Normal Form Structures in Extensive Form Games
Author
Mailaith, Samuelson, and Swinkels (1992) introduce the normal form information set. Normal form information sets capture situations in which players can make certain decisions as if they knew their opponents' had chosen from a particular subset of their strategies. In this paper, we say that an extensive form game represents a normal form game if, for each situation, the corresponding choice in the extnesive form is made with the player knowing that the opponents have chosen from the relevant subset. We show that normal form games exist that cannot be represented. We develop an algorithm that generates a representation whenever one exists and present a necessary and sufficient condition for a normal form game to be representable. Keywords: representation, extensive form game, normal form game, information set, extensive form--normal form equivalence. JEL Classification Numbers: C70, C72.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borr
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borr
(This abstract was borrowed from another version of this item.)
Suggested Citation
Download full text from publisher
As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.
Other versions of this item:
- George J. Mailath, 1993. "Normal Form Structures in Extensive Form Games," Discussion Papers 1041, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Mailath, G.J. & Samuelson, L. & Swinkels, J.M., 1992. "Normal Form Structures in Extensive Form Games," Working papers 9205, Wisconsin Madison - Social Systems.
References listed on IDEAS
- Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993.
"Extensive Form Reasoning in Normal Form Games,"
Econometrica, Econometric Society, vol. 61(2), pages 273-302, March.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Working papers 90-13, Wisconsin Madison - Social Systems.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1991. "extensive Form Reasoning in Normal Form Games," Papers 9130, Tilburg - Center for Economic Research.
- Mailath, G. & Samuelson, L. & Swinkels, J., 1991. "Extensive form reasoning in normal form games," Discussion Paper 1991-30, Tilburg University, Center for Economic Research.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Papers 1-90-1, Pennsylvania State - Department of Economics.
- Kreps, David M & Wilson, Robert, 1982.
"Sequential Equilibria,"
Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
- David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
- David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
- Elmes Susan & Reny Philip J., 1994. "On the Strategic Equivalence of Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 62(1), pages 1-23, February.
- Abreu, Dilip & Pearce, David G., 1984. "On the inconsistency of certain axioms on solution concepts for non-cooperative games," Journal of Economic Theory, Elsevier, vol. 34(1), pages 169-174, October.
- Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
- Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993.
"Extensive Form Reasoning in Normal Form Games,"
Econometrica, Econometric Society, vol. 61(2), pages 273-302, March.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Working papers 90-13, Wisconsin Madison - Social Systems.
- Mailath, G. & Samuelson, L. & Swinkels, J., 1991. "Extensive form reasoning in normal form games," Other publications TiSEM 2a393209-5c6b-4fdd-bed2-5, Tilburg University, School of Economics and Management.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1991. "extensive Form Reasoning in Normal Form Games," Papers 9130, Tilburg - Center for Economic Research.
- Mailath, G. & Samuelson, L. & Swinkels, J., 1991. "Extensive form reasoning in normal form games," Discussion Paper 1991-30, Tilburg University, Center for Economic Research.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Papers 1-90-1, Pennsylvania State - Department of Economics.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Mailath, George J. & Samuelson, Larry & Swinkels, Jeroen M., 1997.
"How Proper Is Sequential Equilibrium?,"
Games and Economic Behavior, Elsevier, vol. 18(2), pages 193-218, February.
- George J. Mailath & Larry Samuelson & Jeroen M. Swinkels, "undated". "How Proper is Sequential Equilibrium," ELSE working papers 045, ESRC Centre on Economics Learning and Social Evolution.
- George J. Mailath, 1996. "How Proper is Sequential Equilibrium?," Discussion Papers 1161, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Mailath, G.J. & Samuelson, L., 1996. "How Proper Is Sequential Equilibrium?," Working papers 9611r, Wisconsin Madison - Social Systems.
- Mailath, G.J. & Samuelson, L., 1996. "How Proper Is Sequential Equilibrium?," Working papers 9611, Wisconsin Madison - Social Systems.
- Steven J. Brams & Christopher B. Jones, 1999. "Catch-22 And King-Of-The-Mountain Games," Rationality and Society, , vol. 11(2), pages 139-167, May.
- Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
- Brams, S.J., 1998. "To Mobilize of Not to Mobilize: Catch 22s in International Crises," Working Papers 98-11, C.V. Starr Center for Applied Economics, New York University.
- Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.
- Shimoji, Makoto, 2004. "On the equivalence of weak dominance and sequential best response," Games and Economic Behavior, Elsevier, vol. 48(2), pages 385-402, August.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Carlos Alós-Ferrer & Klaus Ritzberger, 2020. "Reduced normal forms are not extensive forms," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 281-288, October.
- Bo Chen & Rajat Deb, 2018. "The role of aggregate information in a binary threshold game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 381-414, October.
- Geir B. Asheim & Martin Dufwenberg, 2003.
