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Journal articles on the topic 'Existence of equilibrium'

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Published: 10 March 2023

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1

DEGHDAK, MESSAOUD, and MONIQUE FLORENZANO. "ON THE EXISTENCE OF BERGE'S STRONG EQUILIBRIUM." International Game Theory Review 13, no. 03 (September 2011): 325–40. http://dx.doi.org/10.1142/s0219198911003027.

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In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional space in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibria correspondence and essential games.

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2

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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3

Becker, Robert A., John H. Boyd III, and Ciprian Foias. "The Existence of Ramsey Equilibrium." Econometrica 59, no. 2 (March 1991): 441. http://dx.doi.org/10.2307/2938264.

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4

Bos, Iwan, and Dries Vermeulen. "Equilibrium existence with spillover demand." Economics Letters 208 (November 2021): 110061. http://dx.doi.org/10.1016/j.econlet.2021.110061.

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5

Dastidar, Krishnendu Ghosh. "Existence of Bertrand equilibrium revisited." International Journal of Economic Theory 7, no. 4 (September 21, 2011): 331–50. http://dx.doi.org/10.1111/j.1742-7363.2011.00166.x.

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6

Dasgupta, Partha Sarathi, and Eric S. Maskin. "Debreu’s social equilibrium existence theorem." Proceedings of the National Academy of Sciences 112, no. 52 (December 23, 2015): 15769–70. http://dx.doi.org/10.1073/pnas.1522640113.

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7

Kim, Won Kyu. "A new equilibrium existence theorem." Economics Letters 39, no. 4 (August 1992): 387–90. http://dx.doi.org/10.1016/0165-1765(92)90172-u.

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8

Patriche, Monica. "Equilibrium existence under generalized convexity." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 3 (December 1, 2012): 95–110. http://dx.doi.org/10.2478/v10309-012-01058-8.

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Abstract We introduce, in the first part, the notion of weakly convex pair of correspondences, we give its economic interpretation, we state a fixed point and a selection theorem. Then, by using a tehnique based on a continuous selection, we prove existence theorems of quilibrium for an abstract economy. In the second part, we define the weakly biconvex correspondences, we prove a selection theorem and we also demonstrate the existence of equilibrium for a generalized quasi-game (2003 Kim's model). In the last part of the paper, we give other applications in the game theory, finding equilibrium for abstract economies having correspondences with weakly convex graph. We show that the equilibrium exists without continuity assumptions.

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9

Grimaud, A., and J. J. Laffont. "Existence of a spatial equilibrium." Journal of Urban Economics 25, no. 2 (March 1989): 213–18. http://dx.doi.org/10.1016/0094-1190(89)90035-1.

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10

Wang, S. Y. "Existence of a pareto equilibrium." Journal of Optimization Theory and Applications 79, no. 2 (November 1993): 373–84. http://dx.doi.org/10.1007/bf00940586.

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11

Brookins, Philip, and Dmitry Ryvkin. "Equilibrium existence in group contests." Economic Theory Bulletin 4, no. 2 (October 19, 2015): 265–76. http://dx.doi.org/10.1007/s40505-015-0085-5.

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12

Nielsen, Lars Tyge. "Existence of equilibrium in CAPM." Journal of Economic Theory 52, no. 1 (October 1990): 223–31. http://dx.doi.org/10.1016/0022-0531(90)90076-v.

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13

CUBIOTTI, PAOLO. "EXISTENCE OF GENERALISED PARETO EQUILIBRIA FOR CONSTRAINED MULTIOBJECTIVE GAMES." International Game Theory Review 02, no. 04 (December 2000): 329–44. http://dx.doi.org/10.1142/s021919890000024x.

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A model of multiobjective game is considered where the actual strategy space of each player depends on the other players' behaviour. A notion of generalised Pareto equilibrium is defined, which extends the usual notion of Pareto equilibrium considered in the literature. Existence results for such equilibria are established. In particular, some known results are extended and improved.

