The ultimatum game is important from a sociological perspective, because it illustrates the human unwillingness to accept injustice. The tendency to refuse small offers may also be seen as relevant to the concept of honour.
The extent to which people are willing to tolerate different distributions of the reward from "cooperative" ventures results in inequality that is, measurably, exponential across the strata of management within large corporations. See also: Inequity aversion within companies.
Some see the implications of the ultimatum game as profoundly relevant to the relationship between society and the free market, with Prof. P.J. Hill, (Wheaton College (Illinois)) saying:
I see the [ultimatum] game as simply providing counter evidence to the general presumption that participation in a market economy (capitalism) makes a person more selfish.[18]
History
The first ultimatum game was developed in 1982 as a stylized representation of negotiation, by Güth, Schmittberger, and Schwarze.[19] It has since become a popular economic experiment, and was said to be "quickly catching up with the Prisoner's Dilemma as a prime showpiece of apparently irrational behavior" in a paper by Martin Nowak, Karen
M. Page, and Karl Sigmund.[20]
Variants
In the "competitive ultimatum game" there are many proposers and the responder can accept at most one of their
offers: With more than three (naïve) proposers the responder is usually offered almost the entire endowment[21]
(which would be the Nash Equilibrium assuming no collusion among proposers).
In the "ultimatum game with tipping", a tip is allowed from responder back to proposer, a feature of the trust game, and net splits tend to be more equitable.[22]
The "reverse ultimatum game" gives more power to the responder by giving the proposer the right to offer as many divisions of the endowment as they like. Now the game only ends when the responder accepts an offer or abandons the game, and therefore the proposer tends to receive slightly less than half of the initial endowment.[23]
Robert Aumann's Blackmailer Paradox appears to be a repeated game in which the ultimatum game is played many times by the same players for high stakes.
The pirate game illustrates a variant with more than two participants with voting power, as illustrated in Ian Stewart's "A Puzzle for Pirates".[24]
Notes
[1] Technically, making a zero offer to the responder, and accepting this offer is also a Nash Equilibrium, as the responder's threat to reject the offer is no longer credible since they now gain nothing (materially) by refusing the zero amount offered. Normally, when a player is indifferent between various strategies the principle in Game Theory is that the strategy with an outcome which is Pareto optimally better for the other players is chosen (as a sort of tie-breaker to create a unique NE). However, it is generally assumed that this principle should not apply to an ultimatum game player offered nothing; she is instead assumed to reject the offer although accepting it would be an equally subgame perfect NE. For instance, the University of Wisconsin summary: Testing Subgame Perfection Apart From Fairness in Ultimatum Games (http://econ.ucsd.edu/~jandreon/Publications/ExEc 2006.pdf) from 2002 admits the possibility that the proposer may offer nothing but qualifies the subgame perfect NE with the words (almost nothing) throughout the Introduction.
[2] See Joseph Henrich et al. (2004) and Oosterbeek et al. (2004). [3] http://www.pnas.org/content/105/10/3721.full.pdf+html [4] See Bolton (1991), and Ochs and Roth, A. E. (1989).
[5] Mongolian/Kazakh study conclusion (http://www.psych.upenn.edu/~fjgil/Ultimatum.pdf) from University of Pennsylvania. [6] Social Role in the Ultimate Game (http://radoff.com/blog/2010/05/18/social-role-ultimatum-game/)
[7] A forthcoming paper "On the Behavior of Proposers in Ultimatum Games" Journal of economic behaviour and organization (http://www. elsevier.com/wps/find/journaldescription.cws_home/505559/description) has the thesis that learning will not cause NE-convergence: see the abstract (http://www.qmw.ac.uk/~ugte173/abs/abs.jebo2.html).
[8] See "Do higher stakes lead to more equilibrium play?" (page 18) in 3. Bargaining experiments (http://www.iza.org/teaching/ falk_WS2003/falk_l3_bargaining.pdf), Professor Armin Falk's summary at the Institute for the Study of Labor (http://www.iza.org/ index_html?mainframe=http://www.iza.org/teaching/falk_WS2003).
