The paper goes back to the research of N. N. Krasovskii devoted to two-person zero-sum positional differential games on minmax of non-terminal quality indices, which evaluate a set of system’s states ...realized at given times. The first part of the paper gives a survey of the results concerning existence of the value and saddle point in such differential games. A special attention is paid to the case when the quality index has a certain positional structure. The second part of the paper overviews a method for constructing the value and optimal strategies in the case when the dynamical system is linear in the state vector, and the quality index has the appropriate convexity properties. The method is based on the recurrent procedure of constructing the upper convex hulls of certain auxiliary functions. To illustrate that this method can be numerically realized on modern computers, a model example is considered.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper we study a two-player zero-sum stochastic differential game for a path-dependent stochastic system. Two basic theoretic problems in SDG are addressed: existence of game value and Nash ...equilibrium. Due to the typical non-Markovian structure, the game value is a random field. Dividing the time horizontal into small intervals, we approximate the path-dependent game by a series of state-dependent games. We utilize the state-dependent viscosity solution theory to prove that, under Isaacs' condition the game value exists. In our model, coefficients of diffusion of the system contain control and strategy, are path-dependent, and could be degenerate. The dimension of the state space is high. The existence of approximating Nash equilibrium is given under the formula about nonanticipative strategy with delay.
This article reports a study investigating value co-creation in online games through fan-created mods for effects on motivations, experiences, attitudes, and satisfaction. A study of 95 World of Tank ...players shows that user-created mod programs directly and positively influence players' experiences and attitudes and also indirectly influence satisfaction. The study provides insights showing that mods benefit both game companies and players. Online game companies can use the results of this study to better understand the value of mods and to recognize that they will gain benefits by encouraging their use.
Full text
Available for:
BFBNIB, NUK, PILJ, SAZU, UL, UM, UPUK
Let
A
and
B
be given convex closed bounded nonempty subsets in a Hilbert space
H
; let the first player choose points in the set
A
and let the second one do those in the set
B
. We understand the ...payoff function as the mean value of the distance between these points. The goal of the first player is to minimize the mean value, while that of the second player is to maximize it. We study the structure of optimal mixed strategies and calculate the game value.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
A differential game with asymmetric constraints on the players’ controls and an asymmetric cost functional is considered. In this game hard geometric constraints are imposed on the maximizer, whereas ...the minimizer is soft-constrained by including the control effort term into the cost functional. The sufficient condition is derived, subject to which the program maximin is the game value. In the proof, it is shown that the program maximin is the generalized solution of the Hamilton-Jacobi-Bellman partial differential equation. Examples are presented.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Statistical data regarding causes and number of accidents in enterprises and organisations allow to foresee the average number of traumas for a definite period when no additional means for trauma ...prevention have been provided. The trauma prevention means differ because they require different financing and decreasing the number of traumas. The suggested mathematical methods give the possibility to appraise the means of trauma prevention according to the definite sum invested.
Some accidents are related to individual miss-steps/mistakes at work. Trying to find out the ways for optimal trauma prevention we can take the latter causes as statistical game of “nature” state and certain possible situations of existing in determination. They are impossible to be changed, though some preventive means applied by employees may decrease the trauma cases caused by individual safe control violation.
As soon as the optimal strategy of the aforementioned matrix game is found, the most important preventive means could be determined. They could guarantee the real decrease of the trauma cases in spite of any violations by employees. A certain modification of the straightforward programme making task allows us to get an optimal allocation of means necessary for trauma prevention, thus evaluating the effectiveness of preventive measures when the optimal financing is found as the means are increasing.
Statistical data regarding causes and number of accidents in enterprises and organisations allow to foresee the average number of traumas for a definite period when no additional means for trauma ...prevention have been provided. The trauma prevention means differ because they require different financing and decreasing the number of traumas. The suggested mathematical methods give the possibility to appraise the means of trauma prevention according to the definite sum invested.
Some accidents are related to individual miss-steps/mistakes at work. Trying to find out the ways for optimal trauma prevention we can take the latter causes as statistical game of "nature" state and certain possible situations of existing in determination. They are impossible to be changed, though some preventive means applied by employees may decrease the trauma cases caused by individual safe control violation.
As soon as the optimal strategy of the aforementioned matrix game is found, the most important preventive means could be determined. They could guarantee the real decrease of the trauma cases in spite of any violations by employees. A certain modification of the straightforward programme making task allows us to get an optimal allocation of means necessary for trauma prevention, thus evaluating the effectiveness of preventive measures when the optimal financing is found as the means are increasing.
A zero-sum linear-convex differential game with a quality index that estimates a set of deviations of a motion trajectory at given instants of time from given target points is considered. A case when ...the saddle point condition in a small game, also known as Isaac's condition, does not hold is studied. The game is posed in classes of mixed control strategies of players. A numerical method for computing the game value and optimal strategies is elaborated. Results of numerical experiments in model examples are given.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A linear-convex zero-sum differential game with a nonterminal payoff in the form of the Euclidean norm of a set of deviations of the motion trajectory from given targets at given instants of time is ...considered. A numerical method of approximate computation of the game value and optimal control laws is elaborated. Details of the software implementation are discussed. Results of numerical simulations are given.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
PDF
