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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: 4543; Downloads: 178
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