Skip to main content
Erschienen in: Group Decision and Negotiation 3/2014

01.05.2014

Mixed Equilibrium, Collaborative Dominance and Burning Money: An Experimental Study

verfasst von: Filipe Costa de Souza, Leandro Chaves Rêgo

Erschienen in: Group Decision and Negotiation | Ausgabe 3/2014

Einloggen

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

search-config
loading …

Abstract

We experimentally study three aspects of \(2\times 2\) one-shot games with collaboratively dominant strategies: if subjects play according to the mixed Nash equilibrium; if the collaborative equilibrium has a focal point property; and if the burning money mechanism stimulates a collaborative behavior. First, our results show that players do not seem to play according to the mixed Nash equilibrium and that the collaborative equilibrium does not seem to have focal point properties. In fact, the subjects seem to prefer less risky strategies when compared to efficient ones. Our results also show that a burning money mechanism only helps players to collaborate when it transforms a collaborative profile of strategies into a collaborative equilibrium. This fact is justified because other burning money mechanisms will only help collaboration if the subjects were playing according to de mixed Nash equilibrium. Furthermore, even when burning money mechanisms improved the collaboration rate, such rate’s increase was smaller than the expected by the mixed Nash equilibrium.

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!

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!

Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
For a strong version of the collaborative dominance definition made above, we should simply use a strict inequality signal (\(<\)).
 
2
For the authors, a secure equilibrium is an equilibrium composed by maximin strategies.
 
3
For a brief review about some models of social preferences see Vetshera and Kainz (2012).
 
4
First, Player 1 had to choose between two payoff matrix, one in winch the payoffs were identical to the original Battle of the Sexes (i.e. without burning money) and another in which all payoffs of the Player 1 were reduced (i.e. a game with burning money). Furthermore, Player 2 observed the initial choice made by Player 1 and, thereafter, both choose their strategies simultaneously.
 
5
In a test version of the experiment, the subjects were asked to choose a value from 0 to 100 that represents his (or her) chance of playing a given strategy, as done in Neugebauer et al. (2008). However, the subjects had difficulties in answering this type of question. Thus, we decided to change our approach.
 
6
Traditionally in economic experiments, players repeatedly play a given game against other players and, consequently, have the opportunity to learn from past moves. However, we consider this approach inappropriate for our purposes since we are analyzing games without repeated interactions and played for the first time (i.e., one-shot games).
 
7
Originally, the instructions were written in Portuguese.
 
8
It is important to emphasize that this was the unique case tested in our experiment where we got different results between the types of Players 1 and 2 (since Players 2 showed biased beliefs and Players 1 didn’t). Thus, we think that it is precipitated to propose explanations to justify this mismatch. Maybe, this result can be clarified in future replications of this experiment. But until then, we prefer to look at this mismatch with some reservation.
 
