Browsing by Subject "Equal division"

Now showing 1 - 5 of 5

Open Access
Implementing equal division with an ultimatum threat
(Springer, 2014) Cetemen, E. D.; Karagözoğlu, E.
We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players' demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which involves a harsh punishment. In the modified game , if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage.
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.
Open Access
Moral preferences in bargaining
(Springer, 2024-01-06) Juan-Bartroli, Pau; Karagözoğlu, Emin
We analyze the equilibrium of a bilateral bargaining game (Nash, 1953, Econometrica, 21: 128–140). where at least one of the individuals has a preference for morality (homo moralis). We show that the equilibrium set crucially depends on these moral preferences. Furthermore, our comparative static analyses provide insights into the distributional implications of individuals’ moral concerns and the composition of society. A comparison of the set of equilibria in our model with those under selfish preferences, Kantian equilibrium, fairness preferences, altruistic preferences, and inequality averse preferences reveals important differences.
Open Access
Nash equilibria in claim based estate division problems
(2014) İnel, Abdulkadir
Estate division game is an allocation of an estate between players based on a rule. In this thesis, we consider estate division games and study the necessary and sufficient conditions for division rules under which Nash equilibria induce equal division. Ashlagi, Karag¨ozoˇglu, Klaus (2012) introduce classes of properties for division rules and show that they are sufficient for all Nash equilibria to induce equal division. In this study, we propose a different property, namely conditional full compensation, and prove that it is also a sufficient condition for division rules in order for all Nash equilibria outcomes under these rules to be equal division. We, then, show that under any rule satisfying claims boundedness and conditional equal division lower bound, equal division is a Nash equilibrium outcome. Finally, we prove that letting at least one player get more than the difference between the whole estate and the sum of other players’ claims is a necessary condition for all Nash equilibria to induce equal division.