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Showing papers in "Systems Research and Behavioral Science in 1980"


Journal ArticleDOI
TL;DR: In this article, the authors examined decision making in living systems at the level of the organism and implemented ten simple decision rules, or heuristics, as computer subroutines in a simulation program designed to determine how often each would select alternatives with highest-through-lowest expected value in a series of randomly generated decision situations.
Abstract: This article examines decision making in living systems at the level of the organism. Ten simple decision rules, or heuristics, were implemented as computer subroutines in a simulation program designed to determine how often each would select alternatives with highest-through-lowest expected value in a series of randomly generated decision situations. The decision situations varied in their number of alternatives (2, 4, or 8) and outcomes (2, 4, or 8). Results indicated that most of the heuristics, including some which “ignored” probability information, regularly selected alternatives with highest expected value, and almost never selected alternatives with lowest expected value. Implications of this finding for motivational explanations of heuristic use—as opposed to the more popular cognitive explanations—are discussed.

233 citations


Journal ArticleDOI
TL;DR: The purpose in this chapter is to explore, through an example, the roles of technical competence and of behavior in predicting the outcome of a competitive situation.
Abstract: Our purpose in this chapter is to explore, through an example, the roles of technical competence and of behavior in predicting the outcome of a competitive situation. Of course, factors arising from uncontrollable natural events (such as bad weather) and from human intervention (such as referee error) could have a marked effect on the outcome. In most competition, however, an effort is usually made to minimize the effect of natural causes to avoid unfair outside intervention.

120 citations


Journal ArticleDOI
TL;DR: The languages of action and interaction studied in this paper arise from a formalization of the concept of a “production system” found in several recent empirical studies of human action.
Abstract: The languages of action and interaction studied in this paper arise from a formalization of the concept of a “production system” found in several recent empirical studies of human action. From a systems viewpoint, the concern is with the temporal structure of the activity of living systems-organisms, groups, and/or organizations. The theory is applicable at any of these levels to the extent that actions of units at each level can be appropriately specified. The article starts with the idea that acts of an acting unit are evoked only when certain conditions are satisfied. An action is identified as an act together with the class of conditions under which it is evoked. Formal interest centers on action strings (concatenations of actions that meet criteria derived from episode constraints relating actions) and how well-formed they are. An episode constraint holds between two actions if one of the associated acts establishes a condition in the class evoking the other act. Two basic types of episode constraints are identified and several propositions are proved and conjectures advanced about the type of automaton that will accept only well-formed action strings under various assumptions about the type and number of constraints which obtain. The approach is then generalized to n-party interaction.

43 citations


Journal ArticleDOI
TL;DR: The effect of three complexifying factors on a subject's ability to optimize total welfare in a series of computer models of a welfare administration project over time was studied and suggests that revision of theories of complexity within the social sciences may be necessary.
Abstract: This article applies to decision making at the level of the individual human organism. Observations of real-world systems and simulations of them have suggested that many decision-making environments are extremely complex. Indeed, given the limitations on human information processing capacity derived from laboratory experiments, we should not be able to operate in them at all. The methodology developed allowed the controlled investigation of the interaction of the individuals with dynamic systems. The effect of three complexifying factors on a subject's ability to optimize total welfare in a series of computer models of a welfare administration project over time was studied. The factors of (i) number of elements in the system, (ii) connections between them and (iii) the presence or absence of random variation were realized in a 2 × 2 × 2 analysis of variance research design in which two male and two female undergraduates served as subjects in each cell. Multivariate analyses of variance performed on derived measures of performance and system control demonstrated either insignificant differences, or significant differences in the direction opposite to that predicted. The more complex systems did not always attain poorer levels of performance than simpler systems. The results suggest that revision of theories of complexity within the social sciences may be necessary.

37 citations


Journal ArticleDOI
TL;DR: In this article, a decision-making model for two-person systems is proposed, where each negotiator chooses his bargaining strategy (in part) based upon his expectations concerning the other's strategy, while expecting that the other chooses his strategy based upon corresponding expectations.
Abstract: A new model of decision making is introduced. It can be applied to two person systems, at the level of the group, as well as at the level of the organization, the society, and the supranational system. It is determinate when bargainers' information is complete, incomplete, or erroeous. The paper includes a determinate treatment of the outguessing regress, wherein each negotiator chooses his bargaining strategy (in part) based upon his expectations concerning the other's strategy, while expecting that the other chooses his strategy based upon corresponding expectations. The conditions under which negotiations break down or result in agreements which are less than Pareto optimal are also specified. The paper concludes with an application of the proposed model to manipulative bargaining, where negotiators employ manipulative tactics that alter their own or the other's expectations, utility functions, or alternatives, as well as to metabargaining, i.e., bargaining concerning which manipulative tactics will occur.

