Divide-the-Dollar Game Revisited
In the Divide-the-Dollar (DD) game, two players simultaneously make demands to divide a dollar. Each player receives his demand if the sum of the demands does not exceed one, a payoff of zero otherwise. Note that, in the latter case, both parties are punished severely. A major setback of DD is that each division of the dollar is a Nash equilibrium outcome. Observe that, when the sum of the two demands x and y exceeds one, it is as if Player 1's demand x (or his offer (1âˆ’x) to Player 2) suggests that Player 2 agrees to Î» x > 1 times his demand y so that Player 1's demand and Player 2's modified demand add up to exactly one; similarly, Player 2's demand y (or his offer (1âˆ’y) to Player 1) suggests that Player 1 agrees to Î» yx so that Î» yx+y=1. Considering this fact, we change DD's payoff assignment rule when the sum of the demands exceeds one; here in this case, each player's payoff becomes his demand times his Î»; i.e., each player has to make the sacrifice that he asks his opponent to make. We show that this modified version of DD has an iterated strict dominant strategy equilibrium in which each player makes the egalitarian demand 1/2. We also provide a natural N-person generalization of this procedure. Copyright Kluwer Academic Publishers 2001
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:50:y:2001:i:4:p:295-303. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Christopher F. Baum)
If references are entirely missing, you can add them using this form.