"Deductive Reasoning in Extensive Games,"
Economic Journal, Royal Economic Society, vol. 113(487), pages 305-325, April.
- Asheim,G.B. & Dufwenberg,M., 2000. "Deductive reasoning in extensive games," Memorandum 08/2000, Oslo University, Department of Economics.
- Asheim, Geir B, 2000. "Deductive reasoning in Extensive Games," Research Papers in Economics 2000:7, Stockholm University, Department of Economics.
- Clark, Daniel & Fudenberg, Drew & He, Kevin, 2022.
"Observability, dominance, and induction in learning models,"
Journal of Economic Theory, Elsevier, vol. 206(C).
- Daniel Clark & Drew Fudenberg & Kevin He, 2022. "Observability, Dominance, and Induction in Learning Models," Papers 2201.00776, arXiv.org.
- Daniel Clark & Drew Fudenberg & Kevin He, 2022. "Observability, Dominance, and Induction in Learning Models," PIER Working Paper Archive 22-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Rommeswinkel, Hendrik, 2011. "Measuring Freedom in Games," MPRA Paper 106426, University Library of Munich, Germany, revised 03 Mar 2021.
- Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
- Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.
- John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, University Library of Munich, Germany, revised 18 Sep 1996.
- Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
- Asheim,G.B. & Perea,A., 2000. "Lexicographic probabilities and rationalizability in extensive games," Memorandum 38/2000, Oslo University, Department of Economics.
- Carlos Pimienta & Jianfei Shen, 2014.
"On the equivalence between (quasi-)perfect and sequential equilibria,"
International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
- Carlos Pimienta & Jianfei Shen, 2011. "On the Equivalence between (Quasi)-perfect and sequential equilibria," Discussion Papers 2012-01, School of Economics, The University of New South Wales.
- Dominiak, Adam & Lee, Dongwoo, 2023. "Testing rational hypotheses in signaling games," European Economic Review, Elsevier, vol. 160(C).
- Asheim, G.B. & Dufwenberg, M., 1996.
"Admissibility and Common Knowledge,"
Discussion Paper
1996-16, Tilburg University, Center for Economic Research.
- Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Other publications TiSEM 54bb4094-d109-48b9-8b45-a, Tilburg University, School of Economics and Management.
- Giacomo Bonanno, 2013.
"AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 42(3), pages 567-592, August.
- Giacomo Bonanno, 2010. "AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties," Working Papers 1017, University of California, Davis, Department of Economics.
- Casajus, Andre, 2003. "Weak isomorphism of extensive games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 267-290, December.
- Hauk, Esther & Hurkens, Sjaak, 2002.
"On Forward Induction and Evolutionary and Strategic Stability,"
Journal of Economic Theory, Elsevier, vol. 106(1), pages 66-90, September.
- Esther Hauk & Sjaak Hurkens, 1999. "On forward induction and evolutionary and strategic stability," Economics Working Papers 408, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 1999.
- GRIGIS DE STEFANO, Federico, 2014. "Strategic stability of equilibria: the missing paragraph," LIDAM Discussion Papers CORE 2014015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Srihari Govindan & Robert Wilson, 2012.
"Axiomatic Equilibrium Selection for Generic Two‐Player Games,"
Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
- Govindan, Srihari & Wilson, Robert, 2009. "Axiomatic Equilibrium Selection for Generic Two-Player Games," Research Papers 2021, Stanford University, Graduate School of Business.
- Srihari Govindan & Robert Wilson, 2010. "Axiomatic Equilibrium Selection For Generic Two-Player Games," Levine's Working Paper Archive 661465000000000203, David K. Levine.
- Srihari Govindan & Robert Wilson, 2009. "Axiomatic Equilibrium Selection for Generic two-player games," Levine's Working Paper Archive 814577000000000231, David K. Levine.
- Steven J. Brams & Christopher B. Jones, 1999. "Catch-22 And King-Of-The-Mountain Games," Rationality and Society, , vol. 11(2), pages 139-167, May.
- Giacomo Bonanno, 2011. "Perfect Bayesian equilibrium. Part II: epistemic foundations," Working Papers 111, University of California, Davis, Department of Economics.
More about this item
Keywords
representation; extensive form game; normal form game; information set; extensive form--normal form equivalence. jel classification numbers: c70; (this+abstract+was+borrowed+from+another+version+of+this+item.)(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borr
(this+abstract+was+borrowed+from+another+version+of+this+item.)%22" rel="nofollow">c72.
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borrowed from another version of this item.)
(this abstract was borr
(this abstract was borrowed from another version of this item.);
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borrowed+from+another+version+of+this+item.)
(this+abstract+was+borr
(this+abstract+was+borrowed+from+another+version+of+this+item.)%22 " rel="nofollow">All these keywords.
JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:64:y:1994:i:2:p:325-371. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.