Markov Perfect Equilibria in Multi-Mode Differential Games with Endogenous Timing of Mode Transitions

We study Markov perfect equilibria (MPE) of two-player multi-mode differential games with controlled state dynamics, where one player controls the transition between modes. Different types of MPE are characterized distinguishing between delay equilibria, inducing for some initial conditions mode switches after a positive finite delay, and now or never equilibria, under which, depending on the initial condition, a mode switch occurs immediately or never. These results are applied to analyze the MPE of a game capturing the dynamic interaction between two incumbent firms among which one has to decide when to extend its product range by introducing a new product. The market appeal of the new product can be influenced over time by both firms through costly investments. Under a wide range of market introduction costs a now or never equilibrium coexists with a continuum of delay equilibria, each of them inducing a different time of product introduction.

Computer modeling of differential games

This paper uses differential games for viewing with simple movement and gives examples of viewing processes. The software has been developed and computer modeling of several methods of interaction in a conflict-driven environment has been introduced.

Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies.