• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.495-508
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• 1997

The problem of optimization in choosing of evasion parameters in differential games is considered. Existence of optimal parameters is proved and algorithm of their is shown. The example is cited. This work adjoins investigations [1-11].

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.527-543
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• 2024

In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.379-379
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• 1998

The report presents an approach to constructing or control algorithms for finite dimensional dynamical systems under the deficit of information about dynamical disturbances. The approach is based on the constructions of the extremal shift strategy of the differential game theory.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1989.10a
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• pp.45-50
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• 1989

The above theorm states that much larger classes of differential games have an equilibrium. The most severe assumption is the second one. It requires that state dynamic equations be linear on his own control variables. But, the dynamic programming approach applied in the above is hardly implementable for the purpose of computation. It is very difficult to solve (SP$_{it}$) directly. Notice, however, the problem can be transformed into a Hamiltonian maximization problem which is easy to solve if initial conditions are given. In this way, it is possible to design a solution algorithm to problems with nonlinear constraints. The above two theorems probide a basis for such an algorithm.m.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.97-104
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• 1989

This paper extends the existence proofs of a Nash equilibrium to a more general class of differentila game models with constraints on the control spaces. With the assumptions of continuity, convexity, and compactness, the existence is proved using Kakutani Theorem and via a path-following approach. Furthermore, the proof for a period-by-period optimization of multi-period problems provides an insight to a numerical solution algorithm to differential game models with constraints.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.177-191
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• 2001

We consider a linear differential game described by the delay-differential equation in a Hilbert space H; (※Equations, See Full-text) U and V are Hilbert spaces, and B(t) and C(t) are families of bounded operators on U and V to H, respectively. A(sub)0 generates an analytic semigroup T(t) = e(sup)tA(sub)0 in H. The control variables g, and u and v are supposed to be restricted in the norm bounded sets (※Equations, See Full-text). For given x(sup)0 ∈ H and a given time t > 0, we study $\xi$-approximate controllability to determine x($.$) for a given g and v($.$) such that the corresponding solution x(t) satisfies ∥x(t) - x(sup)0∥ $\leq$ $\xi$($\xi$ > 0 : a given error).

• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.2
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• pp.71-83
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• 1990

This paper concerns the analyses of dynamic adjustments in noncooperative games where the market informations are given at discrete time intervals. During the game period, the market informations are given at discrete time intervals. During the game period, the inventories initially stored by players are to be released one day based to the completely competitive market so as to maximize each player's revenue, where players' parameters are unknown one another. Game results have shown that the continuous dynamic adjustment does not necessarily assure the better revenue, and if a player thinks that his parameter is underestimated by hig opponent, then he is better overestimate his opponent's parameter.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.745-764
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• 2002

In this paper we Study a time-optimal model of pursuit in which the players move on a plane with bounded velocities. This game is supposed to be a nonzero-sum group pursuit game. The main point of the work is to construct and compare cooperative and non-cooperative solutions in the game and make a conclusion about cooperation possibility in differential pursuit games. We consider all possible cooperations of the players in the game. For that purpose for every game $\Gamma(x_0,y_0,z_0)$ we construct the corresponding game in characteristic function form $\Gamma_v(x_0,y_0,z_0)$. We show that in this game there exists the nonempty core for any initial positions of the players. The core can take four various forms depending on initial positions of the players. We study how the core changes when the game is proceeding. For the original agreement (an imputation from the original core) to remain in force at each current instant t it is necessary for the core to be time-consistent. Nonemptiness of the core in any current subgame constructing along a cooperative trajectory and its time-consistency are shown. Finally, we discuss advantages and disadvantages of choosing this or that imputation from the core.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.852-857
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• 1990

The purpose of this paper is to design a robust controller for a class of time-varying systems with bounded disturbance described by the differential equation. The robust desiging method proposed in this paper, called "incentive design method" is different from developed designing methods in the past, and has following properties. The robust control law designed by this method can guarantee a certain value of the cost functional no matter how the disturbance vary within the given bounds. Here, the certain value of the cost functional may not be a saddle-point value, but is the value selected by a system designer. Therefore, the bounded disturbance has at least no bad effect on the value of the cost functional during finite interval of time. The method is based on the theory of incentive differential games. In addition, the form of control law is constructed by the system designer ahead of time. A numerical illustrative example is given in this paper. It is shown from this derivation and this numerical example that the approach developed in this paper is effective and feasible for some practical control problem.l problem.

• Journal of Korea Game Society
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• v.20 no.2
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• pp.123-138
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• 2020

The purpose of this study is to examine the probabilities and expenditures of game users' loot box purchases and to verify if there are differential effects on adults and teenagers. Results show that the purchasing probability of teenagers was significantly lower than that of adults, and the amount was also low or not significant. In addition, loot box purchasing has a positive correlation with the total expenditure on games, but teenage buyers have a lower game spending than adults do. This suggests the possibility that loot boxes are considered as cost-saving products for teenage gamers.