In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believe the portions are equally split. Moreover, the division takes at most n cuts, which is best possible. This extends...

We examine policies directed at regulating tobacco consumption through three types of instruments: (i) an excise tax hindering consumption by increasing the price of cigarettes, (ii) prevention programs helping consumers to make choices that are more time consistent when trading-off the current...

Around 1947, von Neumann showed that for any finite two-person zero-sum game, there is a feasible linear programming (LP) problem consisting of a primal-dual pair of linear programs whose saddle points yield equilibria of the game, thus providing an immediate proof of the minimax theorem from...

In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In...

In this note we show without using any fixed-point theorem argument, that a pair of vectors is an equilibrium point of a bimatrix game if it solves a certain bilinear programming problem. Since the bilinear programming problem we consider has an optimal solution, we are able to prove the...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a...

The main objects here are Nash equilibria in spatial Cournot oligopolies when profits depend on coordinated distribution. Production is non-cooperative, but the subsequent transportation must be performed jointly to minimize costs. Cournot-Nash equilibria for this two-stage game with partial...