Бидний тухай
Багш ажилтан
Хураангуй: ABSTRACT In recent years, due to significant tax revenue losses, transfer pricing has become an issue of concern for tax authorities, policymakers, and academics. In this study, the authors aim to analyze transfer pricing and its impact on fiscal revenue in the case of Mongolia, a developing country with a mining-dominated economy. In our research, we used the arm's length principle to determine transfer pricing and estimate the loss of corporate income tax due to transferring pricing; moreover, we compared the operating profit margin of Mongolia’s mining companies with the Far East and Central Asia Oceania countries. We found that Mongolia has lost about 44.4 billion MNT in corporate income tax revenue from the mining sector over the past seven years, estimated by adjusting the total operating revenue by an average of 10.5% for coal companies and 16.4% for copper companies. This result shows that mining companies are avoiding taxes by mispricing, which negatively affects the budget revenue in Mongolia. This research will contribute to the implementation of the common principles of transfer pricing and reduce tax evasion in Mongolia and similar countries with a mining-dominated economy. Keywords: transfer pricing; tax evasion; loss of tax revenue; mining sector; budget revenue; arm’s length principle (ALP); operating profit margin (OPM)
Abstract. Game theory has numerous applications in applied mathe- matics, economics, and decision theory.There are several books on game theory, all of which deal with Nash and Berge equilibriums. As we noted at the beginning, there is no clear conclusion regarding whether the ap- proach is improved in terms of player performance in terms of both op- timal decision-making and equilibria. We provide numerical experiments for both equilibria.
Abstract. Game theory has numerous applications in applied mathe- matics, economics, and decision theory.There are several books on game theory, all of which deal with Nash and Berge equilibriums. As we noted at the beginning, there is no clear conclusion regarding whether the ap- proach is improved in terms of player performance in terms of both op- timal decision-making and equilibria. We provide numerical experiments for both equilibria. Keywords: Nash equilibrium, Berge equilibrium, global solution, global optimal condition
Abstract: The report introduces multi-period loan interest rate Nash game models in the banking sector under regulatory solvency constraints. By taking solvency constraint as Basel II and modelling economic condition as AR(1) process, we obtain results regarding the existence of loan interest rate equilibrium. Basel II uses a “three pillars” concept, namely, minimum capital requirements (addressing credit risk, market risk, and operational risk), supervisory review, and market discipline. Process of Basel II attracted a lot of interest in quantitative credit risk models in industry, academia, and among regulators. A sensitivity analysis for the solvency constraint model and some numerical results are presented. Keywords: Nash equilibrium model, one factor KMV/Risk metrics model, Basel II solvency constraint, credit rating, loan interest rate
Abstract: The paper deals with a Berge equilibrium problem (BEP). Based on the existence results of Berge equilibrium of Nessah, Larbanic and Tazdait [5], we consider BEP with concave objective functions. The existence of BEP has been proven. BEP reduces to nonsmooth optimization problem. Then using a regularized function, we reduce a problem of finding Berge equilibrium to a nonconvex global optimization problem with a differentiable functions. The later allows to apply optimization methods and algorithms to solve the original problem.
Abstract The paper deals with finding a Berge equilibrium by DC optimization method for the global solution. We examine Berge equilibrium [3], [23] in the bimatrix game for mixed strategies. In [5] we proved an existence of Berge equilibrium in the bimatrix game and redusede the bimatrix game to a nonconvex optimization problem. In this paper we show that a new formulated optimization problem can be also reduced to D.C. programming so that one can apply the global optimality conditions [18]. We provide with numerical experiments done for nonzero sum two person game. Keywords Berge equilibrium, Nash equilibrium, d.c. programming, global optimization, global optimality conditions.
This paper introduces multi–period loan interest rate Nash game models in the banking sector under regulatory solvency constraints. By taking solvency constraint as Basel II and modelling economic condition as AR(1) process, we obtain results regarding the existence of loan interest rate equilibrium. A sensitivity analysis for the solvency constraint model and some numerical results are presented.
In this paper, we obtain results regarding partial derivatives of risk measures. It is a wellknown fact that for a linear loss random variable, partial derivatives of the Value-at-Risk are represented by conditional expectations. We proved that the result for the Value-at-Risk still holds for any risk measures.
