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Journal articles on the topic 'Equilibria'

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Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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1

CANOVAS, SABRINA GOMEZ, PIERRE HANSEN, and BRIGITTE JAUMARD. "NASH EQUILIBRIA FROM THE CORRELATED EQUILIBRIA VIEWPOINT." International Game Theory Review 01, no. 01 (March 1999): 33–44. http://dx.doi.org/10.1142/s0219198999000049.

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We consider Nash equilibria as correlated equilibria and apply polyhedral theory to study extreme Nash equilibrium properties. We obtain an alternate proof that extreme Nash equilibria are extreme correlated equilibria and give some characteristics of them. Furthermore, we study a class of games that have no completely mixed Nash equilibria.

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2

Ohnishi, Kazuhiro. "Non-altruistic Equilibria." Indian Economic Journal 67, no. 3-4 (December 2019): 185–95. http://dx.doi.org/10.1177/0019466220953124.

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Which choice will a player make if he can make one of two choices in which his own payoffs are equal, but his rival’s payoffs are not equal, that is, one with a large payoff for his rival and the other with a small payoff for his rival? This paper introduces non-altruistic equilibria for normal-form games and extensive-form non-altruistic equilibria for extensive-form games as equilibrium concepts of non-cooperative games by discussing such a problem and examines the connections between their equilibrium concepts and Nash and subgame perfect equilibria that are important and frequently encountered equilibrium concepts.

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3

WARD, SEAMUS A., and IAN W. B. THORNTON. "Equilibrium theory and alternative stable equilibria." Journal of Biogeography 25, no. 4 (July 1998): 615–22. http://dx.doi.org/10.1046/j.1365-2699.1998.2540615.x.

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4

Kudryavtsev, Konstantin, and Ustav Malkov. "Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation." Open Computer Science 11, no. 1 (December 17, 2020): 127–34. http://dx.doi.org/10.1515/comp-2020-0210.

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AbstractThe paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

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5

Yang, Qigui, and Xinmei Qiao. "Constructing a New 3D Chaotic System with Any Number of Equilibria." International Journal of Bifurcation and Chaos 29, no. 05 (May 2019): 1950060. http://dx.doi.org/10.1142/s0218127419500603.

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In the chaotic polynomial Lorenz-type systems (including Lorenz, Chen, Lü and Yang systems) and Rössler system, their equilibria are unstable and the number of the hyperbolic equilibria are no more than three. This paper shows how to construct a simple analytic (nonpolynomial) chaotic system that can have any preassigned number of equilibria. A special 3D chaotic system with no equilibrium is first presented and discussed. Using a methodology of adding a constant controller to the third equation of such a chaotic system, it is shown that a chaotic system with any preassigned number of equilibria can be generated. Two complete mathematical characterizations for the number and stability of their equilibria are further rigorously derived and studied. This system is very interesting in the sense that some complex dynamics are found, revealing many amazing properties: (i) a hidden chaotic attractor exists with no equilibria or only one stable equilibrium; (ii) the chaotic attractor coexists with unstable equilibria, including two/five unstable equilibria; (iii) the chaotic attractor coexists with stable equilibria and unstable equilibria, including one stable and two unstable equilibria/94 stable and 93 unstable equilibria; (iv) the chaotic attractor coexists with infinitely many nonhyperbolic isolated equilibria. These results reveal an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of some unusual chaotic systems.

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6

THROUMOULOPOULOS, G. N., and H. TASSO. "Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows." Journal of Plasma Physics 62, no. 4 (October 1999): 449–59. http://dx.doi.org/10.1017/s0022377899008041.

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A recent study on axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas5, 2378 (1998)] is extended to the generic case of helically symmetric equilibria with incompressible flows. It is shown that the equilibrium states of the system under consideration are governed by an elliptic partial differential equation for the helical magnetic flux function containing five surface quantities along with a relation for the pressure. The above-mentioned equation can be transformed to one possessing a differential part identical in form to the corresponding static equilibrium equation, which is amenable to several classes of analytical solutions. In particular, equilibria with electric fields perpendicular to the magnetic surfaces and non-constant-Mach-number flows are constructed. Unlike the case in axisymmetric equilibria with isothermal magnetic surfaces, helically symmetric T = T(ψ) equilibria are overdetermined, i.e. in this case the equilibrium equations reduce to a set of eight ordinary differential equations with seven surface quantities. In addition, the non-existence is proved of incompressible helically symmetric equilibria with (a) purely helical flows and (b) non-parallel flows with isothermal magnetic surfaces and with the magnetic field modulus a surface quantity (omnigenous equilibria).

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7

Liu, Bing, Wanbo Liu, Fennmei Tao, Baolin Kang, and Jiguang Cong. "A Dynamical Analysis of a Piecewise Smooth Pest Control SI Model." International Journal of Bifurcation and Chaos 25, no. 05 (May 2015): 1550068. http://dx.doi.org/10.1142/s0218127415500686.

