Costly Voluntary Disclosure in a Signaling Game
-
Paul Pecorino
und
Mark Van Boening
Abstract
We conduct an experimental analysis of pretrial bargaining, while allowing for the costly disclosure of private information in a signaling game. Under the theory, 100 % of plaintiffs with a weak case are predicted to remain silent, while 100 % of the plaintiffs with a strong case are predicted to voluntarily disclose their type. We find that 75 % of weak plaintiffs remain silent and 67 % of strong plaintiffs reveal their type. In line with theory, weak plaintiffs who reveal their type receive a lower payoff, while strong plaintiffs who reveal their type receive a higher payoff. Plaintiffs with a strong case who reveal their type have a dispute rate which is 50 % points lower than strong plaintiffs who remain silent. Because plaintiffs who reveal their type cannot extract the entire surplus from settlement from the defendant, the incentive to engage in voluntary disclosure is weaker empirically than it is in theory.
Acknowledgements
We would like to thank the Culverhouse College of Commerce and Business Administration for providing financial support and William B. Hankins for his research assistance. We would also like to thank an anonymous referee, Louis Kaplow and participants at the American Law and Economics Association Meeting for providing helpful comments on the paper.
Appendix
Frequency of costly disclosure by session and player A type.
| Frequency with player A discloses her type | Frequency with which individual subjects disclose as predicted | ||||
|---|---|---|---|---|---|
| AL-N | AH-D | AL-N | AH-D | AL-N & AH-D | |
| S1 | 0.708 (51/72) | 0.542 (13/24) | 0.375 (3/8) | 0.375 (3/8) | 0.125 (1/8) |
| S2 | 0.820 (50/61) | 0.657 (23/35) | 0.125 (1/8) | 0.500 (4/8) | 0.000 (0/8) |
| S3 | 0.789 (30/38) | 0.409 (9/22) | 0.400 (2/5) | 0.200 (1/5) | 0.000 (0/5) |
| S4 | 0.767 (33/43) | 0.909 (20/22) | 0.400 (2/5) | 0.600 (3/5) | 0.200 (1/5) |
| S5 | 0.691 (38/55) | 0.826 (19/23) | 0.500 (3/6) | 0.667 (4/6) | 0.500 (3/6) |
Player A-N offers by session.
| AL-N offers 75–225, AH-N offers 375–525 | Other offers | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| n | Pct. (No.) | Mean | Std. Dev. | Median | Range | 226–374 | 375–525 | >525 | ||
| S1 | AL-N | 51 | 0.706 (36) | 196.2 | 31.3 | 200 | 100–225 | 6 | 8 | 1 |
| AH-N | 11 | 0.545 (6) | 491.7 | 12.9 | 500 | 475–525 | 3a | – | 2 | |
| S2 | AL-N | 50 | 0.560 (28) | 192.8 | 32.4 | 200 | 125–225 | 16 | 6 | – |
| AH-N | 12 | 0.917 (11) | 446.0 | 55.5 | 450 | 376–524 | – | – | 1 | |
| S3 | AL-N | 30 | 0.600 (18) | 202.0 | 22.4 | 200 | 138–224 | 5 | 6 | 1 |
| AH-N | 13 | 0.385 (5) | 452.0 | 50.8 | 425 | 401–524 | 3a | – | 5 | |
| S4 | AL-N | 33 | 0.879 (29) | 196.2 | 20.4 | 200 | 150–220 | 2 | 2 | – |
| AH-N | 2 | 0.500 (1) | 450.0 | – | 450 | 450–450 | – | – | 1 | |
| S5 | AL-N | 38 | 0.474 (18) | 195.7 | 28.9 | 192.5 | 150–225 | 9 | 9 | 2 |
| AH-N | 4 | 0.750 (3) | 391.7 | 14.4 | 400 | 375–400 | 1a | – | – | |
aFor AH-N, these are offers<375.
