Table 3. Open in new tab Qualitative...

	Cooperative theories	Noncooperative theories
Efficiency
(1) Matching is efficient in Game 15	Yes	Yes	Yes	Yes	Yes	Yes
(2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30	No	No	No	Yes	No	No
(3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first	No	No	No	Yes	No	No
Players’ payoffs
(1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(3) Difference in payoffs of strong players in efficient matches from exiting first rather than second is positive and higher in Game 30 than in Game 25	–	No	No	Yes	Yes	–
Players’ strategies
(1) Players do not delay	–	–	–	Yes	Yes	Yes
(2) Frequency of efficient proposals by strong players declines from Game 15 to Game 25 to Game 30	–	–	–	Yes	No	No

Cooperative theories

Noncooperative theories

Core

Markov

Carrot

Core

SPB

midpoint

MPE

reversion

and Stick

Efficiency

(1) Matching is efficient in Game 15

Yes

(2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30

Yes

(3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first

Yes

Players’ payoffs

(1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30

–

Yes

–

(2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30

–

Yes

–

(3) Difference in payoffs of strong players in efficient matches from exiting first rather than second is positive and higher in Game 30 than in Game 25

–

Yes

–

Players’ strategies

(1) Players do not delay

–

Yes

(2) Frequency of efficient proposals by strong players declines from Game 15 to Game 25 to Game 30

–

Yes

	Cooperative theories	Noncooperative theories
Efficiency
(1) Matching is efficient in Game 15	Yes	Yes	Yes	Yes	Yes	Yes
(2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30	No	No	No	Yes	No	No
(3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first	No	No	No	Yes	No	No
Players’ payoffs
(1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(3) Difference in payoffs of strong players in efficient matches from exiting first rather than second is positive and higher in Game 30 than in Game 25	–	No	No	Yes	Yes	–
Players’ strategies
(1) Players do not delay	–	–	–	Yes	Yes	Yes
(2) Frequency of efficient proposals by strong players declines from Game 15 to Game 25 to Game 30	–	–	–	Yes	No	No

Table 3.

Open in new tab

Qualitative predictions.

	Cooperative theories			Noncooperative theories
			Core		Markov	Carrot
	Core	SPB	midpoint	MPE	reversion	and Stick
Efficiency
(1) Matching is efficient in Game 15	Yes	Yes	Yes	Yes	Yes	Yes
(2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30	No	No	No	Yes	No	No
(3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first	No	No	No	Yes	No	No
Players’ payoffs
(1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(3) Difference in payoffs of strong players in efficient matches from exiting first rather than second is positive and higher in Game 30 than in Game 25	–	No	No	Yes	Yes	–
Players’ strategies
(1) Players do not delay	–	–	–	Yes	Yes	Yes
(2) Frequency of efficient proposals by strong players declines from Game 15 to Game 25 to Game 30	–	–	–	Yes	No	No

	Cooperative theories			Noncooperative theories
			Core		Markov	Carrot
	Core	SPB	midpoint	MPE	reversion	and Stick
Efficiency
(1) Matching is efficient in Game 15	Yes	Yes	Yes	Yes	Yes	Yes
(2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30	No	No	No	Yes	No	No
(3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first	No	No	No	Yes	No	No
Players’ payoffs
(1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30	–	Yes	Yes	Yes	Yes	–
(3) Difference in payoffs of strong players in efficient matches from exiting first rather than second is positive and higher in Game 30 than in Game 25	–	No	No	Yes	Yes	–
Players’ strategies
(1) Players do not delay	–	–	–	Yes	Yes	Yes
(2) Frequency of efficient proposals by strong players declines from Game 15 to Game 25 to Game 30	–	–	–	Yes	No	No

Notes: We consider a theory to predict an outcome if it would be violated by the opposite finding, in which case we mark the cell “Yes”, and to not predict an outcome if the theory would be violated by the finding, in which case we mark the cell with a “No”. If the theory would be consistent with such a finding, but would also be consistent with the opposite finding, we mark the cell with a “–”.

This Feature Is Available To Subscribers Only