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In this paper, we propose a piecewise smooth SI pest control system to model the process of spraying pesticides and releasing infectious pests. We assume that the pest population consists of susceptible pests and infectious pests, and that the disease spreads horizontally between pests. We take the susceptible pest as the control index on whether to implement chemical control and biological control strategies. Based on the theory of Filippov system, the sliding-mode domain and conditions for the existence of real equilibria, virtual equilibria, pseudo-equilibrium and boundary equilibria are given. Further, we show the global stability of real equilibria (or boundary equilibria) and pseudo-equilibrium. Our results can provide theoretical guidance for the problem of pest control.

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8

Васин, Александр Алексеевич, Alexander Vasin, Ирина Юрьевна Серёгина, and Irina Seregina. "Sequential equlibria in signaling games." Mathematical Game Theory and Applications 14, no. 1 (January 18, 2023): 3–20. http://dx.doi.org/10.17076/mgta_2022_1_42.

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The paper considers Bayesian multi-stage signaling games. Previously formulated for extensive-form games, concepts of sequential equilibrium, separating equilibrium and pooling equilibrium are specified, and calculating methods for these equilibria are also discussed. A competitive collision model with signals indicating rivals' states is studied as a specific example. We determine conditions for existence of separating and pooling equilibria with ordered competition, in which the competition object goes to one of the rivals without a rigid encounter. Model parameters ranges of the equilibria existence are also determined.

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9

Gregoir, Stéphane, and Pierre-Olivier Weill. "Restricted perception equilibria and rational expectation equilibrium." Journal of Economic Dynamics and Control 31, no. 1 (January 2007): 81–109. http://dx.doi.org/10.1016/j.jedc.2005.10.001.

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10

Levine, David K. "Nash equilibria equal competitive equilibria." Economics Letters 25, no. 4 (January 1987): 301–2. http://dx.doi.org/10.1016/0165-1765(87)90080-2.

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11

Zhong, Chongyi, Hui Yang, and Chun Wang. "Refinements of Equilibria for Population Games Based on Bounded Rationality of Agents." Mathematical Problems in Engineering 2020 (April 9, 2020): 1–8. http://dx.doi.org/10.1155/2020/1636294.

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We consider stability of equilibria for population games against slight perturbation on the social state space. We provide a necessary and sufficient condition for the existence of Nash equilibria for perturbed population games, which is very important and interesting. Then, refinements of equilibria for population games are introduced. Equivalent characterizations of perfect equilibrium are given. At last, it is shown that each population game admits at least one perfect (proper, weakly proper, and robust) equilibrium.

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12

HUANG, HUI, and SHUNMING ZHANG. "PROPOSITIONS OF FIVE EQUILIBRIA EXAMPLES FOR 3×2 CES/LES PURE EXCHANGE ECONOMIES." International Journal of Information Technology & Decision Making 03, no. 04 (December 2004): 583–604. http://dx.doi.org/10.1142/s0219622004001264.

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This paper reports numerical examples for a 3 individual 2 good CES/LES pure exchange economy in which 5 equilibria exist. We explore the size of the regions of the parameter space for which 5 equilibria persist, and show these ranges to be very small in each parameter. Other features of the equilibrium manifolds are examined. The number of equilibria can jump from 5 to 3 to 1, or even from 5 to 1. We also find changes of (Kehoe) equilibrium indices from -1 to +1 or from +1 to -1. Then, we provide parameter changes simultaneously in a large range that preserve given 5 equilibria.

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13

FARMER, ROGER E. A., and MICHAEL WOODFORD. "SELF-FULFILLING PROPHECIES AND THE BUSINESS CYCLE." Macroeconomic Dynamics 1, no. 4 (December 1997): 740–69. http://dx.doi.org/10.1017/s1365100597005051.

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We demonstrate that multiple stationary rational-expectations equilibria exist in a version of Lucas's island economy. The existence of these equilibria follows from the fact that there is an indeterminate set of monetary equilibria in the two-period overlapping-generations model. We show how to construct stationary rational-expectations equilibria by randomizing over the set of nonstationary monetary equilibria. In some of our equilibria, a positively sloped Phillips curve exists even though our economy contains no signal-extraction problem as in the original Lucas paper. Our equilibria are indexed by beliefs and are examples of the existence of sunspot equilibria in which allocations may differ across states of nature for which preferences, technology, and endowments are identical. Our technique for constructing stationary sunspot equilibria should prove useful in a wide class of models in which an indeterminate stationary equilibrium exists.

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14

Mossel, Elchanan, Manuel Mueller-Frank, Allan Sly, and Omer Tamuz. "Social Learning Equilibria." Econometrica 88, no. 3 (2020): 1235–67. http://dx.doi.org/10.3982/ecta16465.

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We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce social learning equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.

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15

Krishnamurthy, Vikas S., Miles H. Wheeler, Darren G. Crowdy, and Adrian Constantin. "A transformation between stationary point vortex equilibria." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2240 (August 2020): 20200310. http://dx.doi.org/10.1098/rspa.2020.0310.

