300961 Lecture Notes - Lecture 5: Differential Game, Social Computing, Random Variable
Document Summary
Lecture 5: differential games such as the continuous pursuit and evasion game are continuous games where the evolution of the players" state variables is governed by differential equations. The problem of nding an optimal strategy in a differential game is closely related to the optimal controltheory. In particular, there are two types of strategies: the open-loop strategies are found using the pontryagin maximum principle while the closed-loop strategies are found using bellman"s dynamic programming method: a particular case of differential games are the games with a random time horizon. In such games, the terminal time is a random variable with a given probability distribution function. Therefore, the players maximize the mathematical expectation of the cost function. In general, the evolution of strategies over time according to such rules is modeled as a markov chain with a state variable such as the current strategy pro le or how the game has been played in the recent past.
