Journal articles: 'Nash stability'

1

Lensberg, Terje. "Stability and the Nash solution." Journal of Economic Theory 45, no. 2 (August 1988): 330–41. http://dx.doi.org/10.1016/0022-0531(88)90273-6.

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2

Osborne, Martin J., and Eric Van Damme. "Stability and Perfection of Nash Equilibria." Canadian Journal of Economics 22, no. 2 (May 1989): 447. http://dx.doi.org/10.2307/135684.

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MORGAN, JACQUELINE, and VINCENZO SCALZO. "VARIATIONAL STABILITY OF SOCIAL NASH EQUILIBRIA." International Game Theory Review 10, no. 01 (March 2008): 17–24. http://dx.doi.org/10.1142/s0219198908001741.

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New results on the variational stability of social Nash equilibria are obtained using the class of sequentially pseudocontinuous functions. This class of functions strictly includes the class of sequentially continuous functions and finds a natural motivation in the framework of Choice and Economic Theory since it characterizes the continuity of the preference relations on first countable topological spaces. We investigate the connections with previous results and we show that it is not possible to improve our results further on.

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4

Wang, Lei, Cui Liu, Juan Xue, and Hongwei Gao. "A Note on Strategic Stability of Cooperative Solutions for Multistage Games." Discrete Dynamics in Nature and Society 2018 (November 1, 2018): 1–6. http://dx.doi.org/10.1155/2018/3293745.

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The problem of strategic stability of cooperative solutions for multistage games is studied. The sufficient conditions related to discount factors are presented, which guarantee the existence of Nash or strong Nash equilibria in such games and therefore guarantee the strategic stability of cooperative solutions. The deviating payoffs of players are given directly, which are related closely to these conditions and avoid the loss of super-additivity of a class of general characteristic functions. As an illustration, Nash and strong Nash equilibria are found for the repeated infinite stage Prisoner’s dilemma game.

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Bhadury, J., and H. A. Eiselt. "Stability of Nash equilibria in locational games." RAIRO - Operations Research 29, no. 1 (1995): 19–33. http://dx.doi.org/10.1051/ro/1995290100191.

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6

Alós-Ferrer, Carlos. "Finite Population Dynamics and Mixed Equilibria." International Game Theory Review 05, no. 03 (September 2003): 263–90. http://dx.doi.org/10.1142/s0219198903001057.

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This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2×2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

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Liu, Chenwei, Shuwen Xiang, and Yanlong Yang. "Existence and essential stability of Nash equilibria for biform games with Shapley allocation functions." AIMS Mathematics 7, no. 5 (2022): 7706–19. http://dx.doi.org/10.3934/math.2022432.

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<abstract> <p>We define the Shapley allocation function (SAF) based on the characteristic function on a set of strategy profiles composed of infinite strategies to establish an <italic>n</italic>-person biform game model. It is the extension of biform games with finite strategies and scalar strategies. We prove the existence of Nash equilibria for this biform game with SAF, provided that the characteristic function satisfies the linear and semicontinuous conditions. We investigate the essential stability of Nash equilibria for biform games when characteristic functions are perturbed. We identify a residual dense subclass of the biform games whose Nash equilibria are all essential and deduce the existence of essential components of the Nash equilibrium set by proving the connectivity of its minimal essential set.</p> </abstract>

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OKUGUCHI, KOJI, and TAKESHI YAMAZAKI. "GLOBAL STABILITY OF NASH EQUILIBRIUM IN AGGREGATIVE GAMES." International Game Theory Review 16, no. 04 (December 2014): 1450014. http://dx.doi.org/10.1142/s0219198914500145.

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If an aggregative game satisfies the generalized Hahn conditions, then there exists a unique Nash equilibrium which may not be interior and is globally asymptotically stable under two alternative continuous adjustment processes with non-negativity constraints.