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A new transformation between stationary point vortex equilibria in the unbounded plane is presented. Given a point vortex equilibrium involving only vortices with negative circulation normalized to −1 and vortices with positive circulations that are either integers or half-integers, the transformation produces a new equilibrium with a free complex parameter that appears as an integration constant. When iterated the transformation can produce infinite hierarchies of equilibria, or finite sequences that terminate after a finite number of iterations, each iteration generating equilibria with increasing numbers of point vortices and free parameters. In particular, starting from an isolated point vortex as a seed equilibrium, we recover two known infinite hierarchies of equilibria corresponding to the Adler–Moser polynomials and a class of polynomials found, using very different methods, by Loutsenko (Loutsenko 2004 J. Phys. A: Math. Gen. 37 , 1309–1321 (doi:10.1088/0305-4470/37/4/017)). For the latter polynomials, the existence of such a transformation appears to be new. The new transformation, therefore, unifies a wide range of disparate results in the literature on point vortex equilibria.

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16

Chen, Sheng, and Antonio J. Conejo. "Strategic-Agent Equilibria in the Operation of Natural Gas and Power Markets." Energies 13, no. 4 (February 17, 2020): 868. http://dx.doi.org/10.3390/en13040868.

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We consider strategic gas/power producers and strategic gas/power consumers operating in both gas and power markets. We build a flexible multi-period complementarity model to characterize day-ahead equilibria in those markets. This model is an equilibrium program with equilibrium constraints that characterizes the market behavior of all market agents. Using a realistic case study, we analyze equilibria under perfect and oligopolistic competition. We also analyze equilibria under different levels of information disclosure regarding market outcomes. We study as well equilibria under different ownership schemes: no hybrid agent, some hybrid agents, and only hybrid agents. Finally, we derive policy recommendations for the regulators of both the gas and the power markets.

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17

MUSY, OLIVIER, ANTONIN POTTIER, and TARIK TAZDAIT. "A NEW THEOREM TO FIND BERGE EQUILIBRIA." International Game Theory Review 14, no. 01 (March 2012): 1250005. http://dx.doi.org/10.1142/s0219198912500053.

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This paper examines the existence of Berge equilibrium. Colman et al. provide a theorem on the existence of this type of equilibrium in the paper [Colman, A. M., Körner, T. W., Musy, O. and Tazdaït, T. [2011] Mutual support in games: Some properties of Berge equilibria, J. Math. Psychol.55, 166–175]. This theorem has been demonstrated on the basis of a correspondence with Nash equilibrium. We propose to restate this theorem without using Nash equilibrium, and deduce a method for the computation of Berge equilibria.

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18

Duffy, John, and Daniela Puzzello. "Gift Exchange versus Monetary Exchange: Theory and Evidence." American Economic Review 104, no. 6 (June 1, 2014): 1735–76. http://dx.doi.org/10.1257/aer.104.6.1735.

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We study the Lagos and Wright (2005) model of monetary exchange in the laboratory. With a finite population of sufficiently patient agents, this model has a unique monetary equilibrium and a continuum of non-monetary gift exchange equilibria, some of which Pareto dominate the monetary equilibrium. We find that subjects avoid the gift exchange equilibria in favor of the monetary equilibrium. We also study versions of the model without money where all equilibria involve non-monetary gift exchange. We find that welfare is higher in the model with money than without money, suggesting that money plays a role as an efficiency enhancing coordination device. ( JEL C92, D12, E40, Z13)

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19

Albouy, Alain, and Yanning Fu. "Relative equilibria of four identical satellites." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2109 (June 10, 2009): 2633–45. http://dx.doi.org/10.1098/rspa.2009.0115.

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We consider the Newtonian 5-body problem in the plane, where four bodies have the same mass m , which is small compared with the mass M of the remaining body. We consider the (normalized) relative equilibria in this system and follow them to the limit when m / M →0. In some cases, two small bodies will coalesce at the limit. We call the other equilibria the relative equilibria of four separate identical satellites. We prove rigorously that there are only three such equilibria, all already known after the numerical researches by H. Salo and C. F. Yoder. Our main contribution is to prove that any equilibrium configuration possesses a symmetry, a statement indicated by J. Llibre as the missing key to proving that there is no other equilibrium.

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20

Pálla, Tamás, Arash Mirzahosseini, and Béla Noszál. "Species-Specific, pH-Independent, Standard Redox Potential of Selenocysteine and Selenocysteamine." Antioxidants 9, no. 6 (June 1, 2020): 465. http://dx.doi.org/10.3390/antiox9060465.