[9] Zak PJ, Stanton AA, Ahmadi S (2007), Oxytocin Increases Generosity in Humans. PloSONE 2(11):e1128. (http://www.plosone.org/ article/info:doi/10.1371/journal.pone.0001128;jsessionid=C12706C1A789233D0F59DDFE31C5FD25)
[10] Sanfey, et al. (2002)
[11] Kirk et al. (2011). "Interoception Drives Increased Rational Decision-Making in Meditators Playing the Ultimatum Game". Frontiers in
Neuroscience 5:49. PMC 3082218. PMID 21559066.
[12] Crockett, Molly J.; Luke Clark, Golnaz Tabibnia, Matthew D. Lieberman, Trevor W. Robbins (2008-06-05). "Serotonin Modulates Behavioral Reactions to Unfairness" (http://www.scn.ucla.edu/pdf/Crockett (2008).pdf) (– Scholar search (http://scholar.google.co.uk/ scholar?hl=en&lr=&q=author:Crockett+intitle:Serotonin+Modulates+Behavioral+Reactions+to+Unfairness&as_publication=Science& as_ylo=2008&as_yhi=2008&btnG=Search)). Science 320 (5884): 1155577. doi:10.1126/science.1155577. PMC 2504725. PMID 18535210. . Retrieved 2008-06-22.
[13] Neural Substrates of Decision-Making in Economic Games Scientific Journals International (http://www.scientificjournals.org/ journals2007/articles/1176.pdf)
[14] Oxytocin Increases Generosity in Humans PloSONE 2(11):e1128 (http://www.scientificjournals.org/journals2007/j_of_dissertation. htm)
[15] Koenigs, Michael; Daniel Tranel (January 2007). "Irrational Economic Decision-Making after Ventromedial Prefrontal Damage: Evidence from the Ultimatum Game". Journal of Neuroscience 27 (4): 951–956. doi:10.1523/JNEUROSCI.4606-06.2007. PMC 2490711.
PMID 17251437.
[16] Moretti, Laura; Davide Dragone, Giuseppe di Pellegrino (2009). "Reward and Social Valuation Deficits following Ventromedial Prefrontal Damage". Journal of Cognitive Neuroscience 21 (1): 128–140. doi:10.1162/jocn.2009.21011. PMID 18476758.
[17] See, for example, Gale et al. (1995), Güth and Yaari (1992), Huck and Oechssler (1999), Nowak & Sigmund (2000) and Skyrms (1996) [18] See The Ultimatum game detailed description (http://www.fte.org/capitalism/activities/ultimatum/) as a class room plan from
EconomicsTeaching.org. (This is a more thorough explanation of the practicalities of the game than is possible here.)
[19] Güth et al. (1982), page 367: the description of the game at Neuroeconomics (http://neuroeconomics.typepad.com/neuroeconomics/ 2003/09/what_is_the_ult.html) cites this as the earliest example.
[20] Nowak, M. A.; Page, K. M.; Sigmund, K. (2000). "Fairness Versus Reason in the Ultimatum Game". Science 289 (5485): 1773–1775. doi:10.1126/science.289.5485.1773. PMID 10976075.
[21] Ultimatum game with proposer competition (http://homepage.univie.ac.at/christoph.hauert/gamelab/ultiproposer.html) by the GameLab (http://homepage.univie.ac.at/christoph.hauert/gamelab/).
[22] Ruffle (1998), p. 247.
[23] The reverse ultimatum game and the effect of deadlines is from Gneezy, Haruvy, & Roth, A. E. (2003).
[24] Stewart, Ian (May 1999). "A Puzzle for Pirates" (http://euclid.trentu.ca/math/bz/pirates_gold.pdf). Scientific American 05: 98–99. . Retrieved 3/11/2011.
Ultimatum game 158
References
• Alvard, M. (2004). "The Ultimatum Game, Fairness, and Cooperation among Big Game Hunters" (http:// anthropology.tamu.edu/faculty/alvard/downloads/ultimatum.pdf). In Henrich, J., Boyd, R., Bowles, S., Gintis, H., Fehr, E., and Camerer, C.. Foundations of Human Sociality: Ethnography and Experiments in 15
small-scale societies. Oxford University Press. pp. 413–435.
