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2. Sprague-Grundy function of matroids and related hypergraphsEndre Boros, Vladimir Gurvich, Nhan Bao Ho, Kazuhisa Makino, Peter Muršič, 2019, original scientific article Keywords: matroid, self-dual matroid, impartial game, Sprague-Grundy function, Nim, hypergraph Nim, JM hypergraph Published in RUP: 11.02.2020; Views: 1308; Downloads: 97 Link to full text |
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4. On the Sprague-Grundy function of Exact k-NimEndre Boros, Vladimir Gurvich, Nhan Bao Ho, Kazuhisa Makino, Peter Muršič, 2018, original scientific article Keywords: Moore's Nim, Exact Nim, impartial games, P-position, Sprague-Grundy function Published in RUP: 22.05.2019; Views: 1822; Downloads: 124 Link to full text |
5. Sprague-Grundy function of symmetric hypergraphsEndre Boros, Vladimir Gurvich, Nhan Bao Ho, Kazuhisa Makino, Peter Muršič, 2019, original scientific article Keywords: impartial games, Sprague-Grundy function, Nim, hypergraph Nim, JM formula, JM hypergraph, symmetric hypergraph, transversal-free hypergraph Published in RUP: 22.05.2019; Views: 1828; Downloads: 124 Link to full text |
6. A three-person deterministic graphical game without Nash equilibriaEndre Boros, Vladimir Gurvich, Martin Milanič, Vladimir Oudalov, Jernej Vičič, 2018, original scientific article 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 Published in RUP: 30.03.2018; Views: 3418; Downloads: 173 Link to full text |
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9. Vector connectivity in graphsMartin Milanič, Endre Boros, Ferdinando Cicalese, Pinar Heggernes, Pim Van 't Hof, Romeo Rizzi, 2014, published scientific conference contribution abstract (invited lecture) Keywords: vektorska povezanost, aproksimacijski algoritmi, polinomski algoritmi, NP-poln problem, razcepljeni grafi, kografi, drevesa, vector connectivity, approximation algorithms, poynomial time algorithms, NP-hard problem, split graphs, cographs, trees Published in RUP: 15.10.2015; Views: 3199; Downloads: 250 Link to full text |