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Microscopic redox equilibrium constants and standard redox potential values were determined to quantify selenolate-diselenide equilibria of biological significance. The highly composite, codependent acid-base and redox equilibria of selenolates could so far be converted into pH-dependent, apparent parameters (equilibrium constants, redox potentials) only. In this work, the selenolate-diselenide redox equilibria of selenocysteamine and selenocysteine against dithiothreitol were analyzed by quantitative nuclear magnetic resonance (NMR) methods to characterize the interfering acid-base and redox equilibria. The directly obtained, pH-dependent, conditional redox equilibrium constants were then decomposed by our method into pH-independent, microscopic constants, which characterize the two-electron redox transitions of selenocysteamine and selenocysteine. The 12 different, species-specific parameter values show close correlation with the respective selenolate basicities, providing a tool to estimate otherwise inaccessible site-specific selenolate-diselenide redox potentials of related moieties in large peptides and proteins.

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21

Bellon, Gilles, and Adam H. Sobel. "Multiple Equilibria of the Hadley Circulation in an Intermediate-Complexity Axisymmetric Model." Journal of Climate 23, no. 7 (April 1, 2010): 1760–78. http://dx.doi.org/10.1175/2009jcli3105.1.

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Abstract A model of intermediate complexity based on quasi-equilibrium theory—a version of the Quasi-Equilibrium Tropical Circulation Model with a prognostic atmospheric boundary layer, as well as two free-tropospheric modes in momentum, and one each in moisture and temperature—is used in a zonally symmetric aquaplanet configuration to study the sensitivity of the Hadley circulation to the sea surface temperature (SST) latitudinal distribution. For equatorially symmetric SST forcing with large SST gradients in the tropics, the model simulates the classical double Hadley cell with one equatorial intertropical convergence zone (ITCZ). For small SST gradients in the tropics, the model exhibits multiple equilibria, with one equatorially symmetric equilibrium and two asymmetric equilibria (mirror images of each other) with an off-equatorial ITCZ. Further investigation of the feedbacks at play in the model shows that the assumed vertical structure of temperature variations is crucial to the existence and stability of the asymmetric equilibria. The free-tropospheric moisture–convection feedback must also be sufficiently strong to sustain asymmetric equilibria. Both results suggest that the specific physics of a given climate model condition determine the existence of multiple equilibria via the resulting sensitivity of the convection to free-tropospheric humidity and the vertical structure of adiabatic heating. The symmetry-breaking mechanism and resulting multiple equilibria have their origin in the local multiple equilibria that can be described by a single-column model using the weak temperature gradient approximation. An additional experiment using an SST latitudinal distribution with a relative minimum at the equator shows that the feedbacks controlling these multiple equilibria might be relevant to the double-ITCZ problem.

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22

Kallman, Joshua B., and Leonid E. Zakharov. "Bishop-Taylor equilibria for calibration equilibrium and equilibrium reconstruction codes." Physics of Plasmas 14, no. 7 (July 2007): 072504. http://dx.doi.org/10.1063/1.2749498.

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23

SWISTAK, PIOTR. "What Games? Why Equilibria? Which Equilibria?" Rationality and Society 4, no. 1 (January 1992): 103–16. http://dx.doi.org/10.1177/1043463192004001012.

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24

GEDALIN, M., A. SPITKOVSKY, M. MEDVEDEV, M. BALIKHIN, V. KRASNOSELSKIKH, A. VAIVADS, and S. PERRI. "Relativistic filamentary equilibria." Journal of Plasma Physics 77, no. 2 (February 18, 2010): 193–205. http://dx.doi.org/10.1017/s002237781000005x.

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AbstractPlasma filamentation is often encountered in collisionless shocks and inertial confinement fusion. We develop a general analytical description of the two-dimensional relativistic filamentary equilibrium and derive the conditions for existence of potential-free equilibria. A pseudopotential equation for the vector-potential is constructed for cold and relativistic Maxwellian distributions. The role of counter-streaming is explained. We present single current sheet and periodic current sheet solutions, and analyze the equilibria with electric potential. These solutions can be used to study linear and nonlinear evolution of the relativistic filamentation instability.

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25

Belhaiza, Slim. "On Perfect Nash Equilibria of Polymatrix Games." Game Theory 2014 (September 29, 2014): 1–11. http://dx.doi.org/10.1155/2014/937070.

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When confronted with multiple Nash equilibria, decision makers have to refine their choices. Among all known Nash equilibrium refinements, the perfectness concept is probably the most famous one. It is known that weakly dominated strategies of two-player games cannot be part of a perfect equilibrium. In general, this undominance property however does not extend to n-player games (E. E. C. van Damme, 1983). In this paper we show that polymatrix games, which form a particular class of n-player games, verify the undominance property. Consequently, we prove that every perfect equilibrium of a polymatrix game is undominated and that every undominated equilibrium of a polymatrix game is perfect. This result is used to set a new characterization of perfect Nash equilibria for polymatrix games. We also prove that the set of perfect Nash equilibria of a polymatrix game is a finite union of convex polytopes. In addition, we introduce a linear programming formulation to identify perfect equilibria for polymatrix games. These results are illustrated on two small game applications. Computational experiments on randomly generated polymatrix games with different size and density are provided.