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14

Aase, Knut K. "Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization." ASTIN Bulletin 23, no. 2 (November 1993): 185–211. http://dx.doi.org/10.2143/ast.23.2.2005091.

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AbstractThis paper attempts to give an overview of the pricing of risks in a pure exchange economy, where trade takes place at time zero and where uncertainty is revealed at time one. An economic equilibrium model under uncertainty is formulated, where conditions characterizing a Pareto optimal exchange equilibrium are derived. We present two sets of sufficient conditions for the existence of an equilibrium, and demonstrate how equilibria can be characterized through several examples. Uniqueness of equilibrium is also discussed. Special attention is given to the principal components that the premiums in a reinsurance market must depend upon. We also apply the general theory to the risk exchange problem between a policyholder and an insurer, and in particular we compute market premiums of the resulting optimal contracts.It is emphasized throughout how the formulation of a competitive equilibrium, rather than merely a general risk exchange formulation, is of particular interest in deriving a well-defined and unique set of equilibrium premiums in an insurance market. The theory is put into a framework which is fruitful for extensions beyond the one-period case.

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15

Tarafdar, E., and Xian-Zhi Yuan. "Equilibrium points of random generalized games." International Journal of Mathematics and Mathematical Sciences 21, no. 4 (1998): 791–800. http://dx.doi.org/10.1155/s0161171298001100.

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In this paper, the concepts of random maximal elements, random equilibria and random generalized games are described. Secondly by measurable selection theorem, some existence theorems of random maximal elements forLc-majorized correspondences are obtained. Then we prove existence theorems of random equilibria for non-compact one-person random games. Finally, a random equilibrium existence theorem for non-compact random generalized games (resp., random abstract economics) in topological vector spaces and a random equilibrium existence theorem of non-compact random games in locally convex topological vector spaces in which the constraint mappings are lower semicontinuous with countable number of players (resp., agents) are given. Our results are stochastic versions of corresponding results in the recent literatures.

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16

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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17

Wong, Kam-Chau. "Excess demand functions, equilibrium prices, and existence of equilibrium." Economic Theory 10, no. 1 (June 18, 1997): 39–54. http://dx.doi.org/10.1007/s001990050145.

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18

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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19

Enkhbat, R. "A Note on Anti-Berge Equilibrium for Bimatrix Game." Bulletin of Irkutsk State University. Series Mathematics 36 (2021): 3–13. http://dx.doi.org/10.26516/1997-7670.2021.36.3.

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Game theory plays an important role in applied mathematics, economics and decision theory. There are many works devoted to game theory. Most of them deals with a Nash equilibrium. A global search algorithm for finding a Nash equilibrium was proposed in [13]. Also, the extraproximal and extragradient algorithms for the Nash equilibrium have been discussed in [3]. Berge equilibrium is a model of cooperation in social dilemmas, including the Prisoner’s Dilemma games [15]. The Berge equilibrium concept was introduced by the French mathematician Claude Berge [5] for coalition games. The first research works of Berge equilibrium were conducted by Vaisman and Zhukovskiy [18; 19]. A method for constructing a Berge equilibrium which is Pareto-maximal with respect to all other Berge equilibriums has been examined in Zhukovskiy [10]. Also, the equilibrium was studied in [16] from a view point of differential games. Abalo and Kostreva [1; 2] proved the existence theorems for pure-strategy Berge equilibrium in strategic-form games of differential games. Nessah [11] and Larbani, Tazdait [12] provided with a new existence theorem. Applications of Berge equilibrium in social science have been discussed in [6; 17]. Also, the work [7] deals with an application of Berge equilibrium in economics. Connection of Nash and Berge equilibriums has been shown in [17]. Most recently, the Berge equilibrium was examined in Enkhbat and Batbileg [14] for Bimatrix game with its nonconvex optimization reduction. In this paper, inspired by Nash and Berge equilibriums, we introduce a new notion of equilibrium so-called Anti-Berge equilibrium. The main goal of this paper is to examine Anti-Berge equilibrium for bimatrix game. The work is organized as follows. Section 2 is devoted to the existence of Anti-Berge equilibrium in a bimatrix game for mixed strategies. In Section 3, an optimization formulation of Anti-Berge equilibrium has been formulated.