The paper aims to estimate macroeconomic determinants of SMV for post socialist countries using unbalanced panel data from 1995 to 2020. We evaluated the impacts of stock market and macroeconomic determinants on SMV using Feasible Generalized Least Squares (FGLS) model based on the data of selected eleven post socialist countries in terms of current and previous years. The findings reveal that economic freedom has a strong and good impact at any time; however, although the previous year's TOR had a positive impact, this year it has an unfavorable impact on SMV. Furthermore, the year's inflation and corruption, economic growth, and stock market value have all shown a negative impact. The study's findings serve as a useful reference for stock market practitioners and policymakers in these nations in making decisions.
Abstract In this paper, we consider N players nonconvex quadratic generalized Nash equilibrium problems (GNEP) with jointly convex constraints. We show that the problem can be equivalently reduced to the nonconvex unconstrained optimization problem based on a regularized Nikaido-Isoda function and a gap function. The last problem is also nonconvex, so we reduce it to DC (difference of convex functions) optimization problem and then apply local and global methods and algorithms developed by A.S.Strekalovsky [26]. Numerical results are presented. Keywords: Nonconvex games, Nikaido-Isoda function, Gap functions, DC optimization, Local and Global search methods
Бержийн тэнцвэрийн талаархи анхны ойлголт, томъёоллыг анх Берж (1957) томъсолсон. Жуковский (1985) дифференциал тоглоомын ойлгодтын хүрээнд түүний оновчтой шийдийн шинж, олох аргын талаар чухал үр дүнгүүдийг гарган авсан. Үүнээс өмнөх Бержийн тэнцвэрийн талаархи судалгаанууд ихэвчлэн орос хэл дээр,дифференциал тоглоомын хүрээнд голчлон хийгдэж байсан байна. Бержийн тэнцвэрийг ердийн стратегийн тоглоомуудад саяхан болтол судалж үзээгүй байсан ба Абало (2004) болон Кострева (2005), Болтон, Оккенфельс (2000), Фехр, Шмидт (1999) нар сэтгэлзүйн болон зан үйлийн тоглоомын хувьд Бержийн тэнцвэрийн тухайд онолын болон практикийн, зарим тооцон бодох аргын талаархи судалгааны үр дүнгүүд нь хүлээн зөвшөөрөгдөж, хэвлэгдсэнээр энэ чиглэлийн судалгаа нэлээн эрчимжсэн байна. Одоог хүртэл Бержийн тэнцвэрийн глобаль шийдийг олох тооцоон бодох аргын асуудалд бага анхаарал хандуулж энэ чиглэийн судалгаа маш бага хийгдсэн байна. Тиймээс бидний судалгааны ажлын нэг гол зорилго нь Бержийн тоглоомын глобаль шийдийг олох арга, алгоритмыг боловсруулах явдал юм. Энэ ажилд бид тэг биш нийлбэртэй хоёр хүний тоглоомын Бержийн тэнцвэрийг олох бодлогыг шугаман бус програмчлалын бодлого болгон томьёолж, глобал шийдийг олох нэгэн аргын талаар хийсэн ажлын үр дүнг танилцуулна. Түлхүүр үг: Нэшийн тэнцвэр, Бержийн тэнцвэр, глобаль оптимизаци
Abstract We formulate a new optimization problem to define the capital structure. The problem is fractional programming (FP) which reduces to a linear programming problem (LP). Numerical results based on the balance sheet of APU JSC of Mongolia have been obtained on Matlab. 1. Introduction The capital structure of a company decides how to spend money that the company has earned. Capital structure refers to investing a companys financial resources in ways that will increase its efficiency, and maximize its profits. Therefore, a companys management seeks to allocate its capital in ways that will generate as much as possible for its equity. A company can finance its operation with either equity or debt. A mix of both equity and debt was first formulated by [1]. This study explains the relationship between capital structure and the value of the company. The first their model was based on some strong assumptions such as no brokerage costs, no taxes, and no bankruptcy costs. After that, they relaxed the assumption that there are no corporate taxes in 1963 [2] and no bankruptcy-related costs in 1977. According to [1], the selection between debt and equity does not have any material effect on the value of a company, but when tax and bankruptcy costs are considered, this leads to the existence of an optimal capital structure. However, at that time, some financial theorists have failed to determine its existence. The disadvantage of [1] theory has moved to the trade-off theory of leverage. This theory was proposed by [3]. They attempted to balance the benefits of the tax shield against the present value of the possible