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26

CURRAN, P. F., and L. O. CHUA. "STABILITY OF EQUILIBRIA OF NEURAL NETWORKS." International Journal of Bifurcation and Chaos 09, no. 10 (October 1999): 1941–55. http://dx.doi.org/10.1142/s0218127499001413.

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Sufficient conditions for local and global asymptotic stability of equilibria of some general classes of neural networks are presented. In the event that the interconnection matrix is block diagonally stable it is shown that the equilibrium is globally asymptotically stable if the cells are dissipative at the equilibrium. For a special class of networks the conditions of dissipativity are reduced to more readily-tested conditions of passivity. Equilibria are shown to be asymptotically stable essentially if the cells are locally passive.

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27

DE MARCO, GIUSEPPE, and JACQUELINE MORGAN. "ALTRUISTIC BEHAVIOR AND CORRELATED EQUILIBRIUM SELECTION." International Game Theory Review 13, no. 04 (December 2011): 363–81. http://dx.doi.org/10.1142/s0219198911003118.

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This paper studies new refinement concepts for correlated equilibria based on altruistic behavior of the players and generalizes some refinement concepts previously developed by the authors for Nash equilibria. Effectiveness of the concepts, relations with the corresponding notions for Nash equilibria and with other correlated equilibrium refinements are investigated. The analysis of the topological properties of the set of solutions concludes the paper.

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28

Farmer, Roger E. A., Daniel F. Waggoner, and Tao Zha. "Generalizing the Taylor Principle: Comment." American Economic Review 100, no. 1 (March 1, 2010): 608–17. http://dx.doi.org/10.1257/aer.100.1.608.

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Troy Davig and Eric Leeper (2007) have proposed a condition they call the generalized Taylor principle to rule out indeterminate equilibria in a version of the new-Keynesian model where the parameters of the policy rule follow a Markov-switching process. We show that although their condition rules out a subset of indeterminate equilibria, it does not establish uniqueness of the fundamental equilibrium. We discuss the differences between indeterminate fundamental equilibria included by Davig and Leeper's condition and fundamental equilibria that their condition misses

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29

Moghadas, S. M., and A. B. Gumel. "An epidemic model for the transmission dynamics of HIV and another pathogen." ANZIAM Journal 45, no. 2 (October 2003): 181–93. http://dx.doi.org/10.1017/s1446181100013250.

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AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.

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30

Balder, Erik J., and Nicholas C. Yannelis. "Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium." Economic Theory 38, no. 2 (October 2, 2007): 385–97. http://dx.doi.org/10.1007/s00199-007-0288-6.

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31

Dritschel, David G. "Equilibria and stability of four point vortices on a sphere." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (September 2020): 20200344. http://dx.doi.org/10.1098/rspa.2020.0344.

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This paper discusses the problem of finding the equilibrium positions of four point vortices, of generally unequal circulations, on the surface of a sphere. A random search method is developed which uses a modification of the linearized equations to converge on distinct equilibria. Many equilibria (47 and possibly more) may exist for prescribed circulations and angular impulse. A linear stability analysis indicates that they are generally unstable, though stable equilibria do exist. Overall, there is a surprising diversity of equilibria, including those which rotate about an axis opposite to the angular impulse vector.

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32

Dumitrescu, Dan Dumitru, Rodica Ioana Lung, and Tudor Dan Mihoc. "Meta-Rationality in Normal Form Games." International Journal of Computers Communications & Control 5, no. 5 (December 1, 2010): 693. http://dx.doi.org/10.15837/ijccc.2010.5.2225.

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A new generative relation for Nash equilibrium is proposed. Different types of equilibria are considered in order to incorporate players different rationality types for finite non cooperative generalized games with perfect information. Proposed equilibria are characterized by use of several generative relations with respect to players rationality. An evolutionary technique for detecting approximations for equilibria is used. Numerical experiments show the potential of the method.

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33

CARBONELL-NICOLAU, ORIOL. "ON EQUILIBRIUM REFINEMENT FOR DISCONTINUOUS GAMES." International Game Theory Review 13, no. 03 (September 2011): 269–80. http://dx.doi.org/10.1142/s021919891100299x.

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In moving from finite-action to infinite-action games, standard refinements of the Nash equilibrium concept cease to satisfy certain "natural" properties. For instance, perfect equilibria in compact, continuous games need not be admissible. This paper highlights additional properties of two standard refinement specifications that are not inherited by supersets of the set of finite games. The analysis reveals the following about the behavior of perfectness and strategic stability within a class of (possibly) discontinuous games: (1) Equilibria that assign positive probability to the interior of the set of strategies weakly dominated for some player can be chosen; (2) nonadmissible equilibria need not be ruled out when they are weakly dominated by admissible perfect equilibria; and (3) nonadmissible equilibria may be selected when admissible equilibria are ruled out.