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20

Iskakov, M. B. "Existence theorems for Nash equilibrium and equilibrium in secure strategies." Journal of the New Economic Association 56, no. 4 (2022): 12–27. http://dx.doi.org/10.31737/2221-2264-2022-56-4-1.

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The paper proposes a method for constructing existence theorems for equilibrium in secure strategies (EinSS) on the basis of the well-known existence theorems for Nash equilibrium. The system of defi nitions of the EinSS is interpreted as the development of the logic of rational behavior in the defi nition of Nash equilibrium. It is proved that under the condition of «strong threats» for the existence of EinSS, it is suffi cient to fulfi ll the conditions of the known existence theorem for the Nash equilibrium only on the sets of secure strategies. This statement is formulated both globally and locally, and is an effective tool for application to practical problems. It opens up the possibility of constructing various particular existence theorems for EinSS. As a demonstration of the proposed approach, from the Debreu’s theorem of the existence of social equilibrium, the corresponding theorem of the existence of the EinSS is obtained.

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21

Wen, Kai Ting, and He Rui Li. "The Equilibrium Existence for Constrained Multiobjective Games in GFC-Spaces." Advanced Materials Research 1065-1069 (December 2014): 3450–54. http://dx.doi.org/10.4028/www.scientific.net/amr.1065-1069.3450.

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In this paper, in virtue of a Browder type fixed point theorem in GFC-spaces, equilibrium existence theorems for general quasiequilibrium problems and quasiequilibrium problems are obtained. As application, an existence theorem of weighted Nash-equilibriums for constrained multiobjective games is yielded in GFC-spaces.

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22

Lahiri, Somdeb. "Voluntary Provision of a Public Good in a Strategic Market Game." Recherches économiques de Louvain 79, no. 4 (December 2013): 45–73. http://dx.doi.org/10.1017/s0770451800001949.

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SummaryThe purpose of this paper is to investigate the mutual compatibility of voluntary provision of public good and strategic behavior of consumers in the market for private goods. We study the existence of equilibrium private provision of a public good within general strategic equilibrium framework with a finite number of players. The mechanism for the provision of public good follows the one due to Bergstrom, Blume and Varian (1986) and the trading mechanism for private goods follows the strategic market game with wash sales due to Dubey and Shubik (1986). The new result of the paper is the demonstration of existence of an equilibrium point in pure strategies for finite number of players. Due to the existence of trivial equilibria at which all markets are closed, equilibrium points are constructed as limits of sequences of ε- equilibria of perturbed games.

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23

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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24

Novshek, William. "On the Existence of Cournot Equilibrium." Review of Economic Studies 52, no. 1 (January 1985): 85. http://dx.doi.org/10.2307/2297471.

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25

Isard, Walter, and David J. Ostroff. "EXISTENCE OF A COMPETITIVE INTERREGIONAL EQUILIBRIUM." Papers in Regional Science 4, no. 1 (January 14, 2005): 49–76. http://dx.doi.org/10.1111/j.1435-5597.1958.tb01621.x.

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26

Iusem, Alfredo N., and Wilfredo Sosa. "New existence results for equilibrium problems." Nonlinear Analysis: Theory, Methods & Applications 52, no. 2 (January 2003): 621–35. http://dx.doi.org/10.1016/s0362-546x(02)00154-2.

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27

Tan, Kok-Keong, Zhou Wu, and X. Z. Yuan. "Equilibrium existence theorems with closed preferences." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e1833-e1840. http://dx.doi.org/10.1016/j.na.2005.02.064.

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28

Park, Sehie. "Equilibrium existence theorems in KKM spaces." Nonlinear Analysis: Theory, Methods & Applications 69, no. 12 (December 2008): 4352–64. http://dx.doi.org/10.1016/j.na.2007.10.058.

