Approval mechanism to solve prisoner’s dilemma: comparison with Varian’s compensation mechanism. (English) Zbl 1397.91120
Summary: After having played a prisoner’s dilemma, players can approve or reject the other’s choice of cooperation or defection. If both players approve the other’s choice, the outcome is the result of the chosen strategies in the prisoner’s dilemma; however, if either rejects the other’s choice, the outcome is the same as if they had mutually defected from the prisoner’s dilemma. In theory, such an approval mechanism implements cooperation in backward elimination of weakly dominated strategies, although this is not the case in the subgame perfect Nash equilibrium. By contrast, the compensation mechanism proposed by H. R. Varian [“A solution to the problem of externalities when agents are well-informed”, Am. Econ. Rev. 84, No. 5, 1278–1293 (1994), https://www.jstor.org/stable/2117772] implements cooperation in the latter but not in the former. This result motivates the present experimental study of the two mechanisms. The approval mechanism sessions yield a cooperation rate of 90% in the first period and 93.2% across periods, while the compensation mechanism sessions yield a cooperation rate of 63.3% in the first period and 75.2% across periods. In addition, the backward elimination of weakly dominated strategies better predicts subjects’ behavior than does the subgame perfect Nash equilibrium in both mechanism sessions.
Keywords:
prisoner’s dilemma; Varian’s compensation mechanism; perfect Nash equilibrium; experimental studySoftware:
Z-TreeReferences:
| [1] | Andreoni, J; Varian, H, Preplay contracting in the prisoners’ dilemma, Proc Natl Acad Sci, 96, 10933-10938, (1999) · Zbl 1038.91503 · doi:10.1073/pnas.96.19.10933 |
| [2] | Andreoni, J; Miller, JH, Rational cooperation in the finitely repeated prisoner’s dilemma: experimental evidence, Econ J, 103, 570-585, (1993) · doi:10.2307/2234532 |
| [3] | Banks, JS; Plott, CR; Porter, DP, An experimental analysis of unanimity in public goods provision mechanisms, Rev Econ Stud, 55, 301-322, (1988) · doi:10.2307/2297583 |
| [4] | Beatty, T; Crawford, I, How demanding is the revealed preference approach to demand?, Am Econ Rev, 101, 2782-2795, (2011) · doi:10.1257/aer.101.6.2782 |
| [5] | Blonski, M; Spagnolo, G, Prisoners’ other dilemma, Intl J Game Theory, 44, 61-81, (2015) · Zbl 1319.91031 · doi:10.1007/s00182-014-0419-9 |
| [6] | Bracht, J; Figuieres, C; Ratto, M, Relative performance of two simple incentive mechanisms in a public goods experiment, J Pub Econ, 92, 54-90, (2008) · doi:10.1016/j.jpubeco.2007.04.005 |
| [7] | Brams, SJ; Kilgour, DM; Levin, S (ed.), How democracy resolves conflict in difficult games, 229-241, (2009), Berlin · doi:10.1007/978-3-540-85436-4_14 |
| [8] | Charness, G; Fréchette, GR; Qin, C-Z, Endogenous transfers in the prisoner’s dilemma game: an experimental test of cooperation and coordination, GEB, 60, 287-306, (2007) · Zbl 1134.91347 |
| [9] | Chen, Y; Plott, CR (ed.); Smith, VL (ed.), Incentive-compatible mechanisms for pure public goods: a survey of experimental literature, 625-643, (2008), Amsterdam · doi:10.1016/S1574-0722(07)00067-4 |
| [10] | Cooper, R; DeJong, DV; Forsythe, R; Ross, TW, Cooperation without reputation: experimental evidence from prisoner’s dilemma games, GEB, 12, 187-218, (1996) · Zbl 0848.90148 |
