Game Theory

Petrosjan, Leon A.; Zenkevich, Nikolay A.

doi:10.1142/2875

Cited by 88 publications

(25 citation statements)

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“…In fact, as is known from differential games, see e.g. (Fleming & Soner, 2006;Malaeyev, 2000) or (Petrosjan & Zenkevich, 1996), the upper value V + (t, x, y) represents the unique viscosity solution of the upper Isaac's equation J(t, u, v, x, y…”

Section: With C(t ) Depending Only On the Bounds Of The Norms Of Q Inmentioning

confidence: 99%

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

Kolokoltsov¹

2012

IJSP

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Managing large complex stochastic systems, including competitive interests, when one or several players can control the behavior of a large number of particles (agents, mechanisms, vehicles, subsidiaries, species, police units, etc), say N k for a player k, the complexity of the game-theoretical (or Markov decision) analysis can become immense as N k → ∞. However, under rather general assumptions, the limiting problem as all N k → ∞ can be described by a well manageable deterministic evolution. In this paper we analyze some simple situations of this kind proving the convergence of Nashequilibria for finite games to equilibria of a limiting deterministic differential game.

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Section: With C(t ) Depending Only On the Bounds Of The Norms Of Q Inmentioning

confidence: 99%

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

Kolokoltsov¹

2012

IJSP

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“…, x independently of each other. As we know from the game theory (see, e.g., [1][2][3]) each th player can guarantee a payoff…”

Section: Usefulness Of Cooperation In Person Gamementioning

confidence: 99%

“…In the game theory (see, e.g., [1][2][3]), much attention is given to the cooperative game theory of person. In [4,5], we considered the games of two and three persons from the point of view of the usefulness of combining them in an alliance in order to get additional dividends.…”

Section: Introductionmentioning

confidence: 99%

On the Usefulness of Cooperation in N Person Games

Никольский

Moussa

2016

Journal of Applied Mathematics

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The person games in which each player maximizes his payoff function are considered. We have studied an interesting question for the cooperative game theory about the usefulness of uniting the players in a union. The aim of such cooperation is for each player to get a positive increase to his guaranteed payoff. We have obtained some effective sufficient conditions under which the joining of the players in union is useful for each player. The linear case, specially, is being considered. In the second part of the paper, we have studied the question about the usefulness of cooperation of the players in the presence of the ( + 1)th player, an ill-intentioned destructive player, whose whole aim is not to win but to harm each player individually, and also the union of these players, for example, global terrorism. It should be noted that the considered situation in the second part is related to A. V. Kryazhimskiy's talk delivered in the summer of 2014. We obtain constructive conditions under which the union of the players is beneficial in this situation as well.

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“…By doing so, however, they also suggest how a variety of firms view the role of 'external' sources of assistance in the sequencing of ideas. 10 We found Petrosjan and Mazalov (1996) and Ibragimov (2005) to be particularly useful to our conceptualization of this methodology.…”

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confidence: 92%

Awareness in innovators: from ‘outside the box’ to ‘inside the bubble’

Goorha¹,

Potts

2016

J Glob Entrepr Res

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Innovation is sometimes perceived as a linear and sequential process, and at other times as multidimensional. Based on the common thread of 'awareness' that grounds many theories on innovation, we analyze the idea that a flexible informational awareness accounts for both perceptions within the same overall innovation strategy. To show this, we propose using a simple theoretical setup that yields an intuitive and tractable visualization -in the form of thought bubbles -for the process of innovation. We discuss the application of this visualization to the process of idea search and to the types of knowledge commons.

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Game Theory

Cited by 88 publications

References 0 publications

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

On the Usefulness of Cooperation in N Person Games

Awareness in innovators: from ‘outside the box’ to ‘inside the bubble’

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