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9

Yang, Guanghui, and Hui Yang. "Stability of Weakly Pareto-Nash Equilibria and Pareto-Nash Equilibria for Multiobjective Population Games." Set-Valued and Variational Analysis 25, no. 2 (October 12, 2016): 427–39. http://dx.doi.org/10.1007/s11228-016-0391-6.

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Calvó-Armengol, Antoni, and Rahmi İlkılıç. "Pairwise-stability and Nash equilibria in network formation." International Journal of Game Theory 38, no. 1 (September 18, 2008): 51–79. http://dx.doi.org/10.1007/s00182-008-0140-7.

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11

Lu, Ya Li. "Simulation and Control of a Duopoly Model." Applied Mechanics and Materials 472 (January 2014): 146–51. http://dx.doi.org/10.4028/www.scientific.net/amm.472.146.

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This paper studies the dynamics of a duopoly model with bounded rationality and nonlinear demand function. Based on the stability theorem and Jurys criterions, we prove that the model has two unstable boundary fixed points and a local stable Nash equilibrium. Then we depict the stability region of Nash equilibrium, and investigate the effects of output adjustment speed on the players profit respectively. Theoretical analysis and simulations show that higher output adjustment speed can result in chaotic variation of outputs, and that the Nash equilibrium is the optimal result of duopoly game. To improve the profitability of each player and achieve the optimal game result, we put forth a new scheme combined with the time-delayed feedback control and the limiter control to stabilize the output to Nash equilibrium. Finally, the numerical simulation is adopted to verify the effectiveness and feasibility of the above control scheme.

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12

Gradwohl, Ronen, and Ehud Kalai. "Large Games: Robustness and Stability." Annual Review of Economics 13, no. 1 (August 5, 2021): 39–56. http://dx.doi.org/10.1146/annurev-economics-072720-042303.

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This review focuses on properties related to the robustness and stability of Nash equilibria in games with a large number of players. Somewhat surprisingly, these equilibria become substantially more robust and stable as the number of players increases. We illustrate the relevant phenomena through a binary-action game with strategic substitutes, framed as a game of social isolation in a pandemic environment.

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Zhang, Meng, Hong Ming Yang, and De Lun Yang. "Simulation and Analysis of Dynamic Evolution of Electricity Market Based on Bidding Decisions with Heterogeneous Expectations." Applied Mechanics and Materials 37-38 (November 2010): 1153–56. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.1153.

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Based on different bidding decisions with heterogeneous expectations of market participants, a dynamic model of electricity market considering power network constraints is proposed. This model is represented by a discrete difference equations embedded with the optimization problem of market clearing. By using the nonlinear complementarity function, the complex dynamic behaviors of electricity market are simulated and analyzed. The Nash equilibrium and its stability, the periodic and even chaotic dynamic behaviors beyond the stability region of Nash equilibrium are investigated.

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14

Liu, Jia, Guoliang Liu, Na Li, and Hongliang Xu. "Dynamics Analysis of Game and Chaotic Control in the Chinese Fixed Broadband Telecom Market." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/275123.

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This paper considers a dynamic duopoly Cournot model based on nonlinear cost functions. The model with heterogeneous players and the spillover effect is applied to the Chinese fixed broadband telecom market. We have studied its dynamic game process. The existence and stability of the Nash equilibrium of the system have been discussed. Simulations are used to show the complex dynamical behaviors of the system. The results illustrate that altering the relevant parameters of system can affect the stability of the Nash equilibrium point and cause chaos to occur. With the use of the delay feedback control method, the chaotic behavior of the model has been stabilized at the Nash equilibrium point. The analysis and results will be of great importance for the Chinese fixed broadband telecom market.

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15

Yu, Yu, and Jia-Qian Xu. "The Dynamic Rent-Seeking Games with Policymaker Cost and Competition Intensity." Discrete Dynamics in Nature and Society 2020 (September 25, 2020): 1–11. http://dx.doi.org/10.1155/2020/8081370.