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34

Pham, Viet-Thanh, Sajad Jafari, and Tomasz Kapitaniak. "Constructing a Chaotic System with an Infinite Number of Equilibrium Points." International Journal of Bifurcation and Chaos 26, no. 13 (December 15, 2016): 1650225. http://dx.doi.org/10.1142/s0218127416502254.

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The chaotic systems with hidden attractors, such as chaotic systems with a stable equilibrium, chaotic systems with infinite equilibria or chaotic systems with no equilibrium have been investigated recently. However, the relationships between them still need to be discovered. This work explains how to transform a system with one stable equilibrium into a new system with an infinite number of equilibrium points by using a memristive device. Furthermore, some other new systems with infinite equilibria are also constructed to illustrate the introduced methodology.

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35

Liu, Lirong, Changcheng Xiang, Guangyao Tang, and Yuan Fu. "Sliding Dynamics of a Filippov Forest-Pest Model with Threshold Policy Control." Complexity 2019 (November 11, 2019): 1–17. http://dx.doi.org/10.1155/2019/2371838.

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A novel Filippov forest-pest system with threshold policy control (TPC) is established while an economic threshold (ET) is used to guide switching. The aim of our work is to address how to reasonably and successfully control pests by means of sliding dynamics for the Filippov system. On the basis of the above considerations, conditions for the existence and stability of equilibria of subsystems are addressed, and the sliding segments and several types of equilibria of the proposed system are defined. These equilibria include the regular/virtual equilibrium, pseudoequilibrium, boundary equilibrium, and tangent point. Further, not only are the relations between nullclines and equilibria of the Filippov system discussed, but the relations between pseudoequilibrium, nullclines, and the sliding segment are discussed. More importantly, four cases of sliding bifurcations of the Filippov system with respect to different types of equilibria of subsystems are investigated, and the corresponding biological implications concerning integrated pest management (IPM) are analyzed. Our results show that the points of intersection between nullclines are equilibria of the system, and the two endpoints of the sliding segment are on the nullclines. It is also verified that the pseudoequilibrium is the point of intersection of the sliding segment and nullclines of the Filippov system, and the pseudoequilibrium exists on the sliding segment. More interestingly, sliding dynamics analysis reveals that the Filippov system has sliding limit cycles, a bistable state and a stable refuge equilibrium point, and the optimal time and strategy for controlling pests are provided.

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Miao, Hui, Xamxinur Abdurahman, and Ahmadjan Muhammadhaji. "Global Stability of HIV-1 Infection Model with Two Time Delays." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/163484.

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We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. Our model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium, and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria of the CTL immune response model has been studied.

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Hoyer, Britta, and Stephanie Rosenkranz. "Determinants of Equilibrium Selection in Network Formation: An Experiment." Games 9, no. 4 (November 2, 2018): 89. http://dx.doi.org/10.3390/g9040089.

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Theoretical models on network formation focus mostly on the stability and efficiency of equilibria, but they cannot deliver an understanding of why specific equilibrium networks are selected or whether they are all actually reachable from any starting network. To study factors affecting equilibrium selection, we designed a network formation experiment with multiple equilibria, which can be categorized in terms of the demand on players’ farsightedness and robustness to errors. In a second scenario, we increase the need for farsighted behavior by players, as well as the perceived riskiness of equilibria by adding a stage in which the network is disrupted. This setting allows us to analyze the interplay between the need for farsightedness and perceived risk of errors and its effect on network formation and equilibrium selection.

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Myerson, Roger B., and Philip J. Reny. "Perfect Conditional ε‐Equilibria of Multi‐Stage Games With Infinite Sets of Signals and Actions." Econometrica 88, no. 2 (2020): 495–531. http://dx.doi.org/10.3982/ecta13426.

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We extend Kreps and Wilson's concept of sequential equilibrium to games with infinite sets of signals and actions. A strategy profile is a conditional ε‐equilibrium if, for any of a player's positive probability signal events, his conditional expected utility is within ε of the best that he can achieve by deviating. With topologies on action sets, a conditional ε‐equilibrium is full if strategies give every open set of actions positive probability. Such full conditional ε‐equilibria need not be subgame perfect, so we consider a non‐topological approach. Perfect conditional ε‐equilibria are defined by testing conditional ε‐rationality along nets of small perturbations of the players' strategies and of nature's probability function that, for any action and for almost any state, make this action and state eventually (in the net) always have positive probability. Every perfect conditional ε‐equilibrium is a subgame perfect ε‐equilibrium, and, in finite games, limits of perfect conditional ε‐equilibria as ε → 0 are sequential equilibrium strategy profiles. But limit strategies need not exist in infinite games so we consider instead the limit distributions over outcomes. We call such outcome distributions perfect conditional equilibrium distributions and establish their existence for a large class of regular projective games. Nature's perturbations can produce equilibria that seem unintuitive and so we augment the game with a net of permissible perturbations.

