Editing Game theory (section)

===Alternative game representations===
{{see also|Succinct game}}

Alternative game representation forms are used for some subclasses of games or adjusted to the needs of interdisciplinary research.<ref>{{cite arXiv |last1=Tagiew |first1=Rustam |title=If more than Analytical Modeling is Needed to Predict Real Agents' Strategic Interaction |date=3 May 2011 |eprint=1105.0558 |class=cs.GT }}</ref> In addition to classical game representations, some of the alternative representations also encode time related aspects.
{| class="wikitable sortable"
|-
!Name
!Year
!Means
![[#Game_types|Type of games]]
!Time
|-
|[[Congestion game]]<ref>{{cite journal |last1=Rosenthal |first1=Robert W. | author-link1=Robert W. Rosenthal |title=A class of games possessing pure-strategy Nash equilibria |journal=International Journal of Game Theory |date=December 1973 |volume=2 |issue=1 |pages=65–67 |doi=10.1007/BF01737559|s2cid=121904640 }}</ref>
|1973
|functions
|subset of n-person games, simultaneous moves
|No
|-
|Sequential form<ref>{{cite book |last1=Koller |first1=Daphne | author-link1=Daphne Koller |last2=Megiddo |first2=Nimrod | author-link2=Nimrod Megiddo |last3=von Stengel |first3=Bernhard |title=Proceedings of the twenty-sixth annual ACM symposium on Theory of computing – STOC '94 |chapter=Fast algorithms for finding randomized strategies in game trees |pages=750–759 |date=1994 |doi=10.1145/195058.195451 |isbn=0-89791-663-8 |s2cid=1893272 }}</ref>
|1994
|matrices
|2-person games of imperfect information
|No
|-
|Timed games<ref>{{cite journal |last1=Alur |first1=Rajeev |last2=Dill |first2=David L. |title=A theory of timed automata |journal=Theoretical Computer Science |date=April 1994 |volume=126 |issue=2 |pages=183–235 |doi=10.1016/0304-3975(94)90010-8|doi-access=free }}</ref><ref>{{cite journal |last1=Tomlin |first1=C.J. |last2=Lygeros |first2=J. |last3=Shankar Sastry |first3=S. |title=A game theoretic approach to controller design for hybrid systems |journal=Proceedings of the IEEE |date=July 2000 |volume=88 |issue=7 |pages=949–970 |doi=10.1109/5.871303|s2cid=1844682 }}</ref>
|1994
|functions
|2-person games
|Yes
|-
|Gala<ref>{{cite journal |last1=Koller |first1=Daphne |last2=Pfeffer |first2=Avi |title=Representations and solutions for game-theoretic problems |journal=Artificial Intelligence |date=July 1997 |volume=94 |issue=1–2 |pages=167–215 |doi=10.1016/S0004-3702(97)00023-4 }}</ref>
|1997
|[[First-order logic|logic]]
|n-person games of imperfect information
|No
|-
|[[Graphical game theory|Graphical games]]<ref>{{cite journal |last1=Michael |first1=Michael Kearns |last2=Littman |first2=Michael L. |title=Graphical Models for Game Theory |journal=In UAI |date=2001 |pages=253–260 |citeseerx=10.1.1.22.5705 }}</ref><ref>{{cite arXiv |last1=Kearns |first1=Michael |last2=Littman |first2=Michael L. |last3=Singh |first3=Satinder |title=Graphical Models for Game Theory |date=7 March 2011 |eprint=1301.2281 |class=cs.GT}}</ref>
|2001
|graphs, functions
|n-person games, simultaneous moves
|No
|-
|Local effect games<ref>{{cite conference|last1=Leyton-Brown |first1=Kevin |last2=Tennenholtz |first2=Moshe |title=Local-Effect Games |publisher=Schloss Dagstuhl-Leibniz-Zentrum für Informatik |conference=Dagstuhl Seminar Proceedings |date=2005 |url=https://drops.dagstuhl.de/volltexte/2005/219/pdf/05011.LeytonBrownKevin.Paper.219.pdf|access-date=February 3, 2023}}</ref>
|2003
|functions
|subset of n-person games, simultaneous moves
|No
|-
|[[Game description language|GDL]]<ref>{{cite journal |last1=Genesereth |first1=Michael |last2=Love |first2=Nathaniel |last3=Pell |first3=Barney |title=General Game Playing: Overview of the AAAI Competition |journal=AI Magazine |date=15 June 2005 |volume=26 |issue=2 |pages=62 |doi=10.1609/aimag.v26i2.1813 }}</ref>
|2005
|[[First-order logic|logic]]
|deterministic n-person games, simultaneous moves
|No
|-
|Game Petri-nets<ref>{{cite journal |last1=Clempner |first1=Julio |title=Modeling shortest path games with Petri nets: a Lyapunov based theory |journal=International Journal of Applied Mathematics and Computer Science |date=2006 |volume=16 |issue=3 |pages=387–397 |url=https://eudml.org/doc/207801 }}</ref>
|2006
|[[Petri net]]
|deterministic n-person games, simultaneous moves
|No
|-
|Continuous games<ref>{{cite journal |last1=Sannikov |first1=Yuliy |title=Games with Imperfectly Observable Actions in Continuous Time |journal=Econometrica |date=September 2007 |volume=75 |issue=5 |pages=1285–1329 |doi=10.1111/j.1468-0262.2007.00795.x |url=http://www.dklevine.com/archive/sannikov_games.pdf }}</ref>
|2007
|functions
|subset of 2-person games of imperfect information
|Yes
|-
|PNSI<ref>{{cite book |last1=Tagiew |first1=Rustam |title=2008 International Conference on Computational Intelligence for Modelling Control & Automation |chapter=Multi-Agent Petri-Games |date=December 2008 |pages=130–135 |doi=10.1109/CIMCA.2008.15 |isbn=978-0-7695-3514-2 |s2cid=16679934 }}</ref><ref>{{cite book |last1=Tagiew |first1=Rustam |title=New Challenges in Computational Collective Intelligence |chapter=On Multi-agent Petri Net Models for Computing Extensive Finite Games |volume=244 |date=2009 |pages=243–254 |doi=10.1007/978-3-642-03958-4_21 |publisher=Springer |series=Studies in Computational Intelligence |isbn=978-3-642-03957-7 }}</ref>
|2008
|[[Petri net]]
|n-person games of imperfect information
|Yes
|-
|Action graph games<ref>{{cite arXiv |last1=Bhat |first1=Navin |last2=Leyton-Brown |first2=Kevin |title=Computing Nash Equilibria of Action-Graph Games |date=11 July 2012 |eprint=1207.4128 |class=cs.GT}}</ref>
|2012
|graphs, functions
|n-person games, simultaneous moves
|No
|}