cost of financial distress. Financial articles [1]- [3] are not considered in information to the market. If managers have inside information, [4] showed that their choice of capital structure will signal information to the market in 1977. Under the asymmetric information between management and investors, signals from companies are crucial to obtain financial resources. A signaling theory contexts many concepts for the costly signaling equilibrium discussed by [5], the costless signaling equilibrium proposed by [6], and the signaling paradigm demonstrated by [7]. The theory next of capital structure is the pecking order theory. Originally developed by [8], it considers the role of information asymmetries between companies and capital markets. According to [8], companies use internal funds that are less costly than external funds. Therefore, companies prefer debt to equity because of lower information costs associated with debt issues, while equity is rarely issued. Later, these ideas were tested and confirmed by [9]. Extensive empirical work has been completed in the finance field on the theories of capital structure. In particular, the sensitivity of investments to changes in equity is greater during the financial stress period [10]. Credit constraints are more important for companies with weaker internal finance positions [11]. Companies adjust to long-run financial targets for equity, debt, and leasing, but that additional financing needs follow a pecking order that is stronger for companies with greater asymmetric information problems [12]. However, the application of these theories in terms of mathematical modeling to manage a financial statement of a company is limited. Numerous empirical studies above in the finance field mainly depend on econometrically and statistically test. The purpose of this paper is to construct a mathematical model for the capital structure problem. The paper is organized as follows. In Section 2, we prove auxiliary lemmas for constructing a mathematical model for capital structure. Profit maximization problem as fractional programming is formulated in Section 3. In Section 4, linear programming reduction of fractional programming has been given. Computational results are given in Section 5.
In this paper, we consider nonconvex quadratic generalized Nash equilibrium problems. We reformulate a nonconvex unconstrained optimiza- tion problem by using a regularized Nikaido-Isoda function. After that reformulation, we investigate the equivalent DC (difference of two convex functions) problem. Numerical results are presented.
The paper deals with a Berge equilibrium (Théorie générale des jeux à-personnes, Gauthier Villars, Paris, 1957; Some problems of non-antagonistic differential games, 1985) in the bimatrix game for mixed strategies. Motivated by Nash equilibrium (Ann Math 54(2):286, 1951; Econometrica 21(1):128–140, 1953), we prove an existence of Berge equilibrium in the bimatrix game. Based on Mills theorem (J Soc Ind Appl Math 8(2):397–402, 1960), we reduce the bimatrix game to a nonconvex optimization problem. We illustrate the proposed approach on an example.
The paper deals with a Berge equilibrium (Théorie générale des jeux à-personnes, Gauthier Villars, Paris, 1957; Some problems of non-antagonistic differential games, 1985) in the bimatrix game for mixed strategies. Motivated by Nash equilibrium (Ann Math 54(2):286, 1951; Econometrica 21(1):128–140, 1953), we prove an existence of Berge equilibrium in the bimatrix game. Based on Mills theorem (J Soc Ind Appl Math 8(2):397–402, 1960), we reduce the bimatrix game to a nonconvex optimization problem. We illustrate the proposed approach on an example.
Судалгааны ажлаар 20177 оны монгол улсын салбар хоорондын тэнцлийг ашиглан эдийн засгийн 55 салбарын нэг болох цахилгаан, хий, агааржуулалтын салбарыг цахилгааны эрчим хүч, дулааны эрчим хүч, бусад гэсэн 3 дэд салбар болгон салгаж, эрчим хүчний үйлдвэрлэлийг нэмэгдүүлснээр бусад салбаруудад үзүүлэх нөлөөллийг судлах зорилгоор 57х57 хэмжээстэй болгон дахин байгуулан судалсан болно. Салбар хоорондын тэнцлийн I квадрат нь салбаруудын орц гарцыг өртгөөр нь харуулсан байдаг тул салбарыг дэд салбар болгон задлахад зардлын бүртгэлийн хамсарсан зардлын хуваарилалын аргын нэг болох биет хэмжигдэхүүний аргыг ашиглан дэд салбар болгон салган, Леонтьевийн орц гарцын загварт шугаман алгебрийн аргыг ашиглан бус салбартаа нөлөөлөх нөлөөллийг авч үзсэн.
