LEADER 04033nam 22006975 450 001 9910349337403321 005 20200630151212.0 010 $a9783030266462 010 $a303026646X 024 7 $a10.1007/978-3-030-26646-2 035 $a(CKB)4100000009191125 035 $a(DE-He213)978-3-030-26646-2 035 $a(MiAaPQ)EBC5922491 035 $a(PPN)248602101 035 $a(MiAaPQ)EBC31886953 035 $a(Au-PeEL)EBL31886953 035 $a(OCoLC)1120124564 035 $a(EXLCZ)994100000009191125 100 $a20190907d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Foundations of Game Theory /$fby Rida Laraki, Jérôme Renault, Sylvain Sorin 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XVII, 229 p. 47 illus.) 225 1 $aUniversitext,$x0172-5939 311 08$a9783030266455 311 08$a3030266451 327 $a1 Introduction -- 2 Zero-Sum Games: the Finite Case -- 3 Zero-Sum Games: the General Case -- 4 N-Player games: Rationality and Equilibria -- 5 Equilibrium Manifolds and Dynamics -- 6 Games in Extensive Form -- 7 Correlated Equilibria, Learning, Bayesian Equilibria -- 8 Introduction to Repeated Games -- 9 Solutions to the Exercises -- References. . 330 $aThis book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text. Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability. . 410 0$aUniversitext,$x0172-5939 606 $aGame theory 606 $aMathematical optimization 606 $aMathematics 606 $aSocial sciences 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 606 $aGame Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/W29020 606 $aOptimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26008 606 $aMathematics in the Humanities and Social Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M32000 615 0$aGame theory. 615 0$aMathematical optimization. 615 0$aMathematics. 615 0$aSocial sciences. 615 14$aGame Theory, Economics, Social and Behav. Sciences. 615 24$aGame Theory. 615 24$aOptimization. 615 24$aMathematics in the Humanities and Social Sciences. 676 $a519.3 700 $aLaraki$b Rida$4aut$4http://id.loc.gov/vocabulary/relators/aut$0741259 702 $aRenault$b Jérôme$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSorin$b Sylvain$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349337403321 996 $aMathematical Foundations of Game Theory$92499539 997 $aUNINA