Literatur
Zurück zum Zitat Aumann RJ (1990) Nash Equilibria are not self-enforcing. In: Gabszewicz JJ, Richard JF, Wolsey L (eds) Economic decision making, econometrics, and optimisation: essays in honor of Jacques Dreze. Elsevier Science Publishers, Amsterdam, pp 201–206 Aumann RJ (1990) Nash Equilibria are not self-enforcing. In: Gabszewicz JJ, Richard JF, Wolsey L (eds) Economic decision making, econometrics, and optimisation: essays in honor of Jacques Dreze. Elsevier Science Publishers, Amsterdam, pp 201–206
Zurück zum Zitat Anctil RM et al (2010) Does information transparency decrease coordination failure? Games Econ Behav 70:228–241CrossRef Anctil RM et al (2010) Does information transparency decrease coordination failure? Games Econ Behav 70:228–241CrossRef
Zurück zum Zitat Ben-Porath E, Dekel E (1992) Signaling future actions and the potential for sacrifice. J Econ Theory 57:36–51CrossRef Ben-Porath E, Dekel E (1992) Signaling future actions and the potential for sacrifice. J Econ Theory 57:36–51CrossRef
Zurück zum Zitat Berger U (2011) Learning to cooperate via indirect reciprocity. Games Econ Behav 72:30–37CrossRef Berger U (2011) Learning to cooperate via indirect reciprocity. Games Econ Behav 72:30–37CrossRef
Zurück zum Zitat Bergin J, Bernahardt D (2009) Cooperation through imitation. Games Econ Behav 67:376–388CrossRef Bergin J, Bernahardt D (2009) Cooperation through imitation. Games Econ Behav 67:376–388CrossRef
Zurück zum Zitat Brandts J, Holt A (1995) Limitations of dominance and forward induction: experimental evidence. Econ Lett 49:391–395CrossRef Brandts J, Holt A (1995) Limitations of dominance and forward induction: experimental evidence. Econ Lett 49:391–395CrossRef
Zurück zum Zitat Charness G, Rustichini A (2011) Gender differences in cooperation with group membership. Games Econ Behav 72:77–85CrossRef Charness G, Rustichini A (2011) Gender differences in cooperation with group membership. Games Econ Behav 72:77–85CrossRef
Zurück zum Zitat Chiappori P-A, Levitt S, Groseclose T (2002) Testing mixed-strategy equilibria when players are heterogeneous: the case of penalty kicks in soccer. Am Econ Rev 92:1138–1151CrossRef Chiappori P-A, Levitt S, Groseclose T (2002) Testing mixed-strategy equilibria when players are heterogeneous: the case of penalty kicks in soccer. Am Econ Rev 92:1138–1151CrossRef
Zurück zum Zitat Chuah S et al (2007) Do cultures clash? Evidence from cross-national ultimatum game experiments. J Econ Behav Organ 64:35–48CrossRef Chuah S et al (2007) Do cultures clash? Evidence from cross-national ultimatum game experiments. J Econ Behav Organ 64:35–48CrossRef
Zurück zum Zitat Clark K, Kay S, Sefton M (2001) When are Nash equilibria self-enforcing? An experimental analysis. Int J Game Theory 29:495–515CrossRef Clark K, Kay S, Sefton M (2001) When are Nash equilibria self-enforcing? An experimental analysis. Int J Game Theory 29:495–515CrossRef
Zurück zum Zitat Engelmann D, Fischbacher U (2009) Indirect reciprocity and strategic reputation building in an experimental helping game. Games Econ Behav 67:399–407CrossRef Engelmann D, Fischbacher U (2009) Indirect reciprocity and strategic reputation building in an experimental helping game. Games Econ Behav 67:399–407CrossRef
Zurück zum Zitat Erev I, Bereby-Meyer Y, Roth AE (1999) The effect of adding a constant to all payoffs: experimental investigation, and implications for reinforcement learning models. J Econ Behav Organ 39:111–128CrossRef Erev I, Bereby-Meyer Y, Roth AE (1999) The effect of adding a constant to all payoffs: experimental investigation, and implications for reinforcement learning models. J Econ Behav Organ 39:111–128CrossRef
Zurück zum Zitat Falk A, Fischbacher U (2006) A theory of reciprocity. Games Econ Behav 54:293–315CrossRef Falk A, Fischbacher U (2006) A theory of reciprocity. Games Econ Behav 54:293–315CrossRef
Zurück zum Zitat Fang C et al (2002) On adaptive emergence of trust behavior in the game of stag hunt. Group Decis Negot 11:449–467CrossRef Fang C et al (2002) On adaptive emergence of trust behavior in the game of stag hunt. Group Decis Negot 11:449–467CrossRef
Zurück zum Zitat Golman R, Page SE (2010) Individual and cultural learning in stag hunt games with multiple actions. J Econ Behav Organ 73:359–376CrossRef Golman R, Page SE (2010) Individual and cultural learning in stag hunt games with multiple actions. J Econ Behav Organ 73:359–376CrossRef
