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  • Electronic Resource  (3)
  • 1970-1974  (3)
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  • Electronic Resource  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    On the Stackelberg strategy in nonzero-sum games (1973)
    Springer
    Journal of optimization theory and applications 11 (1973), S. 533-555 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The properties of the Stackelberg solution in static and dynamic nonzero-sum two-player games are investigated, and necessary and sufficient conditions for its existence are derived. Several game problems, such as games where one of the two players does not know the other's performance criterion or games with different speeds in computing the strategies, are best modeled and solved within this solution concept. In the case of dynamic games, linear-quadratic problems are formulated and solved in a Hilbert space setting. As a special case, nonzero-sum linear-quadratic differential games are treated in detail, and the open-loop Stackelberg solution is obtained in terms of Riccati-like matrix differential equations. The results are applied to a simple nonzero-sum pursuit-evasion problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935665
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Additional aspects of the Stackelberg strategy in nonzero-sum games (1973)
    Springer
    Journal of optimization theory and applications 11 (1973), S. 613-626 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Stackelberg strategy in nonzero-sum games is a reasonable solution concept for games where, either due to lack of information on the part of one player about the performance function of the other, or due to different speeds in computing the strategies, or due to differences in size or strength, one player dominates the entire game by imposing a solution which is favorable to himself. This paper discusses some properties of this solution concept when the players use controls that are functions of the state variables of the game in addition to time. The difficulties in determining such controls are also pointed out. A simple two-stage finite state discrete game is used to illustrate these properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935561
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Series Nash solution of two-person, nonzero-sum, linear-quadratic differential games (1971)
    Springer
    Journal of optimization theory and applications 7 (1971), S. 240-257 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is well-known that the Nash equilibrium solution of a two-person, nonzero-sum, linear differential game with a quadratic cost function can be expressed in terms of the solution of coupled generalized Riccati-type matrix differential equations. For high-order games, the numerical determination of the solution of the nonlinear coupled equations may be difficult or even impossible when the application dictates the use of small-memory computers. In this paper, a series solution is suggested by means of a parameter imbedding method. Instead of solving a high-order matrix-Riccati equation, a lower-order matrix-Riccati equation corresponding to a zero-sum game is solved. In addition, lower-order linear equations have to be solved. These solutions to lower-order equations are the coefficients of the series solution for the nonzero-sum game. Cost functions corresponding to truncated solutions are compared with those for exact Nash equilibrium solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00928706
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    Paper (German National Licenses)
    Fulltext
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