Dynamic Noncooperative Game Theory: Second Edition
Recent interest in biological games and mathematical finance make this classic 1982 text a necessity once again. Unlike other books in the field, this text provides an overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and simultaneously stresses the role of different information patterns. The first edition was fully revised in 1995, adding new topics such as randomized strategies, finite games with integrated decisions, and refinements of Nash equilibrium. Readers can now look forward to even more recent results in this unabridged, revised SIAM Classics edition. Topics covered include static and dynamic noncooperative game theory, with an emphasis on the interplay between dynamic information patterns and structural properties of several different types of equilibria; Nash and Stackelberg solution concepts; multi-act games; Braess paradox; differential games; the relationship between the existence of solutions of Riccati equations and the existence of Nash equilibrium solutions; and infinite-horizon differential games.
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admits a unique affine-quadratic Basar behavioral strategies bimatrix continuously differentiable Corollary corresponding cost function decision problems defined Definition denote differential equations differential game discrete-time equilibrium strategies equivalent Example exists extensive form feedback game feedback Stackelberg solution feedback strategies finite game game admits game in extensive given Hence inequalities infinite dynamic games information set information structure leader linear linear-quadratic matrix game minimizing mixed strategies multi-act games N-person N-tuple Nash equilibrium solution Nash solution nodes noncooperative nonunique nonzero-sum games normal form obtained optimal control optimal control problem outcome P1 and P2 pair players Prop pure strategies pursuit-evasion quadratic result Riccati equation saddle saddle-point solution saddle-point strategies satisfied Section security strategy single-act game solution concept Stackelberg strategy stochastic stochastic game strategy for P1 subsection theorem trajectory vector viscosity solution zero-sum game