Player A-D offers by session.
| AL-D offers 75–225, AH-D offers 375–525 | Other offers | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| n | Pct. (No.) | Mean | Std. Dev. | Median | Range | 226–374 | 375–525 | >525 | ||
| S1 | AL-D | 21 | 0.810 (17) | 213.4 | 9.7 | 220 | 200–224 | 2 | 1 | 1 |
| AH-D | 13 | 0.92 (12) | 502.9 | 16.4 | 500 | 475–525 | 1a | – | – | |
| S2 | AL-D | 11 | 0.364 (4) | 181.5 | 35.8 | 178.5 | 145–224 | 6 | 1 | – |
| AH-D | 23 | 0.96 (22) | 485.9 | 32.1 | 475 | 425–525 | – | – | 1 | |
| S3 | AL-D | 8 | 1.00 (8) | 202.9 | 19.6 | 200 | 175–224 | – | – | – |
| AH-D | 9 | 1.0 (9) | 472.3 | 50.8 | 500 | 405–524 | – | – | – | |
| S4 | AL-D | 10 | 0.800 (8) | 165.6 | 31.4 | 145 | 145–225 | 1 | – | 1 |
| AH-D | 20 | 1.0 (20) | 500.0 | 18.0 | 500 | 450–520 | – | – | – | |
| S5 | AL-D | 17 | 0.882 (15) | 192.3 | 37.0 | 200 | 105–224 | – | – | 2 |
| AH-D | 19 | 1.0 (19) | 491.5 | 27.7 | 500 | 435–524 | – | – | – | |
aFor AH-N, this is an offer<375.
Player B dispute rates.
| Dispute rate (ratio) by offer interval | ||||||
|---|---|---|---|---|---|---|
| All offers | 75–225 | 375–525 | 226–374 | >525 | ||
| S1 | AL-N | 0.216 (11/51) | 0.056 (2/36) | 0.625 (5/8) | 0.500 (3/6) | 1.0 (1/1) |
| AH-N | 0.636 (7/11) | 0.000 (0/1) | 0.667 (4/6) | 0.500 (1/2) | 1.0 (2/2) | |
| AL-D | 0.238 (5/21) | 0.118 (2/17) | 0.000 (0/1) | 1.0 (2/2) | 1.0 (1/1) | |
| AH-D | 0.231 (3/13) | 0.000 (0/1) | 0.250 (3/12) | – | – | |
| S2 | AL-N | 0.340 (17/50) | 0.107 (3/28) | 0.833 (5/6) | 0.562 (9/16) | – |
| AH-N | 0.833 (10/12) | – | 0.818 (9/11) | – | 1.0 (2/2) | |
| AL-D | 0.818 (9/11) | 0.500 (2/4) | 1.0 (1/1) | 1.0 (6/6) | – | |
| AH-D | 0.261 (6/23) | – | 0.227 (5/22) | – | 1.0 (1/1) | |
| S3 | AL-N | 0.300 (9/30) | 0.167 (3/18) | 0.500 (3/6) | 0.400 (2/5) | 1.0 (1/1) |
| AH-N | 0.692 (9/13) | 0.000 (0/1) | 0.800 (4/5) | 0.000 (0/2) | 1.0 (5/5) | |
| AL-D | 0.250 (2/8) | 0.250 (2/8) | – | – | – | |
| AH-D | 0.333 (3/9) | – | 0.333 (3/9) | – | – | |
| S4 | AL-N | 0.273 (9/33) | 0.207 (6/29) | 1.0 (2/2) | 0.500 (1/2) | – |
| AH-N | 0.500 (1/2) | – | 0.000 (0/1) | – | 1.0 (1/1) | |
| AL-D | 0.300 (3/10) | 0.125 (1/8) | – | 1.0 (1/1) | 1.0 (1/1) | |
| AH-D | 0.150 (3/20) | – | 0.150 (3/20) | – | – | |
| S5 | AL-N | 0.421 (16/38) | 0.222 (4/18) | 0.778 (7/9) | 0.333 (3/9) | 1.0 (2/2) |
| AH-N | 0.500 (2/4) | – | 0.667 (2/3) | 1.0 (1/1) | – | |
| AL-D | 0.235 (4/17) | 0.113 (2/15) | — | – | 1.0 (2/2) | |
| AH-D | 0.263 (5/19) | – | 0.263 (5/19) | – | – | |
Player AL net payoffs per round by session.
