In: Handbook of Game Theory with Economic Applications
AbstractThis chapter of the Handbook of Game Theory (Vol. 3) provides an overview of the theory of Nash equilibrium and its refinements. The starting-point is the rationalistic approach to games and the question whether there exists a convincing, self-enforcing theory of rational behavior in non-cooperative games. Given the assumption of independent behavior of the players, it follows that a self-enforcing theory has to prescribe a Nash equilibrium, i.e., a strategy profile such that no player can gain by a unilateral deviation. Nash equilibria exist and for generic (finite) games there is a finite number of Nash equilibrium outcomes. The chapter first describes some general properties of Nash equilibria. Next it reviews the arguments why not all Nash equilibria can be considered self-enforcing. For example, some equilibria do not satisfy a backward induction property: as soon as a certain subgame is reached, a player has an incentive to deviate. The concepts of subgame perfect equilibria, perfect equilibria and sequential equilibria are introduced to solve this problem. The chapter defines these concepts, derives properties of these concepts and relates them to other refinements such as proper equilibria and persistent equilibria. It turns out that none of these concepts is fully satisfactory as the outcomes that are implied by any of these concepts are not invariant w.r.t. inessential changes in the game. In addition, these concepts do not satisfy a forward induction requirement. The chapter continues with formalizing these notions and it describes concepts of stable equilibria that do satisfy these properties. This set-valued concept is then related to the other refinements. In the final section of the chapter, the theory of equilibrium selection that was proposed by Harsanyi and Selten is described and applied to several examples. This theory selects a unique equilibrium for every game. Some drawbacks of this theory are noted and avenues for future research are indicated.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
This chapter was published in:
This item is provided by Elsevier in its series Handbook of Game Theory with Economic Applications with number 3-41.
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/bookseriesdescription.cws_home/BS_HE/description
Find related papers by JEL classification:
- C - Mathematical and Quantitative Methods
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.