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29

Nanda, S., and S. Pani. "An existence theorem of Walrasian equilibrium." Applied Mathematics Letters 16, no. 8 (November 2003): 1279–81. http://dx.doi.org/10.1016/s0893-9659(03)90129-7.

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30

Husseini, S. Y., J. M. Lasry, and M. J. P. Magill. "Existence of equilibrium with incomplete markets." Journal of Mathematical Economics 19, no. 1-2 (January 1990): 39–67. http://dx.doi.org/10.1016/0304-4068(90)90035-8.

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31

Tan, Kok-Keong, and Xian-Zhi Yuan. "Existence of equilibrium for abstract economies." Journal of Mathematical Economics 23, no. 3 (May 1994): 243–51. http://dx.doi.org/10.1016/0304-4068(93)00609-z.

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32

Moreno-García, Emma, and Juan Pablo Torres-Martínez. "Equilibrium existence in infinite horizon economies." Portuguese Economic Journal 11, no. 2 (January 21, 2012): 127–45. http://dx.doi.org/10.1007/s10258-012-0079-2.

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33

Sato, Norihisa. "Satiation and existence of competitive equilibrium." Journal of Mathematical Economics 46, no. 4 (July 2010): 534–51. http://dx.doi.org/10.1016/j.jmateco.2010.03.006.

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34

Castellani, Marco, Massimo Pappalardo, and Mauro Passacantando. "Existence results for nonconvex equilibrium problems." Optimization Methods and Software 25, no. 1 (February 2010): 49–58. http://dx.doi.org/10.1080/10556780903151557.

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35

John, Reinhard. "Abraham Wald's equilibrium existence proof reconsidered." Economic Theory 13, no. 2 (February 19, 1999): 417–28. http://dx.doi.org/10.1007/s001990050262.

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36

Patriche, Monica. "Existence of the Equilibrium in Choice." Journal of Optimization Theory and Applications 175, no. 1 (January 3, 2017): 158–71. http://dx.doi.org/10.1007/s10957-016-1047-2.

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37

Cotrina, John, and Yboon García. "Equilibrium Problems: Existence Results and Applications." Set-Valued and Variational Analysis 26, no. 1 (October 17, 2017): 159–77. http://dx.doi.org/10.1007/s11228-017-0451-6.

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38

DONATO, MARIA BERNADETTE, MONICA MILASI, and CARMELA VITANZA. "QUASI-VARIATIONAL APPROACH OF A COMPETITIVE ECONOMIC EQUILIBRIUM PROBLEM WITH UTILITY FUNCTION: EXISTENCE OF EQUILIBRIUM." Mathematical Models and Methods in Applied Sciences 18, no. 03 (March 2008): 351–67. http://dx.doi.org/10.1142/s0218202508002711.

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A Walrasian pure exchange economy with utility functions, a particular case of a general economic equilibrium problem, is considered in this paper. We assume that each agent is endowed with goods and maximizes his utility function, under his budget constraints. We are able to characterize the Walrasian equilibria as solution of an associated quasi-variational inequality. This approach allows us to obtain an existence result of equilibrium solutions. As an application, we provide the explicit equilibrium in the case of two agents and two goods.

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39

Takeshita, Jun-ichi, and Hidefumi Kawasaki. "NECESSITY AND SUFFICIENCY FOR THE EXISTENCE OF A PURE-STRATEGY NASH EQUILIBRIUM." Journal of the Operations Research Society of Japan 55, no. 3 (2012): 192–98. http://dx.doi.org/10.15807/jorsj.55.192.

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40

Keskin, Kerim, and H. Çağrı Sağlam. "On the Existence of Berge Equilibrium: An Order Theoretic Approach." International Game Theory Review 17, no. 03 (September 2015): 1550007. http://dx.doi.org/10.1142/s0219198915500073.

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We propose lattice-theoretical methods to analyze the existence and the order structure of Berge equilibria (in the sense of Zhukovskii) in noncooperative games. We introduce Berge-modular games, and prove that the set of Berge equilibrium turns out to be a complete lattice.

