Showing papers on "Stochastic game published in 1976"
TL;DR: In this paper, a simple differential game between pursuer P and evader E in the neighborhood of a nominal collision course is considered, and the payoff is the terminal lateral miss-distance.
Abstract: We consider a simple differential game between pursuer P and evader E in the neighborhood of a nominal collision course. The payoff is the terminal lateral miss-distance. The control of each player is his acceleration normal to his velocity vector, and both players' controls are bounded. Saddlepoint strategies are deduced for three combinations of the acceleration bounds and are shown to be related to the sign of the derivative of the orientation of the line of sight (L.O.S.).
70 citations
TL;DR: In this article, a generalisation of Gately's concept of player's propensity to disrupt a payoff vector in a three-person characteristic function game has been proposed, and the properties and computational possibilities of this concept are analogous to those of the nucleolus.
Abstract: Gately [1974] recently introduced the concept of an individual player's “propensity to disrupt” a payoff vector in a three-person characteristic function game. As a generalisation of this concept we propose the “disruption nucleolus” of ann-person game. The properties and computational possibilities of this concept are analogous to those of the nucleolus itself. Two numerical examples are given.
57 citations
TL;DR: In this article, a generalization of a previous paper on an airport cost game to the case of an airport profit game is presented, where a fee schedule is obtained by subtracting the payoff vector from the vector of revenues, and it is proved that the fee schedule corresponding to the nucleolus is independent of the revenue vector.
Abstract: This paper represents a generalization of a previous paper on an “airport cost game” to the case of an “airport profit game”. A fee schedule in the airport profit game is obtained by subtracting the payoff vector from the vector of revenues. It is proved that the fee schedule corresponding to the nucleolus is independent of the revenue vector.
54 citations
TL;DR: It is proved by showing that the Laurent series is an approximate solution of the dynamical programming equation for Vn, Vn+1 = fVn, where Vn is the value of an n-stage two person zero sum stochastic game.
Abstract: We show that there exists a Laurent series in a fractional power of n which approximates Vn up to log n, where Vn is the value of an n-stage two person zero sum stochastic game. We prove this result by showing that the Laurent series is an approximate solution of the dynamical programming equation for Vn, Vn+1 = fVn. It seems that our methods could be used to find approximate solutions to other difference equations. Our proof makes repeated use of Tarski's principle for real closed fields.
49 citations
TL;DR: The problem of assigning patrol boats to capture or delay an infiltrator with perishable contraband attempting escape across a long, narrow strait is formulated as a two‐sided time sequential game.
Abstract: The problem of assigning patrol boats, subject to resource constraints, to capture or delay an infiltrator with perishable contraband attempting escape across a long, narrow strait is formulated as a two-sided time sequential game. Optimal mixed strategies are derived for the situation of one patrol boat against one smuggler. Procedures for obtaining numerical solutions for R > 1 patrol boats are discussed.
43 citations
TL;DR: In this article, the problem of minimizing a player's total underachievement of a fixed set of goals is shown to reduce to a linear programming problem, and applications are discussed and illustrative examples are presented.
Abstract: This paper investigates a class of two-person zero-sum multiple payoff games in which each component is deterministic. The problem of minimizing a player's total underachievement of a fixed set of goals is shown to reduce to a linear programming problem. Applications are discussed and illustrative examples are presented.
34 citations
TL;DR: In this paper, the problem of solving the positional problem on the minimax functional at a given instant is studied for the nonlinear, competitively controlled system and iterative processes are proposed, permitting one to find the minimumax of the payoff as a function of position, and also the sets of positional absorption.
Abstract: Solution of the positional problem on the minimax functional at a given instant is studied for the nonlinear, competitively controlled system . Iterative processes are proposed, permitting one to find the minimax of the payoff as a function of position, and also the sets of positional absorption. The cases are considered in which the indicated elements are determined after a single application of operators of special form to the program maximin function and the program absorption set. Bibliography: 18 titles.
30 citations
TL;DR: In this paper, the authors present conditions which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. But they do not consider the case where all players have perfect information.
Abstract: The paper presents conditions which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. When the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary.
28 citations
TL;DR: An equivalence between simplen-person cooperative games and linear integer programs in 0–1 variables is presented and in particular the nucleolus and kernel are shown to be special valid inequalities of the corresponding 0-1 program.
Abstract: An equivalence between simplen-person cooperative games and linear integer programs in 0–1 variables is presented and in particular the nucleolus and kernel are shown to be special valid inequalities of the corresponding 0–1 program. In the special case of weighted majority games, corresponding to knapsack inequalities, we show a further class of games for which the nucleolus is a representation of the game, and develop a single test to show when payoff vectors giving identical amounts or zero to each player are in the kernel. Finally we give an algorithm for computing the nucleolus which has been used successfully on weighted majority games with over twenty players.