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In this paper, a dynamic rent-seeking game incorporating policymaker cost and competition intensity is considered. On the basis of the political environment and rent-seekers with incomplete information set, the locally asymptotic stability of Nash equilibrium is proved. The competition intensity and policymaker cost could enlarge the stability region of Nash equilibrium. The higher the competition intensity is, the more the opponent’s expenditure reduces the player’s success probability, which is beneficial to the maintenance of Nash equilibrium. The higher the policymaker cost is, the less easily both players succeed and the more stable the rent-seeking market is. As the competition parameter decreases or the expenditure parameter increases, there will be chaos in a rent-seeking market. Chaos control is in order to stabilize the equilibrium of the rent-seeking game.

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16

Clempner, Julio B. "On Lyapunov Game Theory Equilibrium: Static and Dynamic Approaches." International Game Theory Review 20, no. 02 (June 2018): 1750033. http://dx.doi.org/10.1142/s0219198917500335.

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This paper suggests a game theory problem in which any feasible solution is based on the Lyapunov theory. The problem is analyzed in the static and dynamic cases. Some properties of Nash equilibria such as existence and stability are derived naturally from the Lyapunov theory. Remarkable is that every asymptotically stable equilibrium point (Nash equilibrium point) admits a Lyapunov-like function and if a Lyapunov-like function exists it converges to a Nash/Lyapunov equilibrium point. We define a Lyapunov-like function as an Lp-norm from the multiplayer objective function to the utopia minimum as a cost function. We propose multiple metrics to find the Nash/Lyapunov equilibrium and the strong Nash/Lyapunov equilibrium. Finding a Nash/Lyapunov equilibrium is reduced to the minimization problem of the Lyapunov-like function. We prove that the equilibrium point properties of Nash and Lyapunov meet in game theory. In order to validate the contributions of the paper, we present a numerical example.

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17

MU, LINGLING, PING LIU, YANYAN LI, and JINZHU ZHANG. "COMPLEXITY OF A REAL ESTATE GAME MODEL WITH A NONLINEAR DEMAND FUNCTION." International Journal of Bifurcation and Chaos 21, no. 11 (November 2011): 3171–79. http://dx.doi.org/10.1142/s021812741103043x.

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In this paper, a real estate game model with nonlinear demand function is proposed. And an analysis of the game's local stability is carried out. It is shown that the stability of Nash equilibrium point is lost through period-doubling bifurcation as some parameters are varied. With numerical simulations method, the results of bifurcation diagrams, maximal Lyapunov exponents and strange attractors are presented. It is found that the chaotic behavior of the model has been stabilized on the Nash equilibrium point by using of nonlinear feedback control method.

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18

Yang, Guanghui, Hui Yang, and Qiqing Song. "Stability of weighted Nash equilibrium for multiobjective population games." Journal of Nonlinear Sciences and Applications 09, no. 06 (June 15, 2016): 4167–76. http://dx.doi.org/10.22436/jnsa.009.06.59.

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19

Jakimowicz, A. "Stability of the Cournot-Nash Equilibrium in Standard Oligopoly." Acta Physica Polonica A 121, no. 2B (February 2012): B—50—B—53. http://dx.doi.org/10.12693/aphyspola.121.b-50.

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20

Iqbal, A., and A. h. Toor. "Stability of Mixed Nash Equilibria in Symmetric Quantum Games." Communications in Theoretical Physics 42, no. 3 (September 15, 2004): 335–38. http://dx.doi.org/10.1088/0253-6102/42/3/335.

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21

Haake, Claus-Jochen, and Bettina Klaus. "Stability and Nash implementation in matching markets with couples." Theory and Decision 69, no. 4 (November 28, 2008): 537–54. http://dx.doi.org/10.1007/s11238-008-9122-2.

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22

Zhang, Anming, and Yimin Zhang. "Stability of a Cournot-Nash equilibrium: The multiproduct case." Journal of Mathematical Economics 26, no. 4 (1996): 441–62. http://dx.doi.org/10.1016/0304-4068(95)00760-1.