In automobile manufacturing, it is a great challenge to select and execute the services with the optimal value, cost and time out of complex processes. Most traditional algorithms only optimize one objective. In this paper, an optimization algorithm for service value and time is proposed under the constraint of deadline, and denoted as SRVT. The proposed algorithm reversely derives the service with the maximum value at each time point, and adds it to the set of candidate solutions in the next iteration. Then, the optimal solutions were selected iteratively from the set. In the end, the maximum service value of the entire workflow was obtained. The proposed SRVT was compared with two traditional algorithms through a case study. The comparison shows that our algorithm can outperform the contrastive algorithms to a certain extent, and strike a balance between service time, service cost and service quality. 29 refs. (Received in September 2019, accepted in January 2020. This paper was with the authors 1 month for 1 revision.) Key Words: Automobile Manufacturing, Workflow, Scheduling Optimization, Maximal Service Quality, Deadline
Энэхүү ажил нь Монгол улсын татварын орчин хөрөнгө оруулалтад ямар нөлөө үзүүлж буйг, хөрөнгө оруулалтад нөлөөлөх хүчин зүйлсийг орчин үеийн хүчтэй арга болох нөлөөллийн шаталсан (иерарх) анализын аргыг хэрэглэж тогтоох, татварын орчны өөрчлөлтөөс хөрөнгө оруулалтын өөрчлөлт хэрхэн хамаарч байгаад мэдрэмжийн шинжилгээ хийж, тэдгээрийн жинг тодорхойлсоны үндсэн дээр татварын орчны өөрчлөлт, шинэчлэл нь хөрөнгө оруулалтад хэрхэн нөлөөлж байгааг тогтоохыг зорьсон.
The nonzero sum four-person game was considered. We show that the game can be reduced to a global optimization problem by extending Mills’ result (J Soc Ind Appl Math 8(2):397–402, 1960). For solving the problem, we propose a global optimization method that combines the ideas of the classical multistart and an estimation of a convexity degree of the function. The proposed algorithm was tested numerically on some problems created by the well-known generator GAMUT (GAMUT is a Suite of Game Generators. http://gamut.stanford.edu) and allowed us to find solutions to the four-person game.
Game theory plays an important role in applied mathematics, economics and decision theory. There are many works devoted to game theory [9], [6], [7], [12], [7]. Most of them deals with finding a Nash equilibrium. Berge equilibrium is a model of cooperation in social dilemmas, including the Prisoner’s Dilemma games [6]. The Berge equilibrium concept was introduced by the French mathematician Claude Berge [3] for coalition games and formalized by Zhukovskii [8], [10] in the context of differential games. Early literature, almost exclusively in Russian, focused on differential games. Berge equilibrium was not examined in conventional strategic games until recently Abalo [1] and Kostreva [2] published the first existence theorems for pure-strategy Berge equilibrium in strategic-form games of differential games. Nessah [10] and Tazdat [11] proposed a new existence theorem. Applications of Berge equilibrium in social science and economics have been considered in [4], [6]. So far little attention has been paid to computational aspects of Berge equilibrium. The main goal this work is to fulfill this gap and develop theory and algorithm of Berge equilibrium for bimatrix game with mixed strategies. We formulate the problem of finding a Berge equilibrium for non zero sum two-person games as a nonlinear programming problem. Global solutions are examined and numerical results are given.
The paper deals with a Berge equilibrium in the bimatrix game for mixed strategies. Motivated by Nash equilibrium , we prove an existence of Berge equilibrium in the bimatrix game. Based on Mills theorem , we reduce the bimatrix game to a nonconvex optimization problem. We illustrate the proposed approach on an example.
Abstract. In this talk, we consider a global method for finding the Nash equilibrium of the non zero sum three person game. Game theory as a part of operations research plays an important role in science, economy and technology as well as in decision theory. There are a lot works devoted to game theory [Neumann et al., 1944, Vorobyev 1984, Germeyer 1976, Strekalovsky et al., 2007, Owen., 1971, Gibbons 1992, Mangasarian 1964]. Most of them deals with two person games or non zero sum two person games. The two person non zero sum game was studied in [Strekalovsky et al., 2007, Strekalovsky et al., 2014, Orlov et al., 2014] based on D.C programming [Strekalovsky., 1980]. The three person game was examined in [Enkhbat et al., 2016] by global optimization techniques use and heuristics methods. So far, less attention has been paid to computational aspects of game theory, specially this class game. Based on Mills’ result [Mills 1960], we derive a sufficient condition for a point to be Nash equilibrium. Next we reduce this optimization problem to D.C. optimization problem with nonconvex constraints and use theory and method of D.C programming composed by Strekalovsky and etc.
