Values in Differential Games
نویسندگان
چکیده
1. Introduction. Two person zero-sum differential games can be considered as control problems with two opposing controllers or players. One player seeks to maximize and one to minimize the pay-off function. The greatest pay-off that the maximizing player can force is termed the lower value of the game and similarly the least value which the minimizing player can force is called the upper value. Our objective is to determine conditions under which these values coincide. In the case of two person zero-sum matrix games, von Neumann showed that if the players are allowed "mixed strategies," i.e., probability measures over the pure strategies, then the values of the game will coincide. By analogy, the authors in collaboration with L. Markus [1] introduced relaxed controls into differential game theory; for a full discussion of relaxed controls the reader is referred to [1]. In this announcement, we define notions of strategy and values and relate these to the approaches adopted by Fleming [3], [4] and Friedman [5]. Using relaxed controls we are able to show that if the "Isaacs con-dition" (3) is satisfied then the upper and lower values are equal, so that the game has value. In particular, if the players are allowed relaxed controls then the game always has value. Detailed proofs of these results will appear in a later publication [2].
منابع مشابه
Government and Central Bank Interaction under Uncertainty: A Differential Games Approach
Abstract Today, debt stabilization in an uncertain environment is an important issue. In particular, the question how fiscal and monetary authorities should deal with this uncertainty is of much importance. Especially for some developing countries such as Iran, in which on average 60 percent of government revenues comes from oil, and consequently uncertainty about oil prices has a large effec...
متن کاملThe Effect of Globalization on the Moral Values Change among the Youth
Globalization constitutes ideas, behavior and personality of people according to values and norms and affects different aspects of life of people (individually and socially). This research has been done in order to study the effect of globalization on moral values of the youth regarding sociology perspective. Statistical universe of this research includes 800 persons in Tehran. This research ha...
متن کاملA TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS
In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...
متن کاملValues in Differential
This is an announcement of results to be proved in detail in a later report in book form. The author introduces a new value, the H-value, into differential games, and proves that six well-known values for games of perfect information now in the literature are special cases of it. He proves that two (in the present slightly altered formulation four) values introduced in 1972 by Elliott and Kalto...
متن کاملar X iv : 0 81 1 . 17 47 v 1 [ m at h . O C ] 1 1 N ov 2 00 8 On a Structure of the Set of Differential Games Values ∗
In this paper the set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal payoff is obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1972