, Volume 50, Issue 4, pp 295303
First online:
DividetheDollar Game Revisited
 Nejat AnbarciAffiliated withDepartment of Economics, Florida International University Email author
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In the DividetheDollar (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 (1−x) to Player 2) suggests that Player 2 agrees to λ_{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 (1−y) to Player 1) suggests that Player 1 agrees to λ_{y}x so that λ_{y}x+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 λ; 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 Nperson generalization of this procedure.
 Title
 DividetheDollar Game Revisited
 Journal

Theory and Decision
Volume 50, Issue 4 , pp 295303
 Cover Date
 200106
 DOI
 10.1023/A:1010363409312
 Print ISSN
 00405833
 Online ISSN
 15737187
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Divide the dollar
 Nash equilibrium
 The egalitarian outcome
 Iterated dominance equilibrium
 Industry Sectors
 Authors

 Nejat Anbarci ^{(1)}
 Author Affiliations

 1. Department of Economics, Florida International University, Miami, FL, 33199, USA