EconPapers    
Economics at your fingertips  
 

Reasonable Nash demand games

Shiran Rachmilevitch ()
Additional contact information
Shiran Rachmilevitch: University of Haifa

Theory and Decision, 2022, vol. 93, issue 2, No 5, 319-330

Abstract: Abstract In the Nash demand game (NDG) n players announce utility demands, the demands are implemented if they are jointly feasible, and otherwise no one gets anything. If the utilities set is the simplex, the game is called “divide-the-dollar”. Brams and Taylor (Theory Decis 37:211–231, 1994) studied variants of divide-the-dollar, on which they imposed reasonableness conditions. I explore the implications of these conditions on general NDGs. In any reasonable NDG, the egalitarian demand profile cannot be obtained via iterated elimination of weakly dominated strategies. Further, a reasonable NDG may fail to have a Nash equilibrium, even in mixed strategies. In the 2-person case, existence of pure strategy equilibrium is equivalent to the existence of a value, in the sense that each player can secure the egalitarian payoff level independent of his opponent’s play. This result does not extend to reasonable NDGs with more than two players. Interestingly, there are results for reasonable NDGs that hold for two and three players, but not for $$n\ge 4$$ n ≥ 4 players.

Keywords: Nash demand game; Divide-the-dollar; Fair division (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s11238-021-09849-6 Abstract (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:theord:v:93:y:2022:i:2:d:10.1007_s11238-021-09849-6

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/11238/PS2

DOI: 10.1007/s11238-021-09849-6

Access Statistics for this article

Theory and Decision is currently edited by Mohammed Abdellaoui

More articles in Theory and Decision from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2022-10-29
Handle: RePEc:kap:theord:v:93:y:2022:i:2:d:10.1007_s11238-021-09849-6