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Daizhan Cheng - One of the best experts on this subject based on the ideXlab platform.

  • On coset weighted potential Game
    Journal of the Franklin Institute, 2020
    Co-Authors: Yuanhua Wang, Daizhan Cheng
    Abstract:

    Abstract In this paper we first define a new kind of potential Games, called coset weighted potential Game, which is a generalized form of weighted potential Game. Using semi-tensor product of matrices, an algebraic method is provided to verify whether a Finite Game is a coset weighted potential Game, and a simple formula is obtained to calculate the corresponding potential function. Then some properties of coset weighted potential Games are revealed. Finally, by resorting to the vector space structure of Finite Games, a new orthogonal decomposition based on coset weights is proposed, the corresponding geometric and algebraic expressions of all the subspaces are given by providing their bases.

  • On skew-symmetric Games
    Journal of the Franklin Institute, 2018
    Co-Authors: Yaqi Hao, Daizhan Cheng
    Abstract:

    Abstract By resorting to the vector space structure of Finite Games, skew-symmetric Games (SSGs) are proposed and investigated as a natural subspace of Finite Games. First of all, for two player Games, it is shown that the skew-symmetric Games form an orthogonal complement of the symmetric Games. Then for a general SSG its linear representation is given, which can be used to verify whether a Finite Game is skew-symmetric. Furthermore, some properties of SSGs are also obtained in the light of its vector subspace structure. Finally, a symmetry-based decomposition of Finite Games is proposed, which consists of three mutually orthogonal subspaces: symmetric subspace, skew-symmetric subspace and asymmetric subspace. An illustrative example is presented to demonstrate this decomposition.

  • From symmetric to skew-symmetric Games
    2017 Chinese Automation Congress (CAC), 2017
    Co-Authors: Yaqi Hao, Daizhan Cheng
    Abstract:

    As a natural dual object of symmetric Game (SG), the skew-symmetric Game (SSG) is proposed and investigated in this paper. First of all, for two player Games, it is shown that both symmetric and skew-symmetric Games are subspaces of Finite Games. Moreover, using the Euclidean space structure of Finite Games, it is proved that the skew-symmetric Games form an orthogonal complement of symmetric Games. Then the linear representation of SSG is presented, which can be used to verify whether a Finite Game is a SSG. Finally, some properties of SSGs are revealed.

  • A survey on potential evolutionary Game and its applications
    Journal of Control and Decision, 2015
    Co-Authors: Daizhan Cheng, Yuanhua Wang, Ting Liu
    Abstract:

    Basic concepts about the Finite potential Games and the networked evolutionary Games (NEGs) are introduced. Some new developments are surveyed, including (i) formulas for verifying whether a Finite Game is (weighted) potential and for calculating the (weighted) potential function; and (ii) the fundamental network equation and strategy profile dynamics of NEGs. Then some applications are introduced, which include: (i) convergence of NEGs; (ii) congestion control; (iii) distributed coverage of graphs.

  • On Finite potential Games
    Automatica, 2014
    Co-Authors: Daizhan Cheng
    Abstract:

    A linear system, called the potential equation (PE), is presented. It is proved that a Finite Game is potential if and only if its potential equation has solution. Some properties of the potential equation are obtained. Based on these properties, a closed form solution of the PE is obtained. Moreover, a formula based on the solution of the PE is obtained to calculate the potential function. Finally, it is proved that a networked evolutionary Game is potential if and only if its fundamental network Game is potential. Some interesting examples are presented to illustrate the theoretical results.

Yaqi Hao - One of the best experts on this subject based on the ideXlab platform.

  • On skew-symmetric Games
    Journal of the Franklin Institute, 2018
    Co-Authors: Yaqi Hao, Daizhan Cheng
    Abstract:

    Abstract By resorting to the vector space structure of Finite Games, skew-symmetric Games (SSGs) are proposed and investigated as a natural subspace of Finite Games. First of all, for two player Games, it is shown that the skew-symmetric Games form an orthogonal complement of the symmetric Games. Then for a general SSG its linear representation is given, which can be used to verify whether a Finite Game is skew-symmetric. Furthermore, some properties of SSGs are also obtained in the light of its vector subspace structure. Finally, a symmetry-based decomposition of Finite Games is proposed, which consists of three mutually orthogonal subspaces: symmetric subspace, skew-symmetric subspace and asymmetric subspace. An illustrative example is presented to demonstrate this decomposition.

  • From symmetric to skew-symmetric Games
    2017 Chinese Automation Congress (CAC), 2017
    Co-Authors: Yaqi Hao, Daizhan Cheng
    Abstract:

    As a natural dual object of symmetric Game (SG), the skew-symmetric Game (SSG) is proposed and investigated in this paper. First of all, for two player Games, it is shown that both symmetric and skew-symmetric Games are subspaces of Finite Games. Moreover, using the Euclidean space structure of Finite Games, it is proved that the skew-symmetric Games form an orthogonal complement of symmetric Games. Then the linear representation of SSG is presented, which can be used to verify whether a Finite Game is a SSG. Finally, some properties of SSGs are revealed.

Pierfrancesco La Mura - One of the best experts on this subject based on the ideXlab platform.

  • TARK - Projective expected utility: a subjective formulation
    Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge - TARK '09, 2009
    Co-Authors: Pierfrancesco La Mura
    Abstract:

    Motivated by classical decision-theoretic paradoxes (Allais 1953, Ellsberg 1961), we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the paradoxes, while retaining significant simplicity and tractability. In particular, every Finite Game within this larger class of preferences still has an equilibrium.