33 citations


Journal ArticleDOI
TL;DR: This work proposes a nonequilibrium model which assigns a probability distribution to the objects of political decision and successfully simulates the results of a series of experiments performed several years ago.
Abstract: It is well known that group decision processes (of which voting processes are an important special case) do not in general have equilibria. In fact, recent work indicates that such processes are characterized by a degree of instability much more extensive than previously recognized. As observers of ongoing political processes, we contend that such instability results simply do not describe real world politics. As an alternative, we propose a nonequilibrium model which assigns a probability distribution to the objects of political decision. Although this Markov model is based on several specific propositions about the process by which legislative bodies move from one position to another, our theoretical results do not depend on these specific propositions: Given alternative substantive assumptions, our model would produce different predictions about outcomes. This version of the model, however, successfully simulates the results of a series of experiments performed several years ago.

29 citations


Journal ArticleDOI
TL;DR: In this article, the role of public phenomena like knowledge and research and development in the economic growth process of a spatially extended economy is analyzed and it is shown with analytical methods as well as with simulation that improving information networks will generally lead to a higher rate of growth in all regions if the economies behave according to the neoclassical paradigm.
Abstract: This paper presents an analysis of the role of public phenomena like knowledge and research and development in the economic growth process of a spatially extended economy. It deals with the organizational level of living systems (regions) and the societal level, and with monetary information flows, chiefly in the decider and channel and net subsystems. Accessibility to knowledge pools is used as a way of connecting regions with each other. It is shown with analytical methods as well as with simulation that improving information networks will generally lead to a higher rate of growth in all regions if the economies behave according to the neoclassical paradigm. Superimposing an accessibility function with spatial frictions in the information flows on a technology with economies of scale leads to uneven but realistic dynamics. In this case there is an increasing inequality of income per capita between regions with different centrality up to a point of maximum inequality with a subsequent convergence thereafter. The analysis demonstrates that increasing research and development activities can, under certain probable technologies, lead to increasing inequalities between rich and poor regions.

29 citations


Journal ArticleDOI
TL;DR: Feedback, feedforward, and feedwithin are three types of strategic information in systems as discussed by the authors, and each type of information enables all levels of living systems and some non-living systems to map the environment, to gain a more realistic self-image, and to adjust performance on the basis of information about past results.
Abstract: Feedback, feedforward, and feedwithin are three types of strategic information in systems. Feedback enables all levels of living systems and some nonliving systems to map the environment, to gain a more realistic self-image, and to adjust performance on the basis of information about past results. Feedforward enables systems to scan environmental situations, to forecast trends, and to adjust performance in anticipation of changing environmental circumstances. Feedwithin enables systems to monitor internal situations and processes, to identify internal system needs, and to coordinate system parts in concerted action of the whole. There are heuristic and applied biases associated with each type of strategic information.

27 citations


Journal ArticleDOI
TL;DR: There was a tendency to overestimate the positive attitudes of the PRO nuclear public, and there was a significant failure to recognize the extent to which issues of psycholo;gical significance contribute negatively to the attitudes of both PRO and CON public groups.
Abstract: The primary purpose of this study is to make an empirical test of how accurate a group of policy makers were in their assessment of the beliefs and attitudes of the public with regard to the use of nuclear energy. The 40 respondents were senior Austrian civil servants responsible for energy matters. The questionnaire used was the same as that employed earlier to measure the attitudes and underlying beliefs of 224 persons selected as a stratified sample of the Austrian public and two subsets of this sample, the 48 most PRO and 47 most CON the use of nuclear energy. The policy makers completed this questionnaire twice: once with respect to their own positions and, on the second occasion, in the role of a typical member of the Austrian public who was either PRO or CON the use of nuclear energy. This experimental design also permitted comparisons between the policy makers' own positions and those of the general public. Public attitudes toward the use of nuclear energy were found, using factor analysis, to be based upon four underlying dimensions of belief: psychological (anxiety-inducing) risks; economic/technical benefits; sociopolitical implications; and environmental/physical risks. The policy makers' own attitudes were found to be significantly more favorable than those of the total public sample; this was primarily because the policy makers' beliefs about psychological risks made a significantly smaller negative contribution to attitude, and their beliefs about environmental risks made a significantly larger positive contribution. The policy makers were able to shift their own (personal) responses in the directions indicated by their role-play assignments to reproduce accurately the overall attitudes of the PRO and CON groups on this controversial topic, although there was a tendency to overestimate the positive attitudes of the PRO nuclear public. In terms of the underlying belief dimensions, however, there was a significant failure to recognize the extent to which issues of psychological significance contribute negatively to the attitudes of both PRO and CON public groups. The policy makers underestimated the negative value both groups assigned to these risks as well as the extent to which the public believed that nuclear energy would lead to such risks.

21 citations



Journal ArticleDOI
TL;DR: This paper pointed out that most of the behavioral scientist's tools, such as regression analysis, are subject to the same criticisms, and to reject them is in effect to throw the baby out with the bath water.
Abstract: Sussman and Zahler have delivered a damaging blow to the use of catastrophe theory in the behavioral sciences. this article points out that most of the behavioral scientist's tools, such as regression analysis, are subject to the same criticisms, and to reject them is in effect to throw the baby out with the bath water.

