Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Theory and Decision
Published in: Theory and Decision 3/2017

20-08-2016

Punishing greediness in divide-the-dollar games

Author: Shiran Rachmilevitch

Published in: Theory and Decision | Issue 3/2017

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Brams and Taylor 1994 presented a version of the divide-the-dollar game (DD), which they call DD1. DD1 suffers from the following drawback: when each player demands approximately the entire dollar, then if the least greedy player is unique, then this player obtains approximately the entire dollar even if he is only slightly less greedy than the other players. I introduce a parametrized family of 2-person DD games, whose “endpoints” (the games that correspond to the extreme points of the parameter space) are (1) a variant of DD1, and (2) a game that completely overcomes the greediness-related problem. I also study an n-person generalization of this family. Finally, I show that the modeling choice between discrete and continuous bids may have far-reaching implications in DD games.
previous article Hard evidence and ambiguity aversion
next article The valuation “by-tranche” of composite investment instruments

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now
Footnotes
1
The 2-person version of this game is a simple version of a slightly more general 2-person game, called the Nash demand game (Nash 1953). DD also has “dual” mechanisms, where each player reports how much he thinks others should obtain; such mechanisms have been studied by De Clippel et al. (2008) for \(n\ge 3\) players. A multi-stage DD game has been studied by Cetemen and Karagözoğlu (2014).
 
2
DD1 has multiple Nash equilibria, but they are all payoff-equivalent. In any equilibrium, each player obtains the egalitarian utility level.
 
3
Abusing terminology a little, I call any divide-the-dollar game a DD game. A general DD game is a game which is identical to the canonical DD that was described in the first paragraph of this Introduction, with the sole exception that when the sum of demands exceeds one, the dollar need not be wasted—it (or a fraction of it) can be distributed in some way among the players.
 
4
See Theorem 1 in BT.
 
5
For cDD1, we have \(u_2(1-\epsilon ,1-2\epsilon )-u_1(1-\epsilon ,1-2\epsilon )=1-2\epsilon -2\epsilon \). Therefore, \(\gamma =1\) for this game.
 
6
In the 2-person case, (ii) is equivalent to punishing the most greedy player.
 
7
This inequality is equivalent to \(2+2(1-\lambda )y>1+y\) or \(1+y[2(1-\lambda )-1]>0\). The latter inequality is true, because its LHS, which is strictly decreasing in \(\lambda \), is strictly greater than \(1-y\ge 0\).
 
8
\(x_n\ge \frac{1+\theta _n}{2}\) and \(\frac{1+\theta _n}{2}\ge \theta _n\).
 
Literature
Anbarci, N. (2001). Divide-the-dollar game revisited. Theory and Decision, 50, 295–303.CrossRef
Brams, S. J., & Taylor, A. D. (1994). Divide the dollar: three solutions and extensions. Theory and Decision, 37, 211–231.CrossRef
Cetemen, E. D., & Karagözoğlu, E. (2014). Implementing equal division with an ultimatum threat. Theory and Decision, 77, 223–236.CrossRef
De Clippel, G., Moulin, H., & Tideman, N. (2008). Impartial division of a dollar. Journal of Economic Theory, 139, 176–191.CrossRef
Nash, J. (1953). Two-person cooperative games. Econometrica, 21, 128–140.CrossRef
Metadata
Title
Punishing greediness in divide-the-dollar games
Author
Shiran Rachmilevitch
Publication date
20-08-2016
Publisher
Springer US
Published in
Theory and Decision / Issue 3/2017
Print ISSN: 0040-5833
Electronic ISSN: 1573-7187
DOI
https://doi.org/10.1007/s11238-016-9568-6

Other articles of this Issue 3/2017

Theory and Decision 3/2017 Go to the issue

OriginalPaper

Hard evidence and ambiguity aversion

OriginalPaper

Catastrophic risk: social influences on insurance decisions

OriginalPaper

The valuation “by-tranche” of composite investment instruments

OriginalPaper

Piecewise linear rank-dependent utility

OriginalPaper

Overlapping coalitions, bargaining and networks

OriginalPaper

Is diversity in capabilities desirable when adding decision makers?

Premium Partner

    Image Credits