| Offers 75–225 | All offers | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| No. | Mean | S.d. | Med. | Range | n | Mean | S.d. | Med. | Range | |||
| S1 | AL-N | 36 | 188.5 | 41.6 | 200 | 75–224 | 51 | 191.5 | 93.7 | 200 | 75–500 | |
| AL-D | 17 | 170.9 | 46.3 | 185 | 50–195 | 21 | 165.7 | 84.3 | 185 | 50–425 | ||
| S2 | AL-N | 28 | 177.7 | 47.7 | 200 | 75–225 | 50 | 168.8 | 84.5 | 182 | 75–425 | |
| AL-D | 4 | 88.8 | 45.2 | 85 | 50–135 | 11 | 64.1 | 31.5 | 50 | 50–135 | ||
| S3 | AL-N | 18 | 178.3 | 51.8 | 200 | 75–224 | 30 | 196.1 | 109.4 | 200 | 75–440 | |
| AL-D | 8 | 143.0 | 60.1 | 162 | 50–199 | 8 | 143.0 | 60.1 | 162 | 50–199 | ||
| S4 | AL-N | 29 | 168.3 | 51.9 | 200 | 75–220 | 33 | 162.3 | 57.8 | 200 | 75–250 | |
| AL-D | 8 | 121.9 | 35.4 | 120 | 50–175 | 10 | 107.5 | 43.5 | 120 | 50–175 | ||
| S5 | AL-N | 18 | 173.3 | 58.9 | 182 | 75–225 | 38 | 178.3 | 110.1 | 172 | 75–465 | |
| AL-D | 15 | 147.7 | 52.9 | 156 | 50–199 | 17 | 136.1 | 59.1 | 150 | 50–199 | ||
Player AH net payoffs per round by session.
| Offers 75–225 | All offers | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| No. | Mean | S.d. | Med. | Range | n | Mean | S.d. | Med. | Range | ||
| S1 | AH-N | 6 | 412.5 | 58.6 | 375 | 375–500 | 11 | 359.1 | 106.8 | 375 | 100–500 |
| AH-D | 12 | 445.0 | 59.4 | 475 | 350–500 | 13 | 422.3 | 99.6 | 475 | 150–500 | |
| S2 | AH-N | 11 | 379.6 | 15.0 | 375 | 375–425 | 12 | 379.2 | 14.4 | 375 | 375–425 |
| AH-D | 22 | 429.2 | 51.2 | 438 | 350–499 | 23 | 425.7 | 52.6 | 425 | 350–499 | |
| S3 | AH-N | 5 | 385.0 | 22.4 | 375 | 375–425 | 13 | 349.2 | 62.5 | 375 | 200–425 |
| AH-D | 9 | 413.4 | 62.0 | 400 | 350–499 | 9 | 413.4 | 62.0 | 400 | 350–499 | |
| S4 | AH-N | 29 | 450.0 | – | 450 | 450–450 | 2 | 412.5 | 53.0 | 412 | 375–450 |
| AH-D | 8 | 456.2 | 49.2 | 475 | 350–495 | 20 | 456.2 | 49.2 | 475 | 350–495 | |
| S5 | AH-N | 3 | 375.0 | 0.00 | 375 | 375–375 | 4 | 364.8 | 20.5 | 375 | 334–375 |
| AH-D | 19 | 432.0 | 56.2 | 449 | 350–499 | 19 | 432.0 | 56.2 | 449 | 350–499 | |
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Supplementary Material
The online version of this article offers supplementary material (DOI:https://doi.org/10.1515/rle-2016-0074).
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- Gang Rivalry and Crime: A Differential Game Approach
- Sharing of Cost Related Information Can Increase Consumer Welfare Under Risk-aversion
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- Optimal Resort to Court-Appointed Experts
- A Law-and-Economics Perspective on Cost-Sharing Rules for a Condo Elevator
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