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23

Chen, Bo, SongSong Li, and YuZhong Zhang. "Strong stability of Nash equilibria in load balancing games." Science China Mathematics 57, no. 7 (April 16, 2014): 1361–74. http://dx.doi.org/10.1007/s11425-014-4814-2.

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24

Yu, Jian, and Dingtao Peng. "Generic stability of Nash equilibria for noncooperative differential games." Operations Research Letters 48, no. 2 (March 2020): 157–62. http://dx.doi.org/10.1016/j.orl.2020.02.001.

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25

Shubik, Martin. "Stability and Perfection of Nash Equilibria (Eric van Damme)." SIAM Review 32, no. 2 (June 1990): 332–33. http://dx.doi.org/10.1137/1032072.

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26

Yu, Hai Dong. "Analysis of Combined Activity in Collaborative Information Seeking Based on Game Theory." Advanced Materials Research 850-851 (December 2013): 1044–47. http://dx.doi.org/10.4028/www.scientific.net/amr.850-851.1044.

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The paper studied the game strategy decisions of alliance leader and members in collaborative information seeking. Based on basic Nash equilibrium model with complete information, it researched Bayesian-Nash equilibrium under incomplete information condition which further implied that the incompleteness of information had effected on the alliance leader’s compensation policy. Furthermore, it revealed a methodology to analyze the stability of Bayesian-Nash equilibrium and gave a detailed algorithm. It provided a framework to systematically explore the relationships between alliance leader and other members while solving work tasks in collaboration.

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27

Wei, Longfei, Haiwei Wang, Jing Wang, and Jialong Hou. "Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market." Discrete Dynamics in Nature and Society 2021 (June 19, 2021): 1–18. http://dx.doi.org/10.1155/2021/3985367.

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This paper investigates the dynamical behaviors of a Stackelberg mixed duopoly game with price competition in the insurance market, involving one state-owned public insurance company and one private insurance company. We study and compare the stability conditions for the Nash equilibrium points of two sequential-move games, public leadership, and private leadership games. Numerical simulations present complicated dynamic behaviors. It is shown that the Nash equilibrium becomes unstable as the price adjustment speed increases, and the system eventually becomes chaotic via flip bifurcation. Moreover, the time-delayed feedback control is used to force the system back to stability.

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28

TANG, ZHILI. "UNCERTAINTY BASED ROBUST OPTIMIZATION IN AERODYNAMICS." Modern Physics Letters B 23, no. 03 (January 30, 2009): 477–80. http://dx.doi.org/10.1142/s0217984909018692.

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The Taguchi robust design concept is combined with the multi-objective deterministic optimization method to overcome single point design problems in Aerodynamics. Starting from a statistical definition of stability, the method finds, Nash equilibrium solutions for performance and its stability simultaneously.

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29

Zhang, Jixiang, and Xuan Xi. "Complexity Analysis of a 3-Player Game with Bounded Rationality Participating in Nitrogen Emission Reduction." Complexity 2020 (April 27, 2020): 1–16. http://dx.doi.org/10.1155/2020/2069614.

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In this paper, a decision-making competition game model concerning governments, agricultural enterprises, and the public, all of which participate in the reduction of nitrogen emissions in the watersheds, is established based on bounded rationality. First, the stability conditions of the equilibrium points in the system are discussed, and the stable region of the Nash equilibrium is determined. Then, the bifurcation diagram, maximal Lyapunov exponent, strange attractor, and sensitive dependence on the initial conditions are shown through numerical simulations. The research shows that the adjustment speed of three players’ decisions may alter the stability of the Nash equilibrium point and lead to chaos in the system. Among these decisions, a government’s decision has the largest effect on the system. In addition, we find that some parameters will affect the stability of the system; when the parameters become beneficial for enterprises to reduce nitrogen emissions, the increase in the parameters can help control the chaotic market. Finally, the delay feedback control method is used to successfully control the chaos in the system and stabilize it at the Nash equilibrium point. The research of this paper is of great significance to the environmental governance decisions and nitrogen reduction management.

