On the existence of Nash equilibria in large games

Salonen, Hannu

doi:10.1007/s00182-009-0180-7

Cited by 11 publications

(7 citation statements)

References 7 publications

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“…Therefore, an interaction between attackers and IDSs in the forward channel is seen as a Nash equilibrium game. Nash has given a mixed strategy Nash equilibrium for a game with a finite set of strategies, moreover, he also proved that at least one mixed strategy exists in the game . In this paper, a cost function is given as

J false(bolda, boldb false) = ρ_{1} \frac{1}{\underline{f} false(bolda, boldb false)} + ρ_{2} \overset{normalΞ}{true} false(bolda, boldb false),

where ρ 1 and ρ 2 are two designed parameters.…”

Section: Modeling and Problem Formulationmentioning

confidence: 99%

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Stability analysis on networked control systems under double attacks with predictive control

Yang

Xia

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, stability of a networked control system under denial‐of‐service and false data injection attacks is analyzed with a predictive control method. To model denial‐of‐service attacks on the forward channel of networked control system, game theory is introduced for obtaining balanced results by denial‐of‐service frequency and duration. Then, measurement outputs of the networked control system are maliciously modified in the feedback channel. Under this double attack strategy, the stability of networked control system with predictive control is analyzed using a switched system method. By comparing three types of attack models, advantages of the double attacks are discussed to illustrate the necessity of this research. A numerical simulation is given to demonstrate effectiveness of the proposed methods on a networked control system under double attacks.

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J false(bolda, boldb false) = ρ_{1} \frac{1}{\underline{f} false(bolda, boldb false)} + ρ_{2} \overset{normalΞ}{true} false(bolda, boldb false),

where ρ 1 and ρ 2 are two designed parameters.…”

Section: Modeling and Problem Formulationmentioning

confidence: 99%

“…Nash has given a mixed strategy Nash equilibrium for a game with a finite set of strategies, moreover, he also proved that at least one mixed strategy exists in the game. 29 In this paper, a cost function is given as…”

Section: Dos Attacks On Forward Channelmentioning

confidence: 99%

Stability analysis on networked control systems under double attacks with predictive control

Yang

Xia

et al. 2019

Intl J Robust & Nonlinear

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“…An account of infinite player games has also been attempted in Ref. [8] to study Nash equilibrium using a different approach, but unlike this work which focuses on quantum games, it is classical and further it does not deal with the question on how cooperation arises in the infinite player case. When temperature in Ising system increases, i.e., β = 1 k B T decreases, the spins become more disordered.…”

Section: Classical Game Theory and 1d Ising Modelmentioning

confidence: 99%

Quantum Nash equilibrium in the thermodynamic limit

Sarkar

Benjamin

2019

Quantum Inf Process

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The quantum Nash equilibrium in the thermodynamic limit is studied for games like quantum Prisoner's dilemma and quantum game of Chicken. A phase transition is seen in both games as function of the entanglement in the game. We observe that for maximal entanglement irrespective of the classical payoffs, majority of players choose quantum strategy over defect in the thermodynamic limit.Quantum game theory is an important extension of classical game theory to the quantum regime. The classical games might be quantized by superposing initial states, entanglement between players or superposition of strategies, for a brief account see [1]. The outcomes of a quantum game is well known for two player case however, we want to investigate the scenario when the number of players goes to infinity, i.e., the thermodynamic limit. In recent times, there have been attempts to extend the two player classical games to the thermodynamic limit by connecting it to the Ising model [2,3,4]. We do a similar analysis and connect two player quantum games to the 1D Ising model in the thermodynamic limit to figure out the strategy chosen by majority of Shubhayan Sarkar

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“…Since there are infinite players (i.e., investors) in our model, the existence theorem of a mixed-strategy equilibrium for finite strategic-form games (Fudenberg and Tirole 1991, p. 29) does not apply to it. For the existence of Nash equilibria in games with infinite players, we refer our readers to Salonen (2010), in which the sufficient conditions for the existence of a mixed-strategy Nash equilibrium in a game with infinite players are studied.…”

Section: Modelmentioning

confidence: 99%