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Title:A three-person deterministic graphical game without Nash equilibria
Authors:ID Boros, Endre (Author)
ID Gurvich, Vladimir (Author)
ID Milanič, Martin (Author)
ID Oudalov, Vladimir (Author)
ID Vičič, Jernej (Author)
Files:URL https://www.sciencedirect.com/science/article/pii/S0166218X18300404?via%3Dihub
 
Language:English
Work type:Unknown
Typology:1.01 - Original Scientific Article
Organization:FAMNIT - Faculty of Mathematics, Science and Information Technologies
Abstract:We give an example of a three-person deterministic graphical game that has no Nash equilibrium in pure stationary strategies. The game has seven positions, four outcomes (a unique cycle and three terminal positions), and its normal form is of size only. Thus, the example strengthens significantly the one obtained in 2014 by Gurvich and Oudalov; the latter has four players, five terminals, and normal form of size . Furthermore, our example is minimal with respect to the number of players. Somewhat similar examples were known since 1975, but they were not related to deterministic graphical games. The small size of our example allows us to verify that it has no Nash equilibrium not only in pure but also in independently mixed (so-called behavioral) strategies. For independently mixed strategies two distinct effective payoffs can be considered: along with the classical Markovian evaluation, we also consider a priori evaluation, which may be a better fit for playing in behavioral strategies
Keywords:deterministic graphical multi-person game, perfect information, Nash equilibrium, directed cycle, terminal position, pure stationary strategy
Year of publishing:2018
Number of pages:str. 294-303
Numbering:#Vol. #217, #Part #2
PID:20.500.12556/RUP-9513 This link opens in a new window
UDC:519.17
ISSN on article:0166-218X
DOI:10.1016/j.dam.2018.01.008 This link opens in a new window
COBISS.SI-ID:1540221636 This link opens in a new window
Publication date in RUP:30.03.2018
Views:4525
Downloads:178
Metadata:XML DC-XML DC-RDF
:
BOROS, Endre, GURVICH, Vladimir, MILANIČ, Martin, OUDALOV, Vladimir and VIČIČ, Jernej, 2018, A three-person deterministic graphical game without Nash equilibria. Discrete applied mathematics [online]. 2018. Vol. 217, no. Part 2, p. 294–303. [Accessed 6 April 2025]. DOI 10.1016/j.dam.2018.01.008. Retrieved from: https://www.sciencedirect.com/science/article/pii/S0166218X18300404?via%3Dihub
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Record is a part of a journal

Title:Discrete applied mathematics
Shortened title:Discrete appl. math.
Publisher:Elsevier
ISSN:0166-218X
COBISS.SI-ID:25342464 This link opens in a new window

Secondary language

Language:English
Keywords:deterministična grafovska večigralska igra, popolna informacija, Nashevo ravnovesje, usmerjen cikel, končna pozicija, čista stacionarna strategija


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