A new proportional procedure for the n−person cake−cutting problem

We present a new cake−cutting procedure which guarantees everybody a proportional share according to his own valuation

A way of explaining unemployment through a wage-setting game

We investigate a duopsonistic wage-setting game in which the rms have a limited number of workplaces. We assume that the rms have heterogeneous productivity, that there are two types of workers with dierent reservation wages and that a worker's productivity is independent of his type. We show that equilibrium unem- ployment arises in the wage-setting game under certain conditions, although the efficient allocation of workers would result in full employment

The political districting problem: A survey

Computer scientists and social scientists consider the political districting problem from different viewpoints. This paper gives an overview of both strands of the literature on districting in which the connections and the differences between the two approaches are highlighted

Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies

We determine the endogenous order of moves in which the firms set their prices in the framework of a capacity-constrained Bertrand-Edgeworth triopoly. A three-period timing game that determines the period in which the firms announce their prices precedes the price-setting stage. We show for the non-trivial case (in which the Bertrand-Edgeworth triopoly has only an equilibrium in non-degenerated mixed-strategies) that the firm with the largest capacity sets its price first, while the two other firms set their prices later. Our result extends a finding by Deneckere and Kovenock (1992) from duopolies to triopolies. This extension was made possible by Hirata's (2009) recent advancements on the mixed-strategy equilibria of Bertrand-Edgeworth games

Endogenous choice of decision variables

In this paper we allow the firms to choose their prices and quantities simultaneously. Quantities are produced in advance and their common sales price is determined by the market. Firms offer their “residual capacities” at their announced prices and the corresponding demand will be served to order. If all firms have small capacities, we obtain the Bertrand solution; while if at least one firm has a sufficiently large capacity, the Cournot outcome and a model of price leadership could emerge

Optimal partisan districting on planar geographies

We show that optimal partisan districting in the plane with geographical constraints is an NP-complete problem

Existence of Pure Strategy Nash Equilibrium in Bertrand-Edgeworth Oligopolies

This article is searching for necessary and sufficient conditions which are to be imposed on the demand curve to guarantee the existence of pure strategy Nash equilibrium in a Bertrand-Edgeworth game with capacity constraints

Quantity-setting games with a dominant firm

We consider a possible game-theoretic foundation of Forchheimer's model of dominant-firm price leadership based on quantity-setting games with one large firm and many small firms. If the large firm is the exogenously given first mover, we obtain Forchheimer's model. We also investigate whether the large firm can emerge as a first mover of a timing game

Which rationing rule does a single consumer follow?

We will investigate the amount of residual demand in a market consisting of only one consumer and two producers. Since there is only one consumer, we cannot really speak about a rationing rule, but we can ask ourselves whether a known rationing rule reflects the consumer’s utility maximizing behavior. We will show that, if the consumer has a Cobb-Douglas utility function, then the amount purchased by the consumer from the high-price firm lies between the values determined according to the efficient rationing rule and the random rationing rule. We will show further, that if the consumer has a quasilinear utility function, then in the economically interesting case his residual demand function will be equal to the residual demand function under efficient rationing

Quantity-setting games with a dominant firm

We consider a possible game-theoretic foundation of Forchheimer's model of dominant-firm price leadership based on quantity-setting games with one large firm and many small firms. If the large firm is the exogenously given first mover, we obtain Forchheimer's model. We also investigate whether the large firm can emerge as a first mover of a timing game