| . | Cooperative theories . | Noncooperative theories . | ||||
|---|---|---|---|---|---|---|
| . | . | . | Core . | . | Markov . | Carrot . |
| . | Core . | SPB . | midpoint . | MPE . | reversion . | and Stick . |
| Efficiency | ||||||
| (1) Matching is efficient in Game 15 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30 | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| (3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| Players’ payoffs | ||||||
| (1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (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 | – | ✗ | ✗ | ✓ | ✓ | – |
| Players’ strategies | ||||||
| (1) Players do not delay | – | – | – | ✓ | ✓ | ✓ |
| (2) Frequency of efficient proposals by strong player declines from Game 15 to Game 25 to Game 30 | – | – | – | ✓ | ✗ | ✗ |
| . | Cooperative theories . | Noncooperative theories . | ||||
|---|---|---|---|---|---|---|
| . | . | . | Core . | . | Markov . | Carrot . |
| . | Core . | SPB . | midpoint . | MPE . | reversion . | and Stick . |
| Efficiency | ||||||
| (1) Matching is efficient in Game 15 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30 | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| (3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| Players’ payoffs | ||||||
| (1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (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 | – | ✗ | ✗ | ✓ | ✓ | – |
| Players’ strategies | ||||||
| (1) Players do not delay | – | – | – | ✓ | ✓ | ✓ |
| (2) Frequency of efficient proposals by strong player declines from Game 15 to Game 25 to Game 30 | – | – | – | ✓ | ✗ | ✗ |
Notes: When a theory is consistent with the data and would be violated by the opposite finding, we mark the cell with a ✓. If the theory does not make this prediction, but is consistent with it, we mark the cell with a –, and if the predictions of the theory are violated by the data, we mark the cell with a ✗.
| . | Cooperative theories . | Noncooperative theories . | ||||
|---|---|---|---|---|---|---|
| . | . | . | Core . | . | Markov . | Carrot . |
| . | Core . | SPB . | midpoint . | MPE . | reversion . | and Stick . |
| Efficiency | ||||||
| (1) Matching is efficient in Game 15 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30 | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| (3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| Players’ payoffs | ||||||
| (1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (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 | – | ✗ | ✗ | ✓ | ✓ | – |
| Players’ strategies | ||||||
| (1) Players do not delay | – | – | – | ✓ | ✓ | ✓ |
| (2) Frequency of efficient proposals by strong player declines from Game 15 to Game 25 to Game 30 | – | – | – | ✓ | ✗ | ✗ |
| . | Cooperative theories . | Noncooperative theories . | ||||
|---|---|---|---|---|---|---|
| . | . | . | Core . | . | Markov . | Carrot . |
| . | Core . | SPB . | midpoint . | MPE . | reversion . | and Stick . |
| Efficiency | ||||||
| (1) Matching is efficient in Game 15 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) The rate of efficient matching declines from Game 15 to Game 25 to Game 30 | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| (3) Games 25 and 30: Efficient outcomes are more likely to be reached if a weak player proposes first | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |
| Players’ payoffs | ||||||
| (1) Strong players’ payoffs increase from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (2) Weak players’ payoffs decrease from Game 15 to Game 25 to Game 30 | – | ✓ | ✓ | ✓ | ✓ | ✓ |
| (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 | – | ✗ | ✗ | ✓ | ✓ | – |
| Players’ strategies | ||||||
| (1) Players do not delay | – | – | – | ✓ | ✓ | ✓ |
| (2) Frequency of efficient proposals by strong player declines from Game 15 to Game 25 to Game 30 | – | – | – | ✓ | ✗ | ✗ |
Notes: When a theory is consistent with the data and would be violated by the opposite finding, we mark the cell with a ✓. If the theory does not make this prediction, but is consistent with it, we mark the cell with a –, and if the predictions of the theory are violated by the data, we mark the cell with a ✗.
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