• Bearden, J. Neil (2001). "Ultimatum Bargaining Experiments: The State of the Art" (http://papers.ssrn.com/ sol3/papers.cfm?abstract_id=626183).
• Bicchieri, Cristina and Jiji Zhang (2008). "An Embarrassment of Riches: Modeling Social Preferences in Ultimatum games", in U. Maki (ed) Handbook of the Philosophy of Economics, Elsevier
• Bolton, G.E. (1991). "A comparative Model of Bargaining: Theory and Evidence". American Economic Review
81: 1096–1136.
• Gale, J., Binmore, K.G., and Samuelson, L. (1995). "Learning to be Imperfect: The Ultimatum Game". Games
and Economic Behavior 8: 56–90. doi:10.1016/S0899-8256(05)80017-X.
• Gneezy, Haruvy, and Roth, A. E. (2003). "Bargaining under a deadline: evidence from the reverse ultimatum game" (http://gsbwww.uchicago.edu/fac/uri.gneezy/vita/deadline.pdf) (PDF – Scholar search (http://scholar. google.co.uk/scholar?hl=en&lr=&q=intitle:Bargaining+under+a+deadline:+evidence+from+the+reverse+ ultimatum+game&as_publication=Games+and+Economic+Behavior&as_ylo=2003&as_yhi=2003& btnG=Search)). Games and Economic Behavior 45 (2): 347. doi:10.1016/S0899-8256(03)00151-9.
• Güth, W., Schmittberger, and Schwarze (1982). "An Experimental Analysis of Ultimatum Bargaining". Journal of
Economic Behavior and Organization 3 (4): 367–388. doi:10.1016/0167-2681(82)90011-7.
• Güth, W. and Yaari, M. (1992). "An Evolutionary Approach to Explain Reciprocal Behavior in a Simple Strategic Game". In U. Witt. Explaining Process and Change – Approaches to Evolutionary Economics. Ann Arbor. pp. 23–34.
• Henrich, Joseph, Robert Boyd, Samuel Bowles, Colin Camerer, Ernst Fehr, and Herbert Gintis (2004).
Foundations of Human Sociality: Economic Experiments and Ethnographic Evidence from Fifteen Small-Scale Societies. Oxford University Press.
• Huck, S. and Oechssler, J. (1999). "The Indirect Evolutionary Approach to Explaining Fair Allocations". Games
and Economic Behavior 28: 13–24. doi:10.1006/game.1998.0691.
• Ochs, J. and Roth, A. E. (1989). "An Experimental Study of Sequential Bargaining". American Economic Review
79: 355–384.
• Oosterbeek, Hessel, Randolph Sloof, and Gijs van de Kuilen (2004). "Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis". Experimental Economics 7 (2): 171–188.
doi:10.1023/B:EXEC.0000026978.14316.74.
• Ruffle, B.J. (1998). "More is Better, but Fair is Fair: Tipping in Dictator and Ultimatum Games". Games and
Economic Behavior 23 (2): 247. doi:10.1006/game.1997.0630..
• Sanfey et al.; Rilling, JK; Aronson, JA; Nystrom, LE; Cohen, JD (2002). "The neural basis of economic decision-making in the ultimatum game". Science 300 (5626): 1755–1758. doi:10.1126/science.1082976. PMID 12805551..
• Skyrms, B. (1996). Evolution of the Social Contract. Cambridge University Press.
• Zak, P.J., Stanton, A.A., Ahmadi, S. (2007). Brosnan, Sarah. ed. "Oxytocin Increases Generosity in Humans" (http://www.neuroeconomicstudies.org/pdf/ZakGenerosity.pdf) (PDF). Public Library of Science ONE 2 (11): e1128.. doi:10.1371/journal.pone.0001128. PMC 2040517. PMID 17987115.
• Angela A. Stanton (2007). "Neural Substrates of Decision-Making in Economic Games" (http://www. scientificjournals.org/journals2007/articles/1176.pdf) (PDF). Scientific Journals International 1 (1): 1–64..
Further reading
• Stanton, Angela (2006). Evolving Economics: Synthesis (http://mpra.ub.uni-muenchen.de/2369/).
External links
• Video lecture on the ultimatum game (http://www.youtube.com/watch?v=xpkxLKV_3d0)