But this is only restricted to two-person normal form games (given intentions can only be modelled in psychological game theory)

Question 34

What is the monetary payoff for player i in the public goods game with punishment?

Answer 34