evolutionary dynamics and extensive form games - ross cressman

[...]... extensive form games with the same (reduced-strategy) normal form are strategically equivalent when played by rational players (e.g., Kolberg and Mertens 1986) These arguments are usually based on transformations of extensive form games similar to those introduced by Thompson (1952) and Dalkey (1953) In particular, Elmes and Reny (1994) show all extensive form games with the same (reduced) normal form. .. acknowledged is financial assistance from Wilfrid Laurier University and the Natural Sciences and Engineering Research Council of Canada Ross Cressman Waterloo, Ontario June 2002 cress-79032 cres79032˙fm January 23, 2003 14:51 Evolutionary Dynamics and Extensive Form Games xiii cress-79032 book January 27, 2003 10:59 1 Introduction Extensive form games, with an explicit description of the sequential nature... extensive form structure of our evolutionary games imparts special properties on the evolutionary dynamic that makes its analysis more tractable than would otherwise be expected This will be shown even when these games have a large number of pure strategies 1.1 Extensive Form versus Normal Form Every (finite) extensive form game has a normal form representation Thus one way to analyze an extensive form. .. how and when normal form evolutionary dynamics do not respect the subgame structure The importance of the extensive form representation for this example, as a means to motivate evolutionary dynamics that respect the subgame structure (e.g., subgame monotone dynamics) , is also discussed there as well as in chapters 9.2 and 9.4 cress-79032 book January 27, 2003 10:59 1.1 Extensive Form versus Normal Form. .. generalize the techniques of dynamic evolutionary game theory to extensive form games The ultimate goal is to gain as prominent a position for dynamic evolutionary game theory applied to extensive form games as the corresponding theory has deservedly attained for normal form games For many readers the formal proofs of the insights that the dynamic analyses of extensive form games provide for models of behavioral... Normal Form Games Although this book emphasizes extensive form games, we begin with a review of dynamic evolutionary game theory for symmetric normal form games. 1 This is partly for historical reasons as the theory of dynamic evolutionary games first developed in the biological literature where extensive form games were initially of little interest Moreover many of the techniques used to analyze the dynamics. .. Neumann and Morgenstern (1944) On the other hand, most dynamic analyses of evolutionary games are based on their normal forms, as evidenced by standard books on the topic (e.g., Hofbauer and Sigmund 1988, 1998; Cressman 1992; Weibull 1995; Vega-Redondo 1996) as well as in other game theory books.1 This is despite the fact that many interesting games are specified more naturally through their extensive forms... symmetric and bimatrix games of chapters 2 and 3 respectively, the multi-locus model of natural selection in chapter 5, and, to a lesser extent, the general asymmetric games of chapter 4 In these chapters (beginning at the end of chapter 2), the book emphasizes how an informal appreciation of the extensive form assists in understanding the theory Chapter 6 summarizes the standard definition of general extensive. .. extensive form games needed for their dynamic analysis Also emphasized here is cress-79032 book January 27, 2003 16 10:59 Chapter 1 Introduction the subgame structure and its relationship to the replicator dynamic The dynamics of extensive form evolutionary games are not well understood for complex game trees without many subgames Instead, chapters 7 and 8 consider two important particular classes of extensive. .. studying evolutionary dynamics as this has been done by numerous authors (see references at the beginning of the Introduction) What has received much less attention is the analyses of these dynamics for games that are more naturally specified through their extensive form This book then focuses on evolutionary dynamics that are adapted to extensive form games It also emphasizes connections between the extensive . America. Library of Congress Cataloging-in-Publication Data Cressman, Ross. Evolutionary dynamics and extensive form games / Ross Cressman. p. cm. — (Economic learning and social evolution ; 5) Includes. Games, Ross Cressman, 2003 ii cress-79032 cres79032˙fm January 23, 2003 14:51 Evolutionary Dynamics and Extensive Form Games Ross Cressman The MIT Press Cambridge, Massachusetts London, England iii cress-79032. Notes 163 6 Extensive Form Games 165 6.1 N-Player Extensive Form Games 166 6.1.1 Strategies and Payoffs 168 6.1.2 Nash Equilibria, Subgames, and Backward Induction 171 6.2 Normal Forms and the Replicator