15 citations
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TL;DR: In this paper, Fair Allocation rules, selecting a payoff for every possible cooperation structure, are studied for games in characteristic function form, and these are proven to be unique, closely related to the Shapley value, and stable for a wide class of games.
Abstract: Graph-theoretic ideas are used to analyze cooperation structures in games. Allocation rules, selecting a payoff for every possible cooperation structure, are studied for games in characteristic function form. Fair allocation rules are defined, and these are proven to be unique, closely related to the Shapley value, and stable for a wide class of games. (This abstract was borrowed from another version of this item.)
5 citations
01 Jan 1976
01 Jan 1976
TL;DR: For a stochastic game with countable state and action spaces, it was shown in this article that the best the remaining player can do is solving a markov decision problem, corresponding to the fixed stationary strategies.
Abstract: For a stochastic game with countable state and action spaces we prove, that solutions in the game where all players are restricted to semi-markov strategies are solutions for the unrestricted game. In addition we show, that if all players, except for one, fix a stationary strategy, then the best the remaining player can do, is solving a markov decision problem, corresponding to the fixed stationary strategies.
TL;DR: In this article, the process of bargaining between management and union during a strike is modelled by a nonlinear stochastic differential game, and a pair of Pareto-optimal strategies is obtained.
Abstract: The process of bargaining between management and union during a strike is modelled by a nonlinear stochastic differential game. It is assumed that the two sides bargain in the mood of a cooperative game. A pair of Pareto-optimal strategies is obtained.
TL;DR: In recent years, business management has been exhorted to become involved in the development of computer-based system applications that will produce high payoffs, but discovered that the techniques for identifying high payoff applications, and for selecting those offering the greatest likelihood of success, were poorly developed.
Abstract: In recent years, business management has been exhorted to become involved in the development of computer-based system applications that will produce high payoffs. As managements responded to this call for involvement, they discovered that the techniques for identifying high payoff applications, and for selecting those offering the greatest likelihood of success, were poorly developed at best. Furthermore, systems people were ill-prepared to view their own operations as managed costs and, as such, subject to scrutiny as an investment on which a return was expected. A systems operation should generate a return on the company's investment in it that is at least as high as that produced by other investments, but with the additional requirement that the systems operation
TL;DR: In this paper, it was shown that a saddle-point solution exists in a two-person zero-sum game whose payoff is given by a matrix which is not completely defined.
Abstract: It is shown that a saddle-point solution exists in a two-person, zero-sum game whose payoff is given by a matrix which is not completely defined. On the other hand, we show that such games do not always have a value, so that a saddle-point solution is not necessarily an optimal solution.
TL;DR: In this paper, a zero-sum, two-player linear differential game of fixed duration is considered in the case when the information is incomplete but a statistical structure gives both players the possibility to spy the value of an unknown parameter in the payoff.
Abstract: A zero-sum, two-player linear differential game of fixed duration is considered in the case when the information is incomplete but a statistical structure gives both players the possibility tospy the value of an unknown parameter in the payoff. Considerations of topological vector spaces and functional analysis allow one to demonstrate, via a classical Sion's theorem, sufficient conditions for the existence of a value.
TL;DR: Saddle points are defined for two-person differential games in which the players have opposing preference orderings over lotteries on a set of qualitative objectives, rather than numerical payoff functions.
Abstract: Saddle points are defined for two-person differential games in which the players have opposing preference orderings over lotteries on a set of qualitative objectives, rather than numerical payoff functions. A simple example is then given of a game without such a qualitative saddle point.
TL;DR: In this article, an analytical paradigm is presented for discriminating among four strategic goals in the mixed-mode three-person game: maximization, security, intracoalition compatibility, and competition.
Abstract: Coalition formation literature indicates that strategies more ameliorative than minimum resource theory appear under a variety of conditions of the competitive environment. These conditions include uncertainty of outcome and indivisibility of payoff. Some investigators have hypothesized that the inadequacies of minimum resource theory can be attributed to strong players using a parity norm and weak players using an equality norm in the bargaining process. The present study examines the plausibility of this hypothesis in the initial partner selection stage of the bargaining process phase of decision processes in systems at the small group level. An analytical paradigm is presented for discriminating among four strategic goals in the mixed motive three-person game: maximization, security, intracoalition compatibility, and competition. The last three goals are nonoptimal under minimum resource theory. Some earlier results that relatively indivisible payoffs lead to a greater incidence of nonpay-off-maximizing strategies than expected under minimum resource theory were supported under conditions of play involving indirect interpersonal interaction. The appropriateness of taking resource position alone as the determinant of a norm for strategy selection consequently must be questioned.