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30

Sarafopoulos, Georges, and Panagiotis G. Ioannidis. "Institutional Reforms and Interaction of Local Governments." International Journal of Productivity Management and Assessment Technologies 3, no. 2 (July 2015): 25–33. http://dx.doi.org/10.4018/ijpmat.2015070103.

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The paper considers the interaction between regions during the implementation of a reform, on regional development through a discrete dynamical system based on replicator dynamics. The existence and stability of equilibria of this system are studied. The authors show that the parameter of the local prosperity may change the stability of equilibrium and cause a structure to behave chaotically. For the low values of this parameter the game has a stable Nash equilibrium. Increasing these values, the Nash equilibrium becomes unstable, through period-doubling bifurcation. The complex dynamics, bifurcations and chaos are displayed by computing numerically Lyapunov numbers, sensitive dependence on initial conditions and the box dimension.

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31

Tu, Hongliang, Xueli Zhan, and Xiaobing Mao. "Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities." Discrete Dynamics in Nature and Society 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/7384150.

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We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos.

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32

Xiang, Shuwen, Shunyou Xia, Jihao Yang, Yanlong He, and Chenwei Liu. "Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria." Journal of Nonlinear Sciences and Applications 10, no. 07 (July 16, 2017): 3599–611. http://dx.doi.org/10.22436/jnsa.010.07.20.

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33

Elsadany, A. A., and A. E. Matouk. "Dynamic Cournot Duopoly Game with Delay." Journal of Complex Systems 2014 (June 19, 2014): 1–7. http://dx.doi.org/10.1155/2014/384843.

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The delay Cournot duopoly game is studied. Dynamical behaviors of the game are studied. Equilibrium points and their stability are studied. The results show that the delayed system has the same Nash equilibrium point and the delay can increase the local stability region.

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34

Bressan, Alberto, and Hongxu Wei. "Dynamic stability of the Nash equilibrium for a bidding game." Analysis and Applications 14, no. 04 (April 27, 2016): 591–614. http://dx.doi.org/10.1142/s0219530515500098.

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A one-sided limit order book is modeled as a noncooperative game for several players. An external buyer asks for an amount [Formula: see text] of a given asset. This amount will be bought at the lowest available price, as long as the price does not exceed an upper bound [Formula: see text]. One or more sellers offer various quantities of the asset at different prices, competing to fulfill the incoming order. The size [Formula: see text] of the order and the maximum acceptable price [Formula: see text] are not a priori known, and thus regarded as random variables. In this setting, we prove that a unique Nash equilibrium exists, where each seller optimally prices his assets in order to maximize his own expected profit. Furthermore, a dynamics is introduced, assuming that each player gradually adjusts his pricing strategy in reply to the strategies adopted by all other players. In the case of (i) infinitely many small players or (ii) two large players with one dominating the other, we show that the pricing strategies asymptotically converge to the Nash equilibrium.

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35

Askar, S. S., and A. Al-khedhairi. "Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control." Discrete Dynamics in Nature and Society 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/2585708.

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Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES) is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu’s mechanism to update their productions. Puu’s mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.

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36

POULSEN, ANDERS. "ON THE EVOLUTIONARY STABILITY OF "TOUGH" BARGAINING BEHAVIOR." International Game Theory Review 05, no. 01 (March 2003): 63–71. http://dx.doi.org/10.1142/s0219198903000891.

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This paper investigates whether "tough" bargaining behavior, which gives rise to inefficiency, can be evolutionarily stable. We show that in a two-stage Nash Demand Game such behavior survives. Indeed, almost all the surplus may be wasted. We also study the Ultimatum Game. Here evolutionary selection wipes out all tough behavior, as long as the Proposer does not directly observe the Responder's commitment to rejecting low offers.

