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Register a new userEntropy Games and Matrix Multiplication Games
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Added by
Eugene Asarin
Publication date
2015
fields
Informatics Engineering
and research's language is
English
Authors
Eugene Asarin
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Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic People. Despot wants to make the set of possible Peoples behaviors as small as possible, while Tribune wants to make it as large as possible.An MMG is played by two players that alternately write matrices from some predefined finite sets. One wants to maximize the growth rate of the product, and the other to minimize it. We show that in general MMGs are undecidable in quite a strong sense.On the positive side, EGs correspond to a subclass of MMGs, and we prove that such MMGs and EGs are determined, and that the optimal strategies are simple. The complexity of solving such games is in NP&coNP.
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Moving target defense (MTD) techniques that enable a system to randomize its configuration to thwart prospective attacks are an effective security solution for tomorrows wireless networks. However, there is a lack of analytical techniques that enable one to quantify the benefits and tradeoffs of MTDs. In this paper, a novel approach for implementing MTD techniques that can be used to randomize cryptographic techniques and keys in wireless networks is proposed. In particular, the problem is formulated as a stochastic game in which a base station (BS), acting as a defender seeks to strategically change its cryptographic techniques and keys in an effort to deter an attacker that is trying to eavesdrop on the data. The game is shown to exhibit a single-controller property in which only one player, the defender, controls the state of the game. For this game, the existence and properties of the Nash equilibrium are studied, in the presence of a defense cost for using MTD. Then, a practical algorithm for deriving the equilibrium MTD strategies is derived. Simulation results show that the proposed game-theoretic MTD framework can significantly improve the overall utility of the defender, while enabling effective randomization over cryptographic techniques.
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to nearby games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games.
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One of the natural objectives of the field of the social networks is to predict agents behaviour. To better understand the spread of various products through a social network arXiv:1105.2434 introduced a threshold model, in which the nodes influenced by their neighbours can adopt one out of several alternatives. To analyze the consequences of such product adoption we associate here with each such social network a natural strategic game between the agents. In these games the payoff of each player weakly increases when more players choose his strategy, which is exactly opposite to the congestion games. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining an existence of a Nash equilibrium, also of a special type, is NP-complete. This implies the same result for a more general class of games, namely polymatrix games. The situation changes when the underlying graph of the social network is a DAG, a simple cycle, or, more generally, has no source nodes. For these three classes we determine the complexity of an existence of (a special type of) Nash equilibria. We also clarify for these categories of games the status and the complexity of the finite best response property (FBRP) and the finite improvement property (FIP). Further, we introduce a new property of the uniform FIP which is satisfied when the underlying graph is a simple cycle, but determining it is co-NP-hard in the general case and also when the underlying graph has no source nodes. The latter complexity results also hold for the property of being a weakly acyclic game. A preliminary version of this paper appeared as [19].
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