Browsing by Subject "Divide-the-dollar game"

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Open Access
(In)efficiency and equitability of equilibrium outcomes in a family of bargaining games
(Springer, 2022-11-21) Karagözoğlu, Emin; Keskin, K.; Sağlam, Çağrı
We construct a parametric family of (modified) divide-the-dollar games: when there is excess demand, some portion of the dollar may disappear and the remaining portion is distributed in a bankruptcy problem. In two extremes, this game family captures the standard divide-the-dollar game of Nash (Econometrica 21:128–140, 1953) (when the whole dollar vanishes) and the game studied in Ashlagi et al. (Math Soc Sci 63:228–233, 2012) (when the whole dollar remains) as special cases. We first show that in all interior members of our game family, all Nash equilibria are inefficient under the proportional rule if there are ‘too many’ players in the game. Moreover, in any interior member of the game family, the inefficiency increases as the number of players increases, and the whole surplus vanishes as the number of players goes to infinity. On the other hand, we show that any bankruptcy rule that satisfies certain normatively appealing axioms induces a unique and efficient Nash equilibrium in which everyone demands and receives an equal share of the dollar. The constrained equal awards rule is one such rule.
Open Access
Kantian equilibria of a class of nash bargaining games
(2021-08) Dizarlar, Atakan
This thesis studies Kantian equilibria (Roemer, 2010) of an n-player bargaining game, which is a modified version of the well-known divide-the-dollar game. It starts with introducing the fundamental concepts of Kantian morality and how Kantian moral theory is captured in economic theory. Then, we first show that the Kantian equilibrium exists under fairly minimal assumptions. Second, if the bankruptcy rule used satisfies equal treatment of equals, and is almost nowhere proportional, then only equal division can prevail in any Kantian equilibrium. On the other hand, we show that an ‘anything goes’ type result emerges only under the proportional rule. Furthermore, using hybrid bankruptcy rules that we construct in a novel fashion, we can characterize the whole equilibrium set. Lastly, we analyse what happens to the equilibrium behavior and the axiomatic properties of the bankruptcy rules under the additive definition of Kantian equilibrium. Our results highlight the interactions between institutions (axiomatic properties of division rules) and agents’ equilibrium behavior.