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37

Li, Yingwei. "Pointwise stability of reaction diffusion fronts." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (March 25, 2019): 2216–54. http://dx.doi.org/10.1017/prm.2019.6.

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AbstractUsing pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential convergence in weighted Lp and Sobolev norms, while capturing the new feature of spatial diffusion at Gaussian rate. Novel features of the argument are a pointwise Green function decomposition reconciling spectral decomposition and short-time Nash-Aronson estimates and an instantaneous tracking scheme similar to that used in the study of stability of viscous shock waves.

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38

Bilò, Vittorio, Angelo Fanelli, Michele Flammini, Gianpiero Monaco, and Luca Moscardelli. "Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation." Journal of Artificial Intelligence Research 62 (June 21, 2018): 315–71. http://dx.doi.org/10.1613/jair.1.11211.

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We consider fractional hedonic games, a subclass of coalition formation games that can be succinctly modeled by means of a graph in which nodes represent agents and edge weights the degree of preference of the corresponding endpoints. The happiness or utility of an agent for being in a coalition is the average value she ascribes to its members. We adopt Nash stable outcomes as the target solution concept; that is we focus on states in which no agent can improve her utility by unilaterally changing her own group. We provide existence, efficiency and complexity results for games played on both general and specific graph topologies. As to the efficiency results, we mainly study the quality of the best Nash stable outcome and refer to the ratio between the social welfare of an optimal coalition structure and the one of such an equilibrium as to the price of stability. In this respect, we remark that a best Nash stable outcome has a natural meaning of stability, since it is the optimal solution among the ones which can be accepted by selfish agents. We provide upper and lower bounds on the price of stability for different topologies, both in case of weighted and unweighted edges. Beside the results for general graphs, we give refined bounds for various specific cases, such as triangle-free, bipartite graphs and tree graphs. For these families, we also show how to efficiently compute Nash stable outcomes with provable good social welfare.

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39

Crawford. "Nash Equilibrium and Evolutionary Stability in Large and Finite Populations." Annales d'Économie et de Statistique, no. 25/26 (1992): 299. http://dx.doi.org/10.2307/20075868.

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40

Olsen, Martin. "Nash Stability in Additively Separable Hedonic Games and Community Structures." Theory of Computing Systems 45, no. 4 (January 27, 2009): 917–25. http://dx.doi.org/10.1007/s00224-009-9176-8.

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41

Carmona, Guilherme, and Konrad Podczeck. "Ex-post stability of Bayes–Nash equilibria of large games." Games and Economic Behavior 74, no. 1 (January 2012): 418–30. http://dx.doi.org/10.1016/j.geb.2011.06.005.

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42

Schilling, René L., and Jian Wang. "Functional inequalities and subordination: stability of Nash and Poincaré inequalities." Mathematische Zeitschrift 272, no. 3-4 (November 26, 2011): 921–36. http://dx.doi.org/10.1007/s00209-011-0964-x.

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Monaco, Gianpiero, Luca Moscardelli, and Yllka Velaj. "Additively Separable Hedonic Games with Social Context." Games 12, no. 3 (September 18, 2021): 71. http://dx.doi.org/10.3390/g12030071.

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In hedonic games, coalitions are created as a result of the strategic interaction of independent players. In particular, in additively separable hedonic games, every player has valuations for all other ones, and the utility for belonging to a coalition is given by the sum of the valuations for all other players belonging to it. So far, non-cooperative hedonic games have been considered in the literature only with respect to totally selfish players. Starting from the fundamental class of additively separable hedonic games, we define and study a new model in which, given a social graph, players also care about the happiness of their friends: we call this class of games social context additively separable hedonic games (SCASHGs). We focus on the fundamental stability notion of Nash equilibrium, and study the existence, convergence and performance of stable outcomes (with respect to the classical notions of price of anarchy and price of stability) in SCASHGs. In particular, we show that SCASHGs are potential games, and therefore Nash equilibria always exist and can be reached after a sequence of Nash moves of the players. Finally, we provide tight or asymptotically tight bounds on the price of anarchy and the price of stability of SCASHGs.

