| . | Game 15 . | Game 25 . | Game 30 . | |||
|---|---|---|---|---|---|---|
| . | Ask . | Accept . | Ask . | Accept . | Ask . | Accept . |
| MPE strong | 10 | 10 | 13.55 | 11.45 | 16.67 | 13.33 |
| MPE weak | 10 | 10 | 8.55 | 6.45 | 6.67 | 4.17 |
| Markov Reversion strong | 10 | 10 | 11.25 | 11.25 | — | — |
| Markov Reversion weak | 10 | 10 | 8.75 | 8.75 | — | — |
| Carrot and Stick strong | 10 | 10 | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| |
| Carrot and Stick weak | 10 | 10 | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| |
| . | Game 15 . | Game 25 . | Game 30 . | |||
|---|---|---|---|---|---|---|
| . | Ask . | Accept . | Ask . | Accept . | Ask . | Accept . |
| MPE strong | 10 | 10 | 13.55 | 11.45 | 16.67 | 13.33 |
| MPE weak | 10 | 10 | 8.55 | 6.45 | 6.67 | 4.17 |
| Markov Reversion strong | 10 | 10 | 11.25 | 11.25 | — | — |
| Markov Reversion weak | 10 | 10 | 8.75 | 8.75 | — | — |
| Carrot and Stick strong | 10 | 10 | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| |
| Carrot and Stick weak | 10 | 10 | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| |
Notes: The amounts players are predicted to ask to keep themselves when making offers and the minimum amounts they would be willing to accept are reported. When strong players make offers to both other strong players and weak players in the equilibrium, they ask to keep the same amount for themselves. The amounts reported are for when all players are still present in the market. When only two players (who can match to each other) are left in the market, there is a unique perfect equilibrium in which both players ask to keep 10 when proposing and are willing to accept offers that give them 10 or more. The amounts reported are for the limit as δ → 1.
| . | Game 15 . | Game 25 . | Game 30 . | |||
|---|---|---|---|---|---|---|
| . | Ask . | Accept . | Ask . | Accept . | Ask . | Accept . |
| MPE strong | 10 | 10 | 13.55 | 11.45 | 16.67 | 13.33 |
| MPE weak | 10 | 10 | 8.55 | 6.45 | 6.67 | 4.17 |
| Markov Reversion strong | 10 | 10 | 11.25 | 11.25 | — | — |
| Markov Reversion weak | 10 | 10 | 8.75 | 8.75 | — | — |
| Carrot and Stick strong | 10 | 10 | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| |
| Carrot and Stick weak | 10 | 10 | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| |
| . | Game 15 . | Game 25 . | Game 30 . | |||
|---|---|---|---|---|---|---|
| . | Ask . | Accept . | Ask . | Accept . | Ask . | Accept . |
| MPE strong | 10 | 10 | 13.55 | 11.45 | 16.67 | 13.33 |
| MPE weak | 10 | 10 | 8.55 | 6.45 | 6.67 | 4.17 |
| Markov Reversion strong | 10 | 10 | 11.25 | 11.25 | — | — |
| Markov Reversion weak | 10 | 10 | 8.75 | 8.75 | — | — |
| Carrot and Stick strong | 10 | 10 | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},14\frac{4}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| | |$(11\frac{1}{9},17\frac{7}{9})$| |
| Carrot and Stick weak | 10 | 10 | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(5\frac{5}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| | |$(2\frac{2}{9},8\frac{8}{9})$| |
Notes: The amounts players are predicted to ask to keep themselves when making offers and the minimum amounts they would be willing to accept are reported. When strong players make offers to both other strong players and weak players in the equilibrium, they ask to keep the same amount for themselves. The amounts reported are for when all players are still present in the market. When only two players (who can match to each other) are left in the market, there is a unique perfect equilibrium in which both players ask to keep 10 when proposing and are willing to accept offers that give them 10 or more. The amounts reported are for the limit as δ → 1.
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