Cooperative game theory, mechanism design/implementation, political economy, learning, equilibrium selection, experimental economics, axiomatic decision theory, and differential games
are among the areas addressed.
The 11 papers in this collection apply stochastic differential games
to technological innovation timing, compare the Nash equilibria for static and dynamic public good games, and examine a Bayesian learning process leading to a mixed strategy Nash equilibrium.
Other areas covered include dynamic programming, optimal control for polynomial systems, multi-variable frequency-domain techniques, and differential games
Chapters cover general optimal control problems, finite-dimensional optimization, optimization of dynamic systems with general performance criteria, terminal equality constraints, the linear quadratic control problem, and linear quadratic differential games
The first is based on the mathematical theory of differential games
Closed-loop (feedback) equilibria are usually preferred, but there are no general existence theorems for closed-loop equilibria in differential games with a freely chosen terminal date.
Hence, in this paper I analyze the intrafirm diffusion of a new process innovation in a differential game model of an oligopoly.
Section 2 presents the differential game model of intrafirm diffusion, and section 3 provides the details of its equilibrium.
The appropriate framework for analyzing this problem is a differential game.
To determine the open-loop equilibrium of this differential game, the standard approach is to form, for each firm i, the Hamiltonian
Russia) have organized the material in this text into two sections: an elementary but systematic exposition of the main ideas of modern game theory with only secondary school level mathematics required and a more detailed discussion of the mathematical methods of the theory that discusses such advanced analysis topics as the differential geometry approach to stability, the abstract dynamic system approach to the analysis of differential games
, Bellman type equations for multi-criteria optimization, turnpikes for stochastic games, and statistical physics (this latter section requires familiarity with calculus, differential equations, linear algebra, and probability).
Other topics covered include differential games
, the use of chaos indicators in rigid body motion, and single-point optimal attitude determination using modified Rodrigues parameters.