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44

Balliu, Alkida, Michele Flammini, Giovanna Melideo, and Dennis Olivetti. "On Non-Cooperativeness in Social Distance Games." Journal of Artificial Intelligence Research 66 (November 11, 2019): 625–53. http://dx.doi.org/10.1613/jair.1.11808.

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We consider Social Distance Games (SDGs), that is cluster formation games in which the utility of each agent only depends on the composition of the cluster she belongs to, proportionally to her harmonic centrality, i.e., to the average inverse distance from the other agents in the cluster. Under a non-cooperative perspective, we adopt Nash stable outcomes, in which no agent can improve her utility by unilaterally changing her coalition, as the target solution concept. Although a Nash equilibrium for a SDG can always be computed in polynomial time, we obtain a negative result concerning the game convergence and we prove that computing a Nash equilibrium that maximizes the social welfare is NP-hard by a polynomial time reduction from the NP-complete Restricted Exact Cover by 3-Sets problem. We then focus on the performance of Nash equilibria and provide matching upper bound and lower bounds on the price of anarchy of Θ(n), where n is the number of nodes of the underlying graph. Moreover, we show that there exists a class of SDGs having a lower bound on the price of stability of 6/5 − ε, for any ε > 0. Finally, we characterize the price of stability 5 of SDGs for graphs with girth 4 and girth at least 5, the girth being the length of the shortest cycle in the graph.

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45

Askar, S. S., and A. Al-khedhairi. "Investigations of Nonlinear Triopoly Models with Different Mechanisms." Complexity 2019 (December 19, 2019): 1–15. http://dx.doi.org/10.1155/2019/4252151.

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This paper studies the dynamic characteristics of triopoly models that are constructed based on a 3-dimensional Cobb–Douglas utility function. The paper presents two parts. The first part introduces a competition among three rational firms on which their prices are isoelastic functions. The competition is described by a 3-dimensional discrete dynamical system. We examine the impact of rationality on the system’s steady state point. Studying the stability/instability of this point, which is Nash equilibrium and is unique in those models, is illustrated. Numerically, we give some global analysis of Nash point and its stability. The second part deals with heterogeneous scenarios. It consists of two different models. In the first model, we assume that one competitor adopts the local monopolistic approximation mechanism (LMA) while the other opponents are rational. The second model assumes two heterogeneous players with LMA mechanism against one rational firm. Studies show that the stability of NE point of those models is not guaranteed. Furthermore, simulation shows that when firms behave rational with symmetric costs, the stability of NE point is achievable.

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T.M., Rofin, and Biswajit Mahanty. "Impact of price adjustment speed on the stability of Bertrand–Nash equilibrium and profit of the retailers." Kybernetes 47, no. 8 (September 3, 2018): 1494–523. http://dx.doi.org/10.1108/k-08-2017-0301.

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Purpose The purpose of this paper is to investigate the impact of price adjustment speed on the stability of Bertrand–Nash equilibrium in the context of a dual-channel supply chain competition. Design/methodology/approach The paper considers a dual-channel supply chain comprising a manufacturer, a traditional retailer and an online retailer. A two-dimensional discrete dynamical system is used to examine the Bertrand competition between the retailers. The retailers are assumed to follow bounded rational expectations. Local stability of Bertrand–Nash equilibrium is investigated with respect to the price adjustment speed. Findings As the price adjustment speed increases, the stability of Bertrand–Nash equilibrium is lost, leading to complex chaotic dynamics. The results showed that chaotic dynamics deteriorates the profit of the retailers. The authors also found that the chaos can be controlled using an adaptive adjustment mechanism and the retailers enjoy higher profit when the chaos is controlled. Practical implications This study helps retail managers to choose an appropriate price adjustment speed to maximize profit. Originality/value The heterogeneity of the retailers is not considered in the studies involving dynamics of retailer competition. This paper contributes to the literature by considering the operational difference between a traditional retailer and an online retailer, i.e. price adjustment speed. In addition, the study establishes a link between price adjustment speed and profit.

