nach oben

Social Choice and Welfare

Erschienen in:

22.01.2018 | Original Paper

Approval mechanism to solve prisoner’s dilemma: comparison with Varian’s compensation mechanism

verfasst von: Tatsuyoshi Saijo, Takehito Masuda, Takafumi Yamakawa

Erschienen in: Social Choice and Welfare | Ausgabe 1/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

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 Varian (Am Econ Rev 84(5):1278–1293, 1994) 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.

Vorheriger Artikel Almost Lorenz dominance

Nächster Artikel Random path to stability in a decentralized market with contracts

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

This holds provided the payoff asymmetry in the underlying prisoner’s dilemma is not too large (Qin 2005).

See Hamaguchi et al. (2003), Bracht et al. (2008), and Midler et al. (2015). For Moore-Repullo SPNE mechanism experiments, see Fehr et al. (2014).

Selten (1975) and Kalai (1981) applied BEWDS to game theory.

In this vein, Saijo et al. (2016), who developed a working paper version of the present paper, characterized the AM using certain no-punishment and no-coercion conditions. Kimbrough and Sheremeta (2013) presented situations in which side payments assumed in the CM—collusion in a market, patent races, and R&D competition—might not be legal. Guala (2012) pointed out that there is little anthropological evidence that humankind has used private punishment.

The AM differs from the money-back guarantee mechanism, as follows. If either player, but not both, chooses C, then the $10 contribution is returned to the cooperator. The money-back guarantee mechanism cannot generate (7,17), while the AM achieves (7,17) if players choose (C, D) and then both choose y. The same argument applies to Brams and Kilgour’s (2009) concept of voting between the outcomes of all-C and all-D in order to overcome PD. The AM has an advantage in terms of welfare compared to the money-back guarantee mechanism and Brams and Kilgour’s (2009) voting. To observe this, consider a case in which only player 1 is sufficiently altruistic that player 1’s utility is given by (player 1’s material payoff) $+{\uprho } $ (player 2’s material payoff), ${\uprho } >4/3$. Assume that players know each other’s payoff function. Then, the outcome of CD maximizes the sum of utilities of two players among four possible outcomes of the PD in Fig. 1. The AM implements CD, while neither the money-back guarantee mechanism nor Brams and Kilgour’s (2009) voting mechanism does.

A path is a list of what each player does in each stage: player 1’s choice between C and D, player 2’s choice between C and D, player 1’s choice between y and n, and player 2’s choice between y and n. For simplicity, hereafter, we write a path as CDny instead of (C, D, n, y). In the AM, we have 96 SPNEs. See Saijo et al. (2016) for more details.

The risk dominance criterion, even with subgame perfection, cannot select the strategy uniquely, unlike in the case of BEWDS. The off-path prediction by risk dominance is redundant. To observe this, consider subgame CD in Fig. 2. According to risk dominance, an NE with greater product deviation loss is more likely to occur (e.g., Blonski and Spagnolo 2015). Since the product of loss deviating from NE (n, y) and that of (n, n) are zero, both are predicted in light of risk dominance. However, seven out of the eight observed choices in subgame CD are (n, y), as reported in Table 2.

These results are due to the discreteness of strategies.

The pairings were anonymous and determined in advance so that no two subjects were paired more than once.

We used Andreoni and Miller’s (1993) method for statistical testing. We first calculated the average cooperation rate for each subject across periods, followed by the test statistic using the averages to eliminate cross-period correlation.

The cooperation rate in the PD is slightly lower than that recorded in previous experiments. For example, Cooper et al. (1996) and Andreoni and Miller (1993) found 20 and 18% cooperation rates, respectively.

Additional experiments on the AM and PD, in which subjects play the game in only one period, provide similar results, suggesting that the AM works without repetition. The data and results are available upon request.

Selten’s index has been used in the literature on testing revealed preference. Our notations follow those of Beatty and Crawford (2011). Forsythe et al. (1996) applied Selten’s index to a voting game experiment.

Although many people advocated the Paris Accord, the national pledges by countries to cut emissions are voluntary and do not involve penalty. “At best, scientists who have analyzed it say it will cut global greenhouse gas emissions by about half the required amount to avert a potential increase in atmospheric temperatures of 2 degrees Celsius or 3.6 degrees Fahrenheit” (NYTimes, 2015).