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Kantorovich, Ye G. "Equilibrium Models of Spatial Interaction with Locational-Capacity Constraints." Environment and Planning A: Economy and Space 24, no. 8 (August 1992): 1077–95. http://dx.doi.org/10.1068/a241077.

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Two types of equilibrium models of urban spatial structures are considered. An equilibrium version of the production-constrained spatial interaction model involving zonal-capacity constraints on allocation is investigated. A model of equilibrium for interacting subsystems is defined (it is a generalisation of Nash equilibria and of some Lowry-type models) and connections between this model and Nash equilibria are investigated. An entropy-projection operator is used for equilibrium urban models with zonal-capacity constraints. Problems of uniqueness of an equilibrium and the convergence of the iterative computational process are studied for these models.

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Yang, Shengxu. "Regional Stability of Switching Control Circuit Systems with Multiple Equilibria." Journal of Physics: Conference Series 2355, no. 1 (October 1, 2022): 012027. http://dx.doi.org/10.1088/1742-6596/2355/1/012027.

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Abstract This paper investigates the stability of systems of multi-equilibrium switching circuits. For a first-order switching circuit system with two subsystems containing unique equilibria and different equilibria, we first establish a sufficient condition for the stability of the region of the multi-equilibrium first-order switching circuit system, and then complete the proof of its stability by means of a general solution of the system state. Secondly, for the second-order multi-equilibrium switching circuit system, the sufficient condition for the stability of the second-order multi-equilibrium switching circuit system is given, and the feasibility of the theorem is finally proved by drawing on existing research results and related sufficient conditions. The conclusions obtained show that the system of first- and second-order multiple equilibria switching circuits in the region is regionally stable after the corresponding switching paths.

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Harks, Tobias, Mona Henle, Max Klimm, Jannik Matuschke, and Anja Schedel. "Multi-Leader Congestion Games with an Adversary." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (June 28, 2022): 5068–75. http://dx.doi.org/10.1609/aaai.v36i5.20439.

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We study a multi-leader single-follower congestion game where multiple users (leaders) choose one resource out of a set of resources and, after observing the realized loads, an adversary (single-follower) attacks the resources with maximum loads causing additional costs for the leaders. For the resulting strategic game among the leaders, we show that pure Nash equilibria fail to exist and therefore, we consider approximate equilibria instead. As our first main result, we show that the existence of a K-approximate equilibrium can always be guaranteed, where K (approximately equal to 1.1974) is the unique solution of a cubic polynomial equation. To this end, we give a polynomial time combinatorial algorithm which computes a K-approximate equilibrium. The factor K is tight, meaning that there is an instance that does not admit an A-approximate equilibrium for any A < K. Thus A = K is the smallest possible value of A such that the existence of an A-approximate equilibrium can be guaranteed for any instance of the considered game. Secondly, we focus on approximate equilibria of a given fixed instance. We show how to compute efficiently a best approximate equilibrium, that is, with smallest possible A among all A-approximate equilibria of the given instance.

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42

Huang, Jicai, Xiaojing Xia, Xinan Zhang, and Shigui Ruan. "Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 26, no. 02 (February 2016): 1650034. http://dx.doi.org/10.1142/s0218127416500346.

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It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results.

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BAUER, CHRISTIAN. "SOLUTION UNIQUENESS IN A CLASS OF CURRENCY CRISIS GAMES." International Game Theory Review 07, no. 04 (December 2005): 531–43. http://dx.doi.org/10.1142/s0219198905000697.

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A common feature of many speculative attack models on currencies is the existence of multiple equilibrium solutions. When choosing the equilibrium strategy, a trader faces Knightian uncertainty about the rational choice of the other traders. We show that the concept of Choquet expected utility maximization under Knightian uncertainty leads to unique equilibria. In games of incomplete information the optimal strategy maximizes the expected utility with respect to a two-dimensional information: environment and rationality. We define a new concept of equilibria, the Choquet-expected-Nash-equilibria, which allows the analysis of decisions under uncertainty, which result in multiple equilibria in standard analysis. We provide uniqueness theorems for a wide class of incomplete information games including global games and apply them to fairly general currency attack models. The uniqueness of the equilibrium remains valid for arbitrary noise distributions, positively correlated signals, the existence of large traders, individual payoff functions, and for the case that non attacking traders suffer a loss in case of a successful attack, as is the case for investors in the attacked country.

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Brautbar, Mickey, Michael Kearns, and Umar Syed. "Private and Third-Party Randomization in Risk-Sensitive Equilibrium Concepts." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 4, 2010): 723–28. http://dx.doi.org/10.1609/aaai.v24i1.7634.

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We consider risk-sensitive generalizations of Nash and correlated equilibria in noncooperative games. We prove that, except for a class of degenerate games, unless a two-player game has a pure Nash equilibrium, it does not have a risk-sensitive Nash equilibrium. We also show that every game has a risk-sensitive correlated equilibrium. The striking contrast between these existence results is due to the different sources of randomization in Nash (private randomization) and correlated equilibria (third-party randomization).

