Game Of Encounter Research Articles

Re-Naming Ourselves: The Political Act of Conceptualizing Identity

We live in a post-ludic society, whereby various kinds of phenomena escape acknowledgment, in virtue of some complex (inter)face that intimidates intellectual effort. It is time for scholars in academia to take the enterprise of naming their experiences, with an eye to the possibility of creating a new domain of order, a new’ivory tower,’ more accustomed to the current every day. Like Bastian Balthazar Bux in The Never-ending Story, by Michael Ende, we need to enter this Fantasia that interpellates us and start giving things and phenomena their right names. The world around us requires our response. We shall prepare ourselves for giving it. In this paper, we want to think of ways of looking at the democratic game of political encounter and rename its new rules, in a quest for new forms of societal transparency.

Comparison of the solutions of linear and non-linear positional differential games of encounter

A positional differential game of encounter of a non-linear, conflict-controlled system with a given target set is considered. Sufficient conditions for a successful encounter of the initial system with the target set are given. The differential game problem of encounter between two objects with restricted manoeuvrability is solved. The equations of motion of the objects and the constraints imposed on the controls are given using the same relations as those in the differential game known /1/ as the “two-car game”. It is assumed that both objects have restricted manoeuvrability and the game takes place over a fixed time interval. A positional strategy is constructed for the pursuer guaranteeing that it arrives at a previously specified distance from the pursued at the instant of game termination. The paper is related to work done in /1–14/.

A necessary optimality condition in a game of encounter at a prescribed instant

A necessary condition is derived, which must be satisfied by the positional strategy minimizing the game's value. It is shown that for a linear system and a convex target function this condition is sufficient. The paper abuts the researches in /1–4/.

On a differential encounter game

A game of the encounter of two objects subject to viscous friction and control forces is examined. The sufficient conditions for the equality of the game's value to the programmed maximin are obtained under constraints of a general form.

Integral constraints on the controls in an encounter game

The players /1/ have, in three, motors of different construction with noninterchangeable fuels. The first motors have, in mathematical notation,“geometric” constraints, the second, “power-integral” constraints, and the third, impulse constraints. The payoff is a prescribed function of position at a fixed termination time. The problem includes as a special cases the game of one motor of any type against any of the three types.

On a method of extremal control

An encounter game problem /1,2/ is analyzed on a prescribed time interval for controlled objects whose dynamics are described by nonlinear differential equations. It is assumed that the game's payoff is a convex function, differentiable in some domain, of the difference between the objects' final states. Under specific conditions a procedure is justified for the formation of an extremal strategy of one of the players, guaranteeing him a game result no worse than in the corresponding programmed maximin problem for the initial position. By example it is shown that in the case of nonlinear systems the procedure described in the paper for constructing the optimal strategy covers certain irregular situations in which the extremal aiming rule developed for linear /1/ and nonlinear /3/ controlled systems is inapplicable. In the case of linear systems the conditions found in the paper ensure the regularity of the encounter game problem and, as shown in /4/, the method proposed for solving the encounter problem occupies an intermediate position between the extremal aiming rule /1,2/ and the direct methods in differential game theory /2,5/.

Optimal pursuit on a plane in the presence of an obstacle

A differential game of simple pursuit is examined in the presence of a convex bounded obstacle or arbitrary form. Both players are prohibited from being inside the obstacle and from intersecting its boundary. The statement of the problem by example of a circular obstacle has been given in the book /1/. A complete solution of the encounter game for the circular obstacle case has been constructed by G.K. Pozharitskii ∗∗ ∗∗ The work was reported in the Institute of Applied Mathematics of the Academy of Sciences of the U.S.S.R at the seminar on the theory of optimal control of motion (see Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No.2, 1979). . A different functional, equal to the players' time of motion up to capture, is used in the present paper; the obstacle's form is not fixed. A method based on the necessary optimality conditions /2,3/ is proposed for the construction of the singular surfaces and the optimal paths in a position pursuit game /4/; -the question of the sufficiency of the proposed construction is not examined. Results of a numerical study for two forms of the obstacle are presented.

Mixed strategies and their application in the encounter-evasion differential games

A positional encounter-evasion differential game with geometric constraints on the players' controls, depending on the system's state, is examined. The concept of the players' mixed strategies is introduced and an alternative is proved which asserts that either the positional encounter game or the positional evasion game is always solvable. The paper continues the investigations in /1–4/.