Andreoni J, Varian H (1999) Preplay contracting in the prisoners’ dilemma. Proc Natl Acad Sci 96(19):10933–10938CrossRef

Andreoni J, Miller JH (1993) Rational cooperation in the finitely repeated prisoner’s dilemma: experimental evidence. Econ J 103(418):570–585CrossRef

Banks JS, Plott CR, Porter DP (1988) An experimental analysis of unanimity in public goods provision mechanisms. Rev Econ Stud 55(2):301–322CrossRef

Beatty T, Crawford I (2011) How demanding is the revealed preference approach to demand? Am Econ Rev 101(6):2782–2795CrossRef

Blonski M, Spagnolo G (2015) Prisoners’ other dilemma. Intl J Game Theory 44(1):61–81CrossRef

Bracht J, Figuieres C, Ratto M (2008) Relative performance of two simple incentive mechanisms in a public goods experiment. J Pub Econ 92(1):54–90CrossRef

Brams SJ, Kilgour DM (2009) How democracy resolves conflict in difficult games. In: Levin S (ed) Games, groups, and the global good. Springer, Berlin, pp 229–241CrossRef

Charness G, Fréchette GR, Qin C-Z (2007) Endogenous transfers in the prisoner’s dilemma game: an experimental test of cooperation and coordination. GEB 60(2):287–306

Chen Y (2008) Incentive-compatible mechanisms for pure public goods: a survey of experimental literature. In: Plott CR, Smith VL (eds) The handbook of experimental economics results. Elsevier, Amsterdam, pp 625–643CrossRef

Cooper R, DeJong DV, Forsythe R, Ross TW (1996) Cooperation without reputation: experimental evidence from prisoner’s dilemma games. GEB 12(2):187–218

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

Fehr E, Gächter S (2000) Cooperation and punishment in public goods experiments. Am Econ Rev 90(4):980–994CrossRef

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

Fischbacher U (2007) z-Tree: Zurich toolbox for ready-made economic experiments. Exp Econ 10(2):171–178CrossRef

Forsythe R, Rietz T, Myerson R, Weber R (1996) An experimental study of voting rules and polls in three-candidate elections. Intl J Game Theory 25(3):355–383CrossRef

Guala F (2012) Reciprocity: weak or strong? What punishment experiments do (and do not) demonstrate. Behav Brain Sci 35(01):1–15CrossRef

Hamaguchi Y, Mitani S, Saijo T (2003) Does the Varian mechanism work? Emissions trading as an example. Intl J Bus Econ 2(2):85–96

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

Kalai E (1981) Preplay negotiations and the prisoner’s dilemma. Math Soc Sci 1(4):375–379CrossRef

Kimbrough EO, Sheremeta RM (2013) Side-payments and the costs of conflict. Intl J Ind Organ 31:278–286CrossRef

Masuda T, Okano Y, Saijo T (2014) The minimum approval mechanism implements the efficient public good allocation theoretically and experimentally. Games Econ Behav 83:73–85CrossRef

Midler E, Figuières C, Willinger M (2015) Choice overload, coordination and inequality: three hurdles to the effectiveness of the compensation mechanism? Soc Choice Welf 45(3):513–535CrossRef

Plott CR, Smith VL (2008) Handbooks in economics 28: handbook of experimental economics results. Elsevier, Amsterdam

Qin CZ (2005) Penalties and rewards as inducements to cooperate. Department of Economics, University of California-Santa Barbara

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

Saijo T, Shen J (2018) Mate choice mechanism for solving a quasi-dilemma. J Behav Exp Econ 72:1–8CrossRef

Selten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. Intl J Game Theory 4(1):25–55CrossRef

Selten R (1991) Properties of a measure of predictive success. Math Soc Sci 21(2):153–167CrossRef

Varian HR (1994) A solution to the problem of externalities when agents are well-informed. Am Econ Rev 84(5):1278–1293

Titel: Approval mechanism to solve prisoner’s dilemma: comparison with Varian’s compensation mechanism
verfasst von: Tatsuyoshi Saijo
Takehito Masuda
Takafumi Yamakawa
Publikationsdatum: 22.01.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 1/2018
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-017-1107-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 1/2018

Cosine similarity and the Borda rule

Almost Lorenz dominance

Deciding about human lives: an experimental measure of risk attitudes under prospect theory

Random path to stability in a decentralized market with contracts

Talents, preferences and income inequality

Fair division with uncertain needs