  • Projective Expected Utility
    Journal of Mathematical Psychology, 2009
    Co-Authors: Pierfrancesco La Mura
    Abstract:

    Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every Finite Game within this larger class of preferences still has an equilibrium.

  • ADT - Game Theory without Decision-Theoretic Paradoxes
    Algorithmic Decision Theory, 2009
    Co-Authors: Pierfrancesco La Mura
    Abstract:

    Most work in Game theory is conducted under the assumption that the players are expected utility maximizers. Expected utility is a very tractable decision model, but is prone to well-known paradoxes and empirical violations (Allais 1953, Ellsberg 1961), which may induce systematic biases in Game-theoretic predictions. La Mura (2009) introduced a projective generalization of expected utility (PEU) which avoids the dominant paradoxes, while remaining quite tractable. We show that every Finite Game with PEU players has an equilibrium, and discuss several examples of PEU Games.

Yannick Viossat - One of the best experts on this subject based on the ideXlab platform.

  • Semi-algebraic sets and equilibria of binary Games
    Operations Research Letters, 2016
    Co-Authors: Guillaume Vigeral, Yannick Viossat
    Abstract:

    Any nonempty, compact, semi-algebraic set in 0 , 1 n is the projection of the set of mixed equilibria of a Finite Game with 2 actions per player on its first n coordinates. A similar result follows for sets of equilibrium payoffs. The proofs are constructive and elementary.

  • Properties and applications of dual reduction
    Economic Theory, 2010
    Co-Authors: Yannick Viossat
    Abstract:

    The dual reduction process, introduced by Myerson, allows a Finite Game to be reduced to a smaller-dimensional Game such that any correlated equilibrium of the reduced Game is an equilibrium of the original Game. We study the properties and applications of this process. It is shown that generic two-player normal form Games have a unique full dual reduction (a known refinement of dual reduction) and all strategies that have probability zero in all correlated equilibria are eliminated in all full dual reductions. Among other applications, we give a linear programming proof of the fact that a unique correlated equilibrium is a Nash equilibrium, and improve on a result due to Nau, Gomez-Canovas and Hansen on the geometry of Nash equilibria and correlated equilibria.

  • Properties and applications of dual reduction
    arXiv: Optimization and Control, 2008
    Co-Authors: Yannick Viossat
    Abstract:

    The dual reduction process, introduced by Myerson, allows to reduce a Finite Game into a smaller dimensional Game such that any equilibrium of the reduced Game is an equilibrium of the original Game. This holds both for Nash equilibrium and correlated equilibrium. We present examples of applications of dual reduction and argue that this is a useful tool to study Nash equilibria and correlated equilibria. We then investigate its properties.

  • Geometry, Correlated Equilibria and Zero-Sum Games
    2003
    Co-Authors: Yannick Viossat
    Abstract:

    This paper is concerned both with the comparative geometry of Nash and correlated equilibria, and with a generalization of zero-sum Games based on correlated equilibria. The set of correlated equilibrium distributions of any Finite Game in strategic form is a polytope, which contains the Nash equilibria. I characterize the class of Games such that this polytope (if not a singleton) contains a Nash equilibrium in its relative interior. This class of Games, though not defined by some antagonistic property, is shown to include and generalize two-player zero-sum Games.

Jacqueline Morgan - One of the best experts on this subject based on the ideXlab platform.

  • Slightly Altruistic Equilibria
    Journal of Optimization Theory and Applications, 2008
    Co-Authors: G. De Marco, Jacqueline Morgan
    Abstract:

    We introduce a refinement concept for Nash equilibria (slightly altruistic equilibrium) defined by a limit process and which captures the idea of reciprocal altruism as presented in Binmore (Proceedings of the XV Italian Meeting on Game Theory and Applications, [2003]). Existence is guaranteed for every Finite Game and for a large class of Games with a continuum of strategies. Results and examples emphasize the (lack of) connections with classical refinement concepts. Finally, it is shown that, under a pseudomonotonicity assumption on a particular operator associated to the Game, it is possible, by selecting slightly altruistic equilibria, to eliminate those equilibria in which a player can switch to a strategy that is better for the others without leaving the set of equilibria.

  • Slightly Altruistic Equilibria in Normal Form Games
    2007
    Co-Authors: Giuseppe De Marco, Jacqueline Morgan
    Abstract:

    We introduce a refinement concept for Nash equilibria (slightly altruistic equilibrium) defined by a limit process and which captures the idea of reciprocal altruism as presented in Binmore (2003). Existence is guaranteed for every Finite Game and for a large class of Games with a continuum of strategies. Results and examples emphasize the (lack of) connections with classical refinement concepts. Finally, it is shown that under a pseudo-monotonicity assumption on a particular operator associated to the Game it is possible, by selecting slightly altruistic equilibria, to eliminate those equilibria in which a player can switch to a strategy that is better for the others without leaving the set of equilibria.

  • Stackelberg Problems: SubGame Perfect Equilibria via Tikhonov Regularization
    Annals of the International Society of Dynamic Games, 2006
    Co-Authors: Jacqueline Morgan, Fioravante Patrone
    Abstract:

    In this chapter we consider a two-stage Game with one leader and one (or more) followers and we investigate the behavior of a Tikhonov regularization when the best reply for the follower(s) is not uniquely determined. More precisely, we show, under mild assumptions in the case of one follower and sufficiently mild in the case of two followers, that a convergent sequence of solutions to regularized two-stage Games generates a subGame perfect equilibrium (SPE) of the original Game, providing a constructive way to approach an SPE in a continuous setting. Various elementary examples show that our results cannot be strengthened up to guaranteeing convergence to a strong or a weak Stackelberg equilibrium and that the method cannot be extended to all of the cases in which two followers play a mixed extension of a Finite Game.