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Van Essen, Matt. "Information complexity, punishment, and stability in two Nash efficient Lindahl mechanisms." Review of Economic Design 16, no. 1 (December 28, 2011): 15–40. http://dx.doi.org/10.1007/s10058-011-0112-4.

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Channuie, Phongpichit, Davood Momeni, and Mudhahir Al Ajmi. "On Nash theory of gravity with matter contents." International Journal of Modern Physics A 36, no. 02 (January 20, 2021): 2150006. http://dx.doi.org/10.1142/s0217751x21500068.

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One of the alternative theories to Einstein’s general theory, a divergence-free theory was proposed by J. Nash with Lagrangian density given by [Formula: see text]. Although it was proved that the Nash theory does not have classical Einstein limits, it has been proven to be formally divergent free and considered to be of interest in constructing theories of quantum gravity. The original Nash gravity without matter contents cannot explain the current acceleration expansion of the Universe. A possible extension of theory is by adding some matter contents to the model. In this work, we generalize Nash theory of gravity by adding the matter fields. In order to examine the effects of this generalization, we first derive the equations of motion in the flat FLRW space–time and examine the behaviors of the solutions by invoking specific forms of the Hubble parameter. We also classify the physical behaviors of the solutions by employing the stability analysis and check the consistency of the model by considering particular cosmological parameters.

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BILÒ, VITTORIO. "THE PRICE OF NASH EQUILIBRIA IN MULTICAST TRANSMISSION GAMES." Journal of Interconnection Networks 11, no. 03n04 (September 2010): 97–120. http://dx.doi.org/10.1142/s0219265910002751.

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We consider the problem of sharing the cost of multicast transmissions in non-cooperative undirected networks where a set of receivers R wants to be connected to a common source s. The set of choices available to each receiver r ∈ R is represented by the set of all (s, r)-paths in the network. Given the choices performed by all the receivers, a public known cost sharing method determines the cost share to be charged to each of them. Receivers are selfish agents aiming to obtain the transmission at the minimum cost share and their interactions create a non-cooperative game. Devising cost sharing methods yielding games whose price of anarchy (price of stability), defined as the worst-case (best-case) ratio between the cost of a Nash equilibrium and that of an optimal solution, is not too high is thus of fundamental importance in non-cooperative network design. Moreover, since cost sharing games naturally arise in socio-economical contests, it is convenient for a cost sharing method to meet some constraining properties. In this paper, we first define several such properties and analyze their impact on the prices of anarchy and stability. We also reconsider all the methods known so far by classifying them according to which properties they satisfy and giving the first non-trivial lower bounds on their price of stability. Finally, we propose a new method, namely the free-riders method, which admits a polynomial time algorithm for computing a pure Nash equilibrium whose cost is at most twice the optimal one. Some of the ideas characterizing our approach have been independently proposed in Ref. 10.

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PIERI, GRAZIANO, and ANNA TORRE. "HADAMARD AND TYKHONOV WELL-POSEDNESS IN TWO PLAYER GAMES." International Game Theory Review 05, no. 04 (December 2003): 375–84. http://dx.doi.org/10.1142/s0219198903001124.

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We give a suitable definition of Hadamard well-posedness for Nash equilibria of a game, that is, the stability of Nash equilibrium point with respect to perturbations of payoff functions. Our definition generalizes the analogous notion for minimum problems. For a game with continuous payoff functions, we restrict ourselves to Hadamard well-posedness with respect to uniform convergence and compare this notion with Tykhonov well-posedness of the same game. The main results are: Hadamard implies Tykhonov well-posedness and the converse is true if the payoff functions are bounded. For a zero-sum game the two notions are equivalent.

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Journal articles on the topic 'Nash stability'

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