We introduce so-called four-players triple game and define Nash equilibrium.
Game theory plays an important role in applied mathematics, mathematical modeling, economicsanddecisiontheory. Therearemanyworksdevotedtogametheory[11,13,19,15]and [16, 17, 9]. Most of them deals with zero sum two person games or nonzero sum two person games. Also, two person non zero sum game was studied in [15, 1, 2] by reducing it to D.C programming. The problem ofnumericalfinding ofa Nashequilibriumin a 3-player polymatrixgame was studied in [1],[2]. In this paper it has found that a game can be completely described by six matrices, and it turns out to be equivalent to the solving a nonconvex optimization problem with a bilinear structure in the objective function. Special methods of local and global search for the optimization problem are proposed and investigated in [8, 5, 7]. Weconsiderthefour-personmatrixgamewhereeachofthemplayswithotherthreeplayers. We call such game four-players triple game. In this game we introduce a definition of Nash equilibrium similarly to [1]. The game reduces to a nonconvex optimization problem. For solving the optmization problem, we propose a global optimization method that combines the ideas of the classical multistart and local search methods.
In previous works R.Enkhbat showed that the Malfatti's problem can be treated as the convex maximization problem and provided with an algorithm based on Global Optimality Condition of A.S.Strekalovsky. In this article we reformulate Malfatti's problem as a D.C. programming problem with a nonconvex constraint. The reduced problem as an optimization problem with D.C. constraints belongs to a class of global optimization. We apply the local and global optimality conditions by A.S.Strekalovsky developed for D.C. programming. Based on local search methods for D.C. programming, we have developed an algorithm for numerical solution of Malfatti's problem. In numerical experiments, initial points of the proposed algorithm are chosen randomly. Global solution have been found all cases.
Abstract. We introduce so-called four-players triple game and define Nash equilibrium. The problem of numerical finding of a Nash equilibrium in a four-players triple game has been examined. Such a game can be completely described by twelve matrices, and it turns out to be equivalent to the solving a nonconvex optimization problem. Special methods of local and global search for the optimization problem are proposed and investigated. The results of computational Numerical results of the test game are presented and analyzed.
Abstract The nonzero sum four-person game was considered. We show that the game can be reduced to a global optimization problem by extending Mills’ result (J Soc Ind Appl Math 8(2):397–402, 1960). For solving the problem, we propose a global optimization method that combines the ideas of the classical multistart and an estimation of a convexity degree of the function. The proposed algorithm was tested numerically on some problems created by the well-known generator GAMUT (GAMUT is a Suite of Game Generators. http://gamut.stanford.edu) and allowed us to find solutions to the four-person game.
N-тоглогчтой тоглоомын Нэшийн тэнцвэрийг олох бодлогыг гло- бал оптимизацийн бодлогод шилжүүлж, шийдийг олох аргуудын талаар [5, 7, 14, 17] бүтээлүүдэд судлагдсан байдаг. Бидний ажлын зорилго нь олон тоглогчтой тоглоомын хувьд Нэшийн тэнцвэрийг олохдоо г³дгэр биш оптимизацийн глобал шийдийг олох эверестик аргуудын нэг болох олон эхлэлт муруй шугамын (Curvilinear Multistart Algorithm [2, 3]) аргыг хэрхэн хэрэглэж болохыг харуулахыг зорьсон. Эжлын хүрээнд Миллсын [5] гаргасан үр дүнг ашиглан глобал оновчтой байх нөхцлийг тодорхойлж, шинээр гарч ирсэн г³дгэр биш оптимизацийн бодлогыг бодох олон эхлэлт муруй шугамын алгоритмыг уг бодлогод тохируулан өөрчилсөн. Алгоритмыг тест бодлогуудад шалгаж, үр дүнг гарган авсан болно. Түлхүүр үг: Нэшийн тэнцвэр, N тоглогчтой тоглоом, холимог стра- теги, олон эхлэлт муруй шугамын арга
N-òîãëîã÷òîé òîãëîîìûí Íýøèéí òýíöâýðèéã îëîõ áîäëîãûã ãëî- áàë îïòèìèçàöèéí áîäëîãîä øèëæ³³ëæ, øèéäèéã îëîõ àðãóóäûí òàëààð [5, 7, 14, 17] á³òýýë³³äýä ñóäëàãäñàí áàéäàã. Áèäíèé àæëûí çîðèëãî íü îëîí òîãëîã÷òîé òîãëîîìûí õóâüä Íýøèéí òýíöâýðèéã îëîõäîî ã³äãýð áèø îïòèìèçàöèéí ãëîáàë øèéäèéã îëîõ ýâåðåñòèê àðãóóäûí íýã áî- ëîõ îëîí ýõëýëò ìóðóé øóãàìûí (Curvilinear Multistart Algorithm [2, 3]) àðãûã õýðõýí õýðýãëýæ áîëîõûã õàðóóëàõûã çîðüñîí. Ýæëûí õ³ðýýíä Ìèëëñûí [5] ãàðãàñàí ³ð ä³íã àøèãëàí ãëîáàë îíîâ÷òîé áàéõ í°õöëèéã òîäîðõîéëæ, øèíýýð ãàð÷ èðñýí ã³äãýð áèø îïòèìèçàöèéí áîäëîãûã áî- äîõ îëîí ýõëýëò ìóðóé øóãàìûí àëãîðèòìûã óã áîäëîãîä òîõèðóóëàí °°ð÷èëñ°í. Àëãîðèòìûã òåñò áîäëîãóóäàä øàëãàæ, ³ð ä³íã ãàðãàí àâñàí áîëíî.
