On properties of division rules lifted by bilateral consistency

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is "lifted" if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic.claims problems, consistency, lifting, constrained equal awards rule, constrained equal losses rule

Consistency, converse consistency, and aspirations in TU-games

In problems of choosing ‘aspirations’ for TU-games, we study two axioms, ‘MW-consistency’ and ‘converse MW-consistency.’ In particular, we study which subsolutions of the aspiration correspondence satisfy MW-consistency and/or converse MW-consistency. We also provide axiomatic characterizations of the aspiration kernel and the aspiration nucleolus

Pairwise stable and stochastically stable networks in the four-person co-author model

The co-author model is introduced by Jackson and Wolinsky (1996, Journal of Economic Theory) as a typical example of the models of network formation. In this note, we study which network is pairwise stable and/or stochastically stable when the number of players is four.

Subgame-perfect free trade networks in a four-country model

Goyal and Joshi (2006, Int Econ Review) apply the notion of ``pairwise stable networks" introduced by Jackson and Wolinsky (1996, J Econ Theory) to a model of free trade network formation, and show that (i) every pairwise stable network is either complete or almost complete (with all countries except one forming direct links), and (ii) the complete network maximizes global welfare. In this note, we use essentially the same model as their model with four countries, and investigate which network is more likely to be realized than others by considering a dynamic process introduced by Jackson and Watts (2002, J Econ Theory).free trade network, network formation, subgame-perfect equilibrium

Simulating a Simple Real Business Cycle Model Using Excel

Simulating the real business cycle models is a popular topic in first-year graduate courses on macroeconomics. Usually, Maple and Matlab are used for this purpose, mainly because they can be used both for solving and for simulating the models. Strulik (2004) demonstrates that Excel can be used both for solving and for simulating a standard RBC model. In this paper, we propose a more elementary approach that might be suitable for undergraduate courses. We illustrate (i) how to solve a simple RBC model by hand and (ii) how to use Excel to simulate the solution.

On the Coincidence of the Shapley Value and the Nucleolus in Queueing Problems

Given a group of agents to be served in a facility, the queueing problem is concerned with finding the order to serve agents and the (positive or negative) monetary compensations they should receive. As shown in Maniquet (2003), the minimal transfer rule coincides with the Shapley value of the game obtained by defining the worth of each coalition to be the minimum total waiting cost incurred by its members under the assumption that they are served before the non-coalitional members. Here, we show that it coincides with the nucleolus of the same game. Thereby, we establish the coincidence of the Shapley value and the nucleolus for queueing problems. We also investigate the relations between the minimal transfer rule and other rules discussed in the literature

Monotone-path Dutta-Ray solutions on convex games

It is well known that on the domain of convex games, the Dutta-Ray solution satisfies many desirable properties such as population-monotonicity, max consistency, converse max consistency, and conditional self-consistency. In this paper, we define a family of possibly non-symmetric and non-homogeneous generalizations of the Dutta-Ray solution, which we refer to as "monotone-path Dutta-Ray solutions." We show that above four properties are preserved by our generalizations.

note: The nucleolus is not aggregate-monotonic on the domain of convex games

We show that the nucleolus is not aggregate-monotonic on the domain of convex games, and that this lack of monotonicity holds even if there are as few as four agents.Nucleolus, convex games, aggregate-monotonicity

Consistency, Converse Consistency, And Aspirations In Coalitional Games

In the problems of choosing "aspirations" for coalitional games, we study two axioms, "MW-consistency" and "converse MW-consistency", introduced by Moldovanu and Winter (1994). We mainly consider two domains: thedomain of all NTU games and the domain of all TU games. In particular, we study which subsolutions of the aspiration correspondence satisfy MW-consistency and/or converse MW-consistency. We also provide axiomatic characterizations of the aspiration kernel and the aspiration nucleolus on the domain of all TU games