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41

Anello, G., and F. Rania. "Existence of General Competitive Equilibria: A Variational Approach." Abstract and Applied Analysis 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/4969253.

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We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities.

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42

Orrillo, Jaime. "Existence of collateral Equilibrium without survival assumption." Estudos Econômicos (São Paulo) 41, no. 1 (March 2011): 7–24. http://dx.doi.org/10.1590/s0101-41612011000100001.

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This paper shows the existence of a collateral equilibrium without assuming any hypotheses on the strict positivity, be they individual initial endowments, including the ex post initial endowments, or aggregated initial endowments. Because of dropping the strict positivity of social initial endowment we fail to get an equilibrium. Instead, we get a quasi-equilibrium. Then, appealing to the concept of irreducibility (introduced by McKenzie in 1959) which is adapted to the collateral model, we show that the quasi-equilibrium is indeed a legitime equilibrium.

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43

Qin, Wenjie, Xuewen Tan, Xiaotao Shi, Marco Tosato, and Xinzhi Liu. "Sliding Dynamics and Bifurcations in the Extended Nonsmooth Filippov Ecosystem." International Journal of Bifurcation and Chaos 31, no. 08 (June 26, 2021): 2150119. http://dx.doi.org/10.1142/s0218127421501194.

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We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider how the existence of the regular equilibrium and the pseudo-equilibrium are related. Then we study the stability of the standard periodic solution (limit cycle), the sliding periodic solutions (grazing or touching cycle) and the dynamics of the pseudo equilibrium, using quantitative analysis techniques related to nonsmooth Filippov systems. Furthermore, as the threshold value is varied, the model exhibits several complex bifurcations which are classified into equilibria, sliding mode, local sliding (boundary node and focus) and global bifurcations (grazing or touching). In conclusion, we discuss the importance of the refuge strategy in a biological setting.

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44

Nessah, Rabia, Moussa Larbani, and Tarik Tazdaït. "Coalitional ZP-Equilibrium in Games and its Existence." International Game Theory Review 17, no. 03 (September 2015): 1550002. http://dx.doi.org/10.1142/s0219198915500024.

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We introduce a solution concept for games in normal form with undetermined parameters, coalitional ZP-equilibrium, based on the notions of Z-equilibrium of [Zhukovskii and Chikrii [1994] Linear quadratic differential games, Kiev, Naoukova Doumka] and ZS-equilibrium of [Larbani and Lebbah [1999] A concept of equilibrium for a game under uncertainity. Europ. J. Oper. Res.117, 145–156]. For each coalition structure, ZP-equilibrium ensures both the stability of the partition and equilibrium of coalitional strategies (in Pareto sense). We show that under some quasiconcavity conditions on payoff functions, the coalitional ZP-equilibrium exists in compact, convex and continuous normal form games involving undetermined parameters.

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45

Yi, Taishan, and Qingguo Li. "Unstable sets, heteroclinic orbits and generic quasi-convergence for essentially strongly order-preserving semiflows." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (September 23, 2009): 797–807. http://dx.doi.org/10.1017/s0013091506000320.

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AbstractWe present conditions guaranteeing the existence of non-trivial unstable sets for compact invariant sets in semiflows with certain compactness conditions, and then establish the existence of such unstable sets for an unstable equilibrium or a minimal compact invariant set, not containing equilibria, in an essentially strongly order-preserving semiflow. By appealing to the limit-set dichotomy for essentially strongly order-preserving semiflows, we prove the existence of an orbit connection from an equilibrium to a minimal compact invariant set, not consisting of equilibria. As an application, we establish a new generic convergence principle for essentially strongly order-preserving semiflows with certain compactness conditions.

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46

Julien, Ludovic. "Moneda, intercambios efectivos y desempleo keynesiano." Lecturas de Economía, no. 59 (October 30, 2009): 149–76. http://dx.doi.org/10.17533/udea.le.n59a2702.