| [11] | Davenport C (2015) Nations approve landmark climate accord in Paris. New York Times. Retrieved November 7, 2017 http://www.nytimes.com/2015/12/13/world/europe/climate-change-accord-paris.html · Zbl 0477.90095 |
| [12] | Fehr, E; Gächter, S, Cooperation and punishment in public goods experiments, Am Econ Rev, 90, 980-994, (2000) · doi:10.1257/aer.90.4.980 |
| [13] | Fehr E, Powell M, Wilkening T (2014) Handing out guns at a knife fight: behavioral limitations of subgame-perfect implementation, ECON - Working Paper 171, University of Zurich |
| [14] | Fischbacher, U, Z-tree: zurich toolbox for ready-made economic experiments, Exp Econ, 10, 171-178, (2007) · doi:10.1007/s10683-006-9159-4 |
| [15] | Forsythe, R; Rietz, T; Myerson, R; Weber, R, An experimental study of voting rules and polls in three-candidate elections, Intl J Game Theory, 25, 355-383, (1996) · Zbl 0864.90027 · doi:10.1007/BF02425262 |
| [16] | Guala, F, Reciprocity: weak or strong? what punishment experiments do (and do not) demonstrate, Behav Brain Sci, 35, 1-15, (2012) · doi:10.1017/S0140525X11000069 |
| [17] | Hamaguchi, Y; Mitani, S; Saijo, T, Does the Varian mechanism work? emissions trading as an example, Intl J Bus Econ, 2, 85-96, (2003) |
| [18] | Huang X, Masuda T, Okano Y, Saijo T (2017) Cooperation among behaviorally heterogeneous players in social dilemma with stay or leave decisions. University of Arizona Department of Economics Working Paper series 2017-16 |
| [19] | Kalai, E, Preplay negotiations and the prisoner’s dilemma, Math Soc Sci, 1, 375-379, (1981) · Zbl 0477.90095 · doi:10.1016/0165-4896(81)90015-9 |
| [20] | Kimbrough, EO; Sheremeta, RM, Side-payments and the costs of conflict, Intl J Ind Organ, 31, 278-286, (2013) · doi:10.1016/j.ijindorg.2012.01.005 |
| [21] | Masuda, T; Okano, Y; Saijo, T, The minimum approval mechanism implements the efficient public good allocation theoretically and experimentally, Games Econ Behav, 83, 73-85, (2014) · Zbl 1284.91153 · doi:10.1016/j.geb.2013.10.003 |
| [22] | Midler, E; Figuières, C; Willinger, M, Choice overload, coordination and inequality: three hurdles to the effectiveness of the compensation mechanism?, Soc Choice Welf, 45, 513-535, (2015) · Zbl 1341.91036 · doi:10.1007/s00355-014-0840-9 |
| [23] | Plott CR, Smith VL (2008) Handbooks in economics 28: handbook of experimental economics results. Elsevier, Amsterdam |
| [24] | Qin CZ (2005) Penalties and rewards as inducements to cooperate. Department of Economics, University of California-Santa Barbara |
| [25] | Saijo T, Okano Y, Yamakawa T (2016) The approval mechanism experiment: a solution to prisoner’s dilemma. KUT-SDES Working Paper no. 2015-12 (Revised), Kochi University of Technology · Zbl 1319.91031 |
| [26] | Saijo, T; Shen, J, Mate choice mechanism for solving a quasi-dilemma, J Behav Exp Econ, 72, 1-8, (2018) · doi:10.1016/j.socec.2017.10.004 |
| [27] | Selten, R, Reexamination of the perfectness concept for equilibrium points in extensive games, Intl J Game Theory, 4, 25-55, (1975) · Zbl 0312.90072 · doi:10.1007/BF01766400 |
| [28] | Selten, R, Properties of a measure of predictive success, Math Soc Sci, 21, 153-167, (1991) · Zbl 0729.90550 · doi:10.1016/0165-4896(91)90076-4 |
| [29] | Varian, HR, A solution to the problem of externalities when agents are well-informed, Am Econ Rev, 84, 1278-1293, (1994) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
