We consider a class of differential games with transition equations that are homogeneous of degree one. For any game G with a discount rate r, consider a Markov perfect equilibrium (MPE) with strategies that are linear in the state variables. We show that the time paths of the control variables...

In this paper, we complement the work of Kemp and Shimomura (2002) by considering the case of many donors playing a dynamic non-cooperative game of foreign aid. We consider two models. Model 1 deals with the case where donor countries continually feel the warm glow of from the act of giving....

We consider the class of differential games with transition dynamics and constraints that are homogeneous of degree one. We show that if the integrand of the objective function is homogeneous of degree , then best replies to linear homogeneous Markov strategies are linear homogeneous, and the...

We analyze duopolistic competition between horizontally differentiated firms selling durable goods or services subject to congestion. At each point of time, new customers buy one unit of the commodity from one of the firms, by comparing present prices and future congestion rates. We study the...

Competition between political parties is a process that unfolds over time whereas formal theories of party competition have tended to take an essentially static, or one-shot, approach. This leaves some gaps in our understanding of the dynamics of campaigning. The aim of this paper is to make up...

This paper deals with the issue of shelf-space allocation and advertising decisions in marketing channels. We consider a network composed of a unique retailer offering the products of two competing manufacturers. The retailer controls the amount of shelf-space to allocate to both brands, while...

We investigate an impulse control differential game arising in a problem of option pricing in mathematical finance. In a previous paper, it was shown that its Value function in ℝ3 could be described as a pair of functions affine in one of the variables, joined on a 2D manifold. Depending on...

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an...

The literature on advertising and promotions can be divided in two categories. A first group of models assume that promotion contributes (positively) to the goodwill towards the product, and a second group assumes that promotions reduce that goodwill. In this paper we build a differential game...

Examples with zero-sum linear differential games of fixed terminal time and a convex terminal payoff function depending on two components of the phase vector are considered. Such games can have an indifferent zone with constant value function. The level set of the value function associated with...