Theorem on the alternative for a nonstationary differential encounter-evasion game: PMM vol. 42, no. 6, 1978, pp. 1123–1126

A position encounter-evasion differential game with non-stationary geometric constraints on the players' controls is analyzed. It is proved that the alternative is valid for this game, stating that either the position encounter game or the position evasion game is always solvable. The proof uses constructions analogous to the corresponding ones from [1].

Impulse- differential encounter game: PMM vol. 42, n≗2, 1978, pp. 210–218

An optimal program distribution of the finite number of impulse feed -in instants for one of the players is constructed in an isotropic impulse-differential game. Sufficient uniqueness conditions for this sequence are given. The game examined in the paper can also be treated as the problem of optimal multi-impulse correction of motion. The paper continues the research in [1–3] and in subject matter is similar to [4–6].

On the continuous dependence of a linear encounter game on a parameter: PMM vol. 40, n≗ 2, 1976, pp. 207–212

We examine an encounter game problem for linear objects whose equations of motion are integrally continuous relative to a certain parameter. We establish sufficient conditions ensuring, in the regular case, the continuity of the game's value and the semicontinuity of the set of the players' optimal motions with respect to variations of this parameter.

On a sufficient condition for nonlinear position games of encounter: PMM vol. 40, n≗1, 1976, pp. 168–171

We examine an encounter game problem for a nonlinear conflict-controlled system. We have shown that sufficient conditions for a successful completion of the nonlinear position encounter game problem being examined can be derived, under specified assumptions, from the regularity conditions of suitable differential games. As an example we analyze the solution of the geometric-coordinate encounter problem for two objects (material points) whose motions are described by quasi-linear differential equations; there is a “gap” in the control system of the first (pursuing) object. The paper is closely related to the investigations in [1–4].

Stabilization in a linear differential game with integral constraints on the players' control resources: PMM vol. 40, n≗ 3, 1976, pp. 439–445

We examine an encounter game problem for a linear controlled system. We assume that the controls of the first and second players are subject to integral constraints. Using the idea of control with a guide [1] and the methods of stabilization theory [2], we construct a stabilized control procedure ensuring a stable encounter of the motions generated by it with a specified target set. The contents of the paper is related to the investigations in [1, 3–5].

Linear differential encounter game with a functional target: PMM vol. 40, n≗ 2, 1976, pp. 222–229

For a conflict-controlled system described by ordinary linear differential equations we study the problem of constructing a control method ensuring under conditions of uncertainty the existence of specified properties on a certain segment of the system's trajectory. We indicate sufficient conditions for the solvability of the problem and a method for constructing the resolving controls. The paper is related to the investigations in [1–7].

Book Review: The Encounter Game.

Book Review: The Encounter Game.

Review of Elements of encounter; The encounter game; Beyond words: The story of sensitivity training and the encounter movement; and Encounter groups: First facts.

Review of Elements of encounter; The encounter game; Beyond words: The story of sensitivity training and the encounter movement; and Encounter groups: First facts.

Book Reviews

Teaching for Career Development in the Elementary School by Walter Wernick.Career Education: The New Frontier by Ralph Ressler.Pupils as Persons: Case Studies in Pupil Personnel Work by Bruce R. Amble and Richard W. Bradley.Contemporary Approaches to Interest Measurement edited by Donald G. Zytowski.Theories of Counseling and Psychotherapy by Cecil H. Patterson.School Intervention edited by William L. Claiborn and Robert Cohen.The Encounter Game by Bruce L. Maliver.The Gestalt Approach and Eye Witness to Therapy by Fritz Perls. Edited by Richard Bandler.An Introduction to Counseling: A Handbook by George D. Demos and Bruce Grant.Mental Health Care in the World of Work by Hyman J. Weiner, Sheila H. Akabas, and John J. Sommer.

On an encounter game problem under composite controls: PMM vol. 38, n≗ 3, 1974, pp. 402–408

We examine a nonlinear differential game of the encounter of a conflict-controlled phase point with a given set. We prove sufficient conditions for the successful termination of the game in the class of mixed strategies. These conditions are based on the extremal construction introduced in [1] and modified here to conform to the question being discussed.

On minimal observations in a game of encounter: PMM vol. 37, n≗3, 1973, pp. 426–433

We consider the differential game of the encounter of “isotropic rockets” [1]. Its solution, under the condition of complete informativeness of the players, has been constructed in [2]. We investigate the question of the minimal information needed by the players to realize a saddle situation. The statement of similar game problems with incomplete information has been given in [3].

On a linear differential game of encounter: PMM vol. 37, N°1, 1973, pp.14–22

We examine the problem of the encounter of conflict-controlled objects with a specified set at a fixed instant of time. We present one condition under which such a problem has a solution. The results are closely related to those in [1–7].