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91.
This paper is an attempt to throw some light on the issue of whether defining history-dependent state variables in a differential game does allow for a dynamic play of precommitment equilibria. We suggest the application of trigger strategies in a state-feedback context. Based on a punishment mode in Markov perfect strategies and being able to detect even past deviations followed by histories returning to equilibrium, these subgame-perfect strategies lead to the enforcement of certain outcomes by means of dynamic rules of strategic interaction. The last part of our exposition is devoted to specific game structures under which a trigger equilibrium can be used as well as a punishment mode.  相似文献   
92.
This paper solves an aiming and evasion game in which a gunner with a number of shots attempts to hit an evader moving along the positivex-axis. The gunner's aiming of the evader is complicated by the fact that there is a delay due to the time taken for the shot to reach the evader from the gunner.  相似文献   
93.
Open-loop multilevel Stackelberg strategies in deterministic, sequential decision-making problems for continuous linear systems and quadratic criteria are developed. Characterization of the Stackelberg controls via the solution of a higher-order square-matrix-Riccati differential equation is established; also, the basic structural properties of the coefficient matrices of this differential equation are established, and the basic structural properties of its solution are inferred.This work was supported in part by the Energy Research and Development Administration, Contract No. ERDA E(49-18)-2088.on leave from the Mihailo Pupin Institute, Belgrade, Yugoslavia.  相似文献   
94.
The problem of searching the extremum of a scalar function of a vector argument is considered. It is assumed that a finite set of algorithms, each of which is capable of finding the extremum, is specified. Every algorithm is characterized by a given number of operators each of which is identified with the state of the system. Each algorithm is defined by a transition probability matrix over the possible states (operators) and a corresponding matrix of the respective changes in the value of the function toward the extremal point.A procedure is given for selecting an optimal sequence of algorithms which maximizes the total expected change in the value of the function toward the optimum.  相似文献   
95.
The paper presents a non-probabilistic approach to continuous-time trading where, in analogy to the binomial option-pricing model, terminal payoffs resulting from a given trading strategy are meaningful ‘state-by-state’, i.e., path-by-path. In particular, we obtain results of the form: “If a certain trading strategy is applied and if the realized price trajectory satisfies a certain analytical property, then the terminal payoff is.…” This way, derivation of the Black and Scholes formula and its extension become an exercise in the analysis of a certain class of real functions. While results of the above forms are of great interest if the analytical property in question is believed to be satisfied for almost all realized price trajectories (for example, if the price is believed to follow a certain stochastic process which has this property with probability 1), they are valid regardless of the stochastic process which presumably generates the possible price trajectories or the probability assigned to the set of all paths having this analytical property.  相似文献   
96.
Hillas (1990) introduced a definition of strategic stability based on perturbations of the best reply correspondence that satisfies all of the requirements given by Kohlberg and Mertens (1986). Hillas et al. (2001) point out though that the proofs of the iterated dominance and forward induction properties were not correct. They also provide a proof of the IIS property, a stronger version of both iterated dominance and forward induction, using the results of that paper. In this note we provide a direct proof of the IIS property.Received February 2002  相似文献   
97.
Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.This paper is dedicated to the memory of Professor John V. Breakwell.The authors would like to express their sincere and grateful appreciation to Professors R. Bulirsch and K. H. Well for their encouraging interest in this work.  相似文献   
98.
Non-zero sum discounted stochastic games with uncountable state space and state in-dependent transitions have stationary equilibrium strategies.  相似文献   
99.
A model of collective bargaining in differential games, similar to one considered by Leitmann (Ref. 1), is proposed. Optimal threat strategies are then found and compared with Leitmann's solution. Nash-optimal threat strategies are also found and compared with the other two solutions.The author would like to thank Professor G. Leitmann of the University of California for bringing the author's attention to this subject.  相似文献   
100.
A general model is proposed for the stochastic version of the single-machine allocation problem. Sufficient conditions are given to ensure that there is an optimal strategy given by a fixed permutation of the job set. Additional results are given for an important special case of the general model involving simple jobs. The paper concludes with material concerning the evaluation of fixed permutations as strategies under conditions more general than the sufficient conditions mentioned above.  相似文献   
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