scholarly journals Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Wenjin Guan ◽  
Wei Yuan ◽  
Sheng Li
Keyword(s):  
Nash Equilibrium ◽  
Default Risk ◽  
Investment Strategy ◽  
Relative Performance ◽  
Equilibrium Strategy ◽  
Optimal Time ◽  
Household Expenditure ◽  
Value Functions ◽  
Nash Equilibrium Strategy ◽  
The Mind

Considering the mind of rivalry between families, each family focuses not only on its own wealth but also on other families, especially neighbors. In this paper, we investigate the non-zero-sum mean-variance game between two families with a random household expenditure under the default risk and relative performance. Applying the stochastic control theory within the framework of the game theory, the extended Hamilton–Jacobi–Bellman equation equations are derived. By solving this equation, we obtain the Nash equilibrium strategies of the two families and the corresponding equilibrium value functions. We also provide a numerical example to analyze the effects of relevant parameters on Nash equilibrium strategy and on the utility loss due to the mind of rivalry.

scholarly journals Spatial correlated games

2017 ◽  
Vol 4 (11) ◽  
pp. 171361 ◽  
Author(s):  
Ramón Alonso-Sanz
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Strategy ◽  
Variable Degree ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Nash Equilibrium Strategy ◽  
Link Type

This article studies correlated two-person games constructed from games with independent players as proposed in Iqbal et al. (2016 R. Soc. open sci. 3 , 150477. ( doi:10.1098/rsos.150477 )). The games are played in a collective manner, both in a two-dimensional lattice where the players interact with their neighbours, and with players interacting at random. Four game types are scrutinized in iterated games where the players are allowed to change their strategies, adopting that of their best paid mate neighbour. Particular attention is paid in the study to the effect of a variable degree of correlation on Nash equilibrium strategy pairs.

scholarly journals Non-Cooperative Spectrum Access Strategy Based on Impatient Behavior of Secondary Users in Cognitive Radio Networks

Electronics ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 995 ◽  
Author(s):  
Zeng ◽  
Liu ◽  
Wang ◽  
Lan
Keyword(s):  
Cognitive Radio ◽  
Nash Equilibrium ◽  
Learning Ability ◽  
Equilibrium Strategy ◽  
Spectrum Access ◽  
Secondary Users ◽  
Nash Equilibrium Strategy ◽  
Pricing Scheme ◽  
The Social ◽  
Limited Spectrum

In the cognitive radio network (CRN), secondary users (SUs) compete for limited spectrum resources, so the spectrum access process of SUs can be regarded as a non-cooperative game. With enough artificial intelligence (AI), SUs can adopt certain spectrum access strategies through their learning ability, so as to improve their own benefit. Taking into account the impatience of the SUs with the waiting time to access the spectrum and the fact that the primary users (PUs) have preemptive priority to use the licensed spectrum in the CRN, this paper proposed the repairable queueing model with balking and reneging to investigate the spectrum access. Based on the utility function from an economic perspective, the relationship between the Nash equilibrium and the socially optimal spectrum access strategy of SUs was studied through the analysis of the system model. Then a reasonable spectrum pricing scheme was proposed to maximize the social benefits. Simulation results show that the proposed access mechanism can realize the consistency of Nash equilibrium strategy and social optimal strategy to maximize the benefits of the whole cognitive system.

scholarly journals Stochastic Brownian Game of Absolute Dominance

2014 ◽  
Vol 51 (2) ◽  
pp. 436-452
Author(s):  
Shangzhen Luo
Keyword(s):  
Nash Equilibrium ◽  
Value Function ◽  
The Other ◽  
Equilibrium Strategy ◽  
Minimax Criterion ◽  
Nash Equilibrium Strategy ◽  
Suitable Parameter ◽  
The Difference ◽  
The Value Function ◽  
Absolute Dominance

In this paper we study a reinsurance game between two insurers whose surplus processes are modeled by arithmetic Brownian motions. We assume a minimax criterion in the game. One insurer tries to maximize the probability of absolute dominance while the other tries to minimize it through reinsurance control. Here absolute dominance is defined as the event that liminf of the difference of the surplus levels tends to -∞. Under suitable parameter conditions, the game is solved with the value function and the Nash equilibrium strategy given in explicit form.

Stochastic Brownian Game of Absolute Dominance

2014 ◽  
Vol 51 (02) ◽  
pp. 436-452 ◽  
Author(s):  
Shangzhen Luo
Keyword(s):  
Nash Equilibrium ◽  
Value Function ◽  
The Other ◽  
Equilibrium Strategy ◽  
Minimax Criterion ◽  
Nash Equilibrium Strategy ◽  
Suitable Parameter ◽  
The Difference ◽  
The Value Function ◽  
Absolute Dominance

In this paper we study a reinsurance game between two insurers whose surplus processes are modeled by arithmetic Brownian motions. We assume a minimax criterion in the game. One insurer tries to maximize the probability of absolute dominance while the other tries to minimize it through reinsurance control. Here absolute dominance is defined as the event that liminf of the difference of the surplus levels tends to -∞. Under suitable parameter conditions, the game is solved with the value function and the Nash equilibrium strategy given in explicit form.

scholarly journals Defending Against Man-In-The-Middle Attack in Repeated Games

2017 ◽  
Author(s):  
Shuxin Li ◽  
Xiaohong Li ◽  
Jianye Hao ◽  
Bo An ◽  
Zhiyong Feng ◽  
...  
Keyword(s):  
Nash Equilibrium ◽  
Repeated Games ◽  
Information Leakage ◽  
Solution Concept ◽  
Equilibrium Strategy ◽  
Nash Equilibrium Strategy ◽  
Man In The Middle ◽  
Unique Nash Equilibrium ◽  
Simultaneous Move ◽  
Mitm Attack

The Man-in-the-Middle (MITM) attack has become widespread in networks nowadays. The MITM attack would cause serious information leakage and result in tremendous loss to users. Previous work applies game theory to analyze the MITM attack-defense problem and computes the optimal defense strategy to minimize the total loss. It assumes that all defenders are cooperative and the attacker know defenders' strategies beforehand. However, each individual defender is rational and may not have the incentive to cooperate. Furthermore, the attacker can hardly know defenders' strategies ahead of schedule in practice. To this end, we assume that all defenders are self-interested and model the MITM attack-defense scenario as a simultaneous-move game. Nash equilibrium is adopted as the solution concept which is proved to be always unique. Given the impracticability of computing Nash equilibrium directly, we propose practical adaptive algorithms for the defenders and the attacker to learn towards the unique Nash equilibrium through repeated interactions. Simulation results show that the algorithms are able to converge to Nash equilibrium strategy efficiently.

Sign in / Sign up

Export Citation Format

Share Document