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El objetivo de este artículo es construir un modelo que produzca equilibrios con desempleo involuntario en una economía monetaria descentralizada. La existencia del desempleo involuntario reposa aquí sobre la organización monetaria de las transacciones. En tal economía, la moneda juega un papel esencial en la medida que permite la realización descentralizada de las transacciones y la determinación de los precios de mercado tanto en el equilibrio como en el desequilibrio. Palabras clave: desempleo involuntario, equilibrio, desempleo keynesiano. Clasificación JEL: B20, E12, E40. Abstract: This paper aims at building up a simple model of a decentralized monetary economy with Keynesian unemployment. The existence of involuntary unemployment is based on the organization of trades. Money plays a critical role in coordinating decentralized transactions in equilibrium and in disequilibrium. Without perfect expectations, trades occur out of equilibrium. However, Keynesian unemployment is essentially an equilibrium phenomenom. Key words: involuntary unemployment, equilibrium, Keynesian unemployment. JEL: B20, E12, E40. Résumé: L’objectif de ce papier est d’édifier un modèle qui produit des équilibres avec chômage involontaire dans une économie monétaire décentralisée. L’existence du chômage involontaire repose ici sur l’organisation monétaire des transactions. Dans une telle économie, la monnaie joue un rôle essentiel dans la mesure où elle permet la réalisation décentralisée des transactions et la détermination des prix de marché tant à l’équilibre qu’en déséquilibre. Mots clés: chômage involuntaire, équilibre, chômage keynésien. JEL: B20, E12, E40.

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47

Suherman, Sofita, Fatmawati Fatmawati, and Cicik Alfiniyah. "Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Penyakit Ebola dengan Penanganan Medis." Contemporary Mathematics and Applications (ConMathA) 1, no. 1 (August 9, 2019): 19. http://dx.doi.org/10.20473/conmatha.v1i1.14772.

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Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 >1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.

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48

Huang, Tieying, and Jiuqiang Liu. "Fuzzy Strong Nash Equilibria in Generalized Fuzzy Games with Application in Urban Public-Sports Services." Mathematics 10, no. 20 (October 13, 2022): 3784. http://dx.doi.org/10.3390/math10203784.

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In this paper, we apply the existence of solutions of the Ky Fan minimax inequality to establish the existence of fuzzy strong Nash equilibria in generalized fuzzy games and strong Nash equilibria in fuzzy coalition generalized games. We then show some applications of our existence results about the strong Nash equilibrium in urban public-sports services.

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Balaj, Mircea. "Existence results for quasi-equilibrium problems under a weaker equilibrium condition." Operations Research Letters 49, no. 3 (May 2021): 333–37. http://dx.doi.org/10.1016/j.orl.2021.02.005.

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50

Wijaya, Karunia Putra, Edy Soewono, and Thomas Götz. "On the existence of a nontrivial equilibrium in relation to the basic reproductive number." International Journal of Applied Mathematics and Computer Science 27, no. 3 (September 1, 2017): 623–36. http://dx.doi.org/10.1515/amcs-2017-0044.

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AbstractEquilibrium analysis in autonomous evolutionary models is of central importance for developing long term treatments. This task typically includes checks on the existence and stability of some equilibria. Prior to touching on the stability, one often attempts to determine the existence where the basic reproductive numberℛ0plays a critical role as a threshold parameter. When analyzing a nontrivial equilibrium (e.g., an endemic, boundary, or coexistence equilibrium) whereℛ0is explicit, we usually come across a typical result: ifℛ0>1, then a nontrivial equilibrium exists in the biological sense. However, for more sophisticated models,ℛ0can be too complicated to be revealed in terms of the involving parameters; the task of relating the formulation of a nontrivial equilibrium toℛ0thus becomes intractable. This paper shows how to mitigate such a problem with the aid of functional analysis, adopting the framework of a nonlinear eigenvalue problem. An equilibrium equation is first to be transformed into a canonical equation in a lower dimension, and then the existence is confirmed under several conditions. Three models are tested showing the applicability of this approach.

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