Basics of Game Theory

This chapter provides a brief overview of basic concepts in game theory. These include game formulations and classifications, games in extensive vs. in normal form, games with continuous action (strategy) sets vs. finite strategy sets, mixed vs. pure strategies, and games with uncoupled (orthogonal) vs. coupled action sets. The next section reviews basic solution concepts, among them Nash equilibria being of most relevance. The chapter is concluded with some remarks on the rationality assumption and learning in classical games. The following chapters will introduce these concepts formally.

[1]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[2]  T. Vincent,et al.  Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics , 2005 .

[3]  J. M. Smith.  The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

[4]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[5]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[6]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

[7]  Cem U. Saraydar,et al.  Pricing and power control in a multicell wireless data network , 2001, IEEE J. Sel. Areas Commun..

[8]  Scott Shenker,et al.  Learning in Network Contexts: Experimental Results from Simulations , 2001, Games Econ. Behav..

[9]  J. Nash.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[10]  Jeff S. Shamma,et al.  Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria , 2005, IEEE Transactions on Automatic Control.

[11]  T. Vincent,et al.  Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics: The Darwinian game , 2005 .

[12]  Vijay Krishna,et al.  On the Convergence of Fictitious Play , 1998, Math. Oper. Res..

[13]  J. Robinson.  AN ITERATIVE METHOD OF SOLVING A GAME , 1951, Classics in Game Theory.

[14]  Eitan Altman,et al.  Multiuser rate-based flow control , 1998, IEEE Trans. Commun..

[15]  Eitan Altman,et al.  A survey on networking games in telecommunications , 2006, Comput. Oper. Res..

[16]  William H. Sandholm,et al.  Population Games And Evolutionary Dynamics , 2010, Economic learning and social evolution.

[17]  Eitan Altman,et al.  Nash equilibria for combined flow control and routing in networks: asymptotic behavior for a large number of users , 2002, IEEE Trans. Autom. Control..

[18]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[19]  David M. Kreps,et al.  Learning Mixed Equilibria , 1993 .

[20]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[21]  A. I. Subbotin,et al.  Game-Theoretical Control Problems , 1987 .

[22]  Lacra Pavel,et al.  A noncooperative game approach to OSNR optimization in optical networks , 2006, IEEE Transactions on Automatic Control.