Монгол улсын болон эдийн засгийн бүсүүдийн үйлдвэрлэлийн чадамжийн чанарын тоон үнэлгээ болон бүс бүрийн хувьд хөгжлийн төлөв байдлын прогноз хийсэн үр дүнгүүдийн талаар авч үзэх болно. 1990 онд Монгол Улсад болсон ардчилсан өөрчлөлт нь эдийн засгийн хөгжлийн бодлогод баримталж байсан төвлөрсөн төлөвлөгөөт зарчмаас татгалзан, нээлттэй зах зээлийн системд шилжсэнээр нийгэм эдийн засгийн хүрээнд олон шинэ асуудал дэвшигдэн гарч байна. Эдийн засгийн хүрээнд чөлөөт зах зээлийн онолыг Монгол орны нөхцөлд чөлөөт өрсөлдөөн бөгөөд тэрхүү өрсөлдөөн явагдах нөхцөлийг буй болгох нь өнөөгийн шилжилтийн процессын зорилго болж байна. Энэ утгаар сүүлийн жилүүдэд бүс нутгийн бие даасан хөгжлийн талаар яригдаж судлаачдын анхаарлыг татах болсон. Бүс нутгийн хөгжлийн нээлттэй зах зээлийн нөхцөлд хөхиүлэн дэмжихийн тулд түүнд хандаж байсан уламжлалт хандлагыг төрийн болон шинжлэх ухааны талаас эрс өөрчлөх шаардлага гарч байгаа юм. Энд бид зөвхөн бүс нутгийн хөгжлийн асуудалтай уялдан гарч буй шинжлэх ухааны асуудлуудыг дурдаж тэдгээрийг шийдвэрлэхэд нэгдмэл ямар арга зүйг баримтлах талаар зарим санааг дэвшүүлж байгаа болно.
Энэхүү ажилд хэрэглэгчийн өгөгдлийн сантай харилцах харьцааг хэрэглээний мэдээллийн системийн автоматжуулалт, програм, хөгжлийн асуудлыг шийдэх нэгэн аргын тухай авч үзсэн. Энэ асуудлыг шийдэх “Декларатив өвөрмөц тодорхойлолт”-од суурилсан мэдээллийн сангийн боловсруулалтын автоматжуулсан мэдээллийн системийг үүсгэх технологи, арга хэрэгслийн системийг боловсруулж, дэвшүүлсэн болно. Уг ажлаар дэвшүүлсэн арга нь өгөгдлийн сангийн загваруудыг судлах, боловсруулах тохиромжтой арга юм.
Abstract. The nonzero sum n-person game has been considered. It is well known that the game can be reduced to a global optimization problem [5; 7; 14]. By extending Mills’ result [5], we derive global optimality conditions for a Nash equilibrium. In order to solve the problem numerically, we apply the Curvilinear Multistart Algorithm [2; 3] developed for finding global solutions in nonconvex optimization problems. The proposed algorithm was tested on three and four person games. Also, for the test purpose, we have considered competitions of 3 companies at the bread market of Ulaanbaatar as the three person game and solved numerically.