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Chen, Fengde ,., Yanbo ,. Chong, and Shangming Chen. "Global Stability of a Commensal Symbiosis Model With Holling Ii Functional Response and Feedback Controls." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 17 (June 16, 2022): 279–86. http://dx.doi.org/10.37394/23203.2022.17.32.

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A commensal symbiosis model with Holling II functional response and feedback controls is proposed and studied in this paper. The system admits four equilibria, and three boundary equilibria are unstable, only positive equilibrium is locally asymptotically stable. By applying the comparison theorem of differential equation, we show that the unique positive equilibrium is globally attractive. Numeric simulations show the feasibility of the main result.

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Onuchic, Paula, and Debraj Ray. "Signaling and Discrimination in Collaborative Projects." American Economic Review 113, no. 1 (January 1, 2023): 210–52. http://dx.doi.org/10.1257/aer.20211729.

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We study collaborative work in pairs when potential collaborators are motivated by the reputational implications of (joint or solo) projects. In equilibrium, individual collaboration strategies both influence and are influenced by the public assignment of credit for joint work across the two partners. We investigate the fragility of collaboration to small biases in the public’s credit assignment. When collaborators are symmetric, symmetric equilibria are often fragile, and in nonfragile equilibria individuals receive asymmetric collaborative credit based on payoff-irrelevant “identities.” We study payoff distributions across identities within asymmetric equilibria, and compare aggregate welfare across symmetric and asymmetric equilibria. (JEL A11, D82, I23)

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Wang, Xiong, Viet-Thanh Pham, and Christos Volos. "Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium." Complexity 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/7138971.

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After the report of chaotic flows with line equilibrium, there has been much attention to systems with uncountable equilibria in the past five years. This work proposes a new system with an infinite number of equilibrium points located on a closed curve. It is worth noting that the new system generates chaotic behavior as well as hidden attractors. Dynamics of the system with closed curve equilibrium have been investigated by using phase portraits, bifurcation diagram, maximal Lyapunov exponents, and Kaplan–York dimension. In addition, we introduce an electronic implementation of the theoretical system to verify its feasibility. Antisynchronization ability of the new system with infinite equilibria is studied by applying an adaptive control. This study suggests that there exist other chaotic systems with uncountable equilibria in need of further investigation.

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Luo, Demou, and Qiru Wang. "Global Dynamics of a Holling-II Amensalism System with Nonlinear Growth Rate and Allee Effect on the First Species." International Journal of Bifurcation and Chaos 31, no. 03 (March 15, 2021): 2150050. http://dx.doi.org/10.1142/s0218127421500504.

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Of concern is the global dynamics of a two-species Holling-II amensalism system with nonlinear growth rate. The existence and stability of trivial equilibrium, semi-trivial equilibria, interior equilibria and infinite singularity are studied. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, the global dynamics of the model is performed. Next, we incorporate Allee effect on the first species and offer a new analysis of equilibria and bifurcation discussion of the model. Finally, several numerical examples are performed to verify our theoretical results.

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Deckelbaum, Alan. "Can quantum entanglement implement classical correlated equilibria?" Quantum Information and Computation 14, no. 5&6 (May 2014): 493–516. http://dx.doi.org/10.26421/qic14.5-6-7.

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We ask whether players of a classical game can partition a pure quantum state to implement classical correlated equilibrium distributions. The main contribution of this work is an impossibility result: we provide an example of a classical correlated equilibrium that cannot be securely implemented without useful information leaking outside the system. We study the model where players of a classical complete information game initially share an entangled pure quantum state. Players may perform arbitrary local operations on their subsystems, but no direct communication (either quantum or classical) is allowed. We explain why, for the purpose of implementing classical correlated equilibria, it is desirable to restrict the initial state to be pure and to restrict communication. In this framework, we define the concept of pure quantum correlated equilibrium (PQCE) and show that in a normal form game, any outcome distribution implementable by a PQCE can also be implemented by a classical correlated equilibrium (CE), but that the converse is false. We extend our analysis to extensive form games, and compare the power of PQCE to extensive form classical correlated equilibria (EFCE) and immediate-revelation extensive form correlated equilibria (IR-EFCE).

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Ennis, Huberto M. "ON RANDOM MATCHING, MONETARY EQUILIBRIA, AND SUNSPOTS." Macroeconomic Dynamics 5, no. 1 (February 2001): 132–42. http://dx.doi.org/10.1017/s1365100501018065.

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We study comparative statics results for the steady-state monetary equilibria of a simple random matching model of money with endogenous prices and no extrinsic uncertainty. Some of the results appear counterintuitive (both when take-it-or-leave-it offer or when Nash–Rubinstein bargaining is used in the model). Consistency of the equilibrium expectations causes the partial equilibrium intuitions to be reversed. We then proceed to apply the new insights to the analysis of sunspot equilibria in these type of models of bilateral trade with money.

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