Search

The preceding chapter dealt with differential games in which all players make their moves simultaneously. We now turn to a class of differential games in which some players have priority of moves over other players. To simplify matters, we focus mostly on the case where there are only two players. The player who has the right to move first is called the leader and the other player is called the follower. A well-known example of this type of hierarchical-moves games is the Stackelberg model of duopoly, which is often contrasted with the Cournot model of duopoly. The plan of this chapter is as follows. In section 5.1 we review the one-shot Cournot duopoly game and the corresponding one-shot Stackelberg game. We also present a modified version of the one-shot Stackelberg game as a quick means of raising the issue of time inconsistency (sometimes referred to as dynamic inconsistency) in Stackelberg games, which we further expound in the rest of the chapter. In sections 5.2 and 5.3 we define the concepts of open-loop Stackelberg equilibrium and (nondegenerate) Markovian Stackelberg equilibrium for differential games. We show in section 5.2 that open-loop Stackelberg equilibria are, in general, not time consistent. There are, of course, exceptions to this rule which we also consider. In section 5.3 we turn to the analysis of nondegenerate Markovian Stackelberg equilibria. In general, it is difficult to find such equilibria. However, we are able to provide some rules of thumb which work in a number of situations.

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.