Zurück zum Zitat Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press, London Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press, London
Zurück zum Zitat Hofstede GJ, Jonker CM, Verwaart T (2012) Cultural differentiation of negotiation agents. Group Decis Negot 21:79–98CrossRef Hofstede GJ, Jonker CM, Verwaart T (2012) Cultural differentiation of negotiation agents. Group Decis Negot 21:79–98CrossRef
Zurück zum Zitat Huck S, Müller W (2005) Burning money and (pseudo) first-mover advantages: an experimental study on forward induction. Games Econ Behav 51:109–127CrossRef Huck S, Müller W (2005) Burning money and (pseudo) first-mover advantages: an experimental study on forward induction. Games Econ Behav 51:109–127CrossRef
Zurück zum Zitat Maskin E (2011) Commentary: Nash equilibrium and mechanism design. Games Econ Behav 71:9–11CrossRef Maskin E (2011) Commentary: Nash equilibrium and mechanism design. Games Econ Behav 71:9–11CrossRef
Zurück zum Zitat Neugebauer T, Poulsen A, Schram A (2008) Fairness and reciprocity in the hawk-dove game. J Econ Behav Organ 66:243–250CrossRef Neugebauer T, Poulsen A, Schram A (2008) Fairness and reciprocity in the hawk-dove game. J Econ Behav Organ 66:243–250CrossRef
Zurück zum Zitat Ochs J (1995) Games with unique mixed strategy equilibria: an experimental study. Games Econ Behav 10:200–217CrossRef Ochs J (1995) Games with unique mixed strategy equilibria: an experimental study. Games Econ Behav 10:200–217CrossRef
Zurück zum Zitat Rankin FW, Van Huyck JB, Battalio RC (2000) Strategic similarity and emergent conventions: evidence from similar stag hunt games. Games Econ Behav 32:315–337CrossRef Rankin FW, Van Huyck JB, Battalio RC (2000) Strategic similarity and emergent conventions: evidence from similar stag hunt games. Games Econ Behav 32:315–337CrossRef
Zurück zum Zitat Rey-Biel P (2009) Equilibrium play and best response to (stated) beliefs in normal form games. Games Econ Behav 65:572–585CrossRef Rey-Biel P (2009) Equilibrium play and best response to (stated) beliefs in normal form games. Games Econ Behav 65:572–585CrossRef
Zurück zum Zitat Rydval O, Ortmann A (2005) Loss avoidance as selection principle: evidence from simple stag-hunt games. Econ Lett 88:101–107CrossRef Rydval O, Ortmann A (2005) Loss avoidance as selection principle: evidence from simple stag-hunt games. Econ Lett 88:101–107CrossRef
Zurück zum Zitat Sáez-Martí M (1997) On the asymptotic convergence to mixed equilibrium in \(2\times 2\) asymmetric games. Int J Game Theory 26:549–559CrossRef Sáez-Martí M (1997) On the asymptotic convergence to mixed equilibrium in \(2\times 2\) asymmetric games. Int J Game Theory 26:549–559CrossRef
Zurück zum Zitat Sethi R, Somanathan E (2003) Understanding reciprocity. J Econ Behav Organ 50:1–27CrossRef Sethi R, Somanathan E (2003) Understanding reciprocity. J Econ Behav Organ 50:1–27CrossRef
Zurück zum Zitat Stanca L (2009) Measuring indirect reciprocity: whose back do we scratch? J Econ Psychol 30:190–202CrossRef Stanca L (2009) Measuring indirect reciprocity: whose back do we scratch? J Econ Psychol 30:190–202CrossRef
Zurück zum Zitat Van Damme E (1989) Stable equilibria and forward induction. J Econ Theory 48:476–496CrossRef Van Damme E (1989) Stable equilibria and forward induction. J Econ Theory 48:476–496CrossRef
Zurück zum Zitat Van Huyck JB, Battalio RC, Beil RO (1990) Tacit coordination games, strategic uncertainty, and coordination failure. Am Econ Rev 80:234–248 Van Huyck JB, Battalio RC, Beil RO (1990) Tacit coordination games, strategic uncertainty, and coordination failure. Am Econ Rev 80:234–248
Zurück zum Zitat Walker M, Wooders J (2001) Minimax play at Wimbledon. Am Econ Rev 91:1521–1538CrossRef Walker M, Wooders J (2001) Minimax play at Wimbledon. Am Econ Rev 91:1521–1538CrossRef
Metadaten
Titel
Mixed Equilibrium, Collaborative Dominance and Burning Money: An Experimental Study
verfasst von
Filipe Costa de Souza
Leandro Chaves Rêgo
Publikationsdatum
01.05.2014
Verlag
Springer Netherlands
Erschienen in
Group Decision and Negotiation / Ausgabe 3/2014
Print ISSN: 0926-2644
Elektronische ISSN: 1572-9907
DOI
https://doi.org/10.1007/s10726-013-9341-y

Weitere Artikel der Ausgabe 3/2014

Group Decision and Negotiation 3/2014 Zur Ausgabe

Premium Partner