Journal ArticleDOI
TL;DR: The antianxiety tranquilizers relieve anxiety and certain other neurotic symptoms, but do not counteract stress, fear, or anxiety caused by schizophrenia and other psychiatric disorders.
Abstract: This paper, on the use of antianxiety drugs to relieve certain neurotic symptoms, involves decision making at the level of the individual organism. The words "anxiety," "fear," and "stress" are often used interchangeably in everyday English. In medical usage "anxiety" denotes a state caused by an internal danger, while "fear" is a response to an external danger. "Stress" is the sum total of the bodily responses which occur when the organism has to adapt to a change. The antianxiety tranquilizers relieve anxiety and certain other neurotic symptoms, but do not counteract stress, fear, or anxiety caused by schizophrenia and other psychiatric disorders. The antianxiety drugs are now being most frequently prescribed for the relief and prevention of emotional distress that might accompany a physical disorder. Somatic illness can cause stress and fear, but does not usually induce neurotic anxiety. In patients suffering from physical disorders, treatment with antianxiety drugs appears justified only in the presence of an underlying psychoneurotic condition.

Journal ArticleDOI
TL;DR: This article deals with system-wide birth (origination or reproduction) and death (termination) processes in systems at the organization level, which can be described by a classical exponential for in the United States.
Abstract: This article deals with system-wide birth (origination or reproduction) and death (termination) processes in systems at the organization level. The birth and death processes can be described by a classical exponential for in the United States. The number of bureaus, outside the defense and postal services, is approximately equal to Poe(b-m)t, where P0 is the number of bureaus at some time zero, b = .0217 is the birth rate, and m = .0043 is the death rate. This suggests an absence of predators, but no shortage of sustenance for bureaus. The groth in the number of bureaus is not controlled in the executive departments of the national government of the United States.

Journal ArticleDOI
TL;DR: In this article, the bargaining set theory does not necessarily predict minimal winning coalitions in voting games with transferable value (i.e., games of division), on the other hand, in games of exchange or log rolling, it is shown that bargaining set predicts equitable or fair payoffs.
Abstract: This article discusses decision making at the level of the society. Although voting games by rational actors are known to be highly unstable, it has been argued that only minimal winning coalitions should form. The bargaining set is presented as an empirically and theoretically relevant solution theory. This theory assigns stable outcomes to some coalitions. It is shown that bargaining set theory does not necessarily predict minimal winning coalitions in voting games with transferable value (i.e., games of division). On the other hand, in games of exchange or log rolling, it is shown that the bargaining set predicts equitable or fair payoffs. This result lends weight to the size principle for this class of games.

Journal ArticleDOI
TL;DR: In this article, the authors deal with collective decision making by voting procedures in living systems at the levels of groups, organizations, societies, or supranational systems, and present general principles which permit the determination of the likelihood of agreement, and disagreement, between plurality and Condorcet outcomes when system size is large.
Abstract: This article deals with collective decision making by voting procedures in living systems at the levels of groups, organizations, societies, or supranational systems. General principles are outlined which permit the determination of the likelihood of agreement, and disagreement, between plurality and Condorcet outcomes when system size is large, for any number of alternatives in virtually any culture. A method is developed which ascertains, for any number of alternatives, the system in which the likelihood of plurality/Condorcet disagreement reaches a maximum. The hypothesis that an inverse relation exists between the probability of plurality distortion and the probability of the paradox of voting is disproved. Methodological issues arising from previous work are considered.

Journal ArticleDOI
TL;DR: In this paper, the authors consider prisoner's dilemma games and report an experiment on 2 × 2 games in which motivational pressures have been separated out as far as possible, in particular in six of the eight games one of the players is indifferent between his strategies with regard to his own payoffs; so that the predominance of choices of the one or the other strategies can be attributed to motivations which take only the other's payoffs into account.
Abstract: In deciding between the two alternatives of a nonconstant-sum 2 × 2 game, a player can be thought to be subjected to conflicting pressures to choose the one or the other. Thus in prisoner's dilemma the pressure to choose the dominating (noncooperative) strategy is opposed by the pressure to choose the cooperative strategy which contains the Pareto optimal outcome which both players prefer. In this game, as in many others, motivations to choose a strategy may be confounded. Thus, the dominating strategy in prisoner's dilemma is dictated by the “sure thing principle” and by the prospect of getting the largest payoff and by a desire to avoid unreciprocated cooperation. The present paper reports an experiment on 2 × 2 games in which motivational pressures have been separated out as far as possible. In particular, in six of the eight games one of the players is indifferent between his strategies with regard to his own payoffs; so that the predominance of choices of the one or the other strategies can be attributed to motivations which take only the other's payoffs into account.

Journal ArticleDOI
K. K. Fung1
TL;DR: In this article, a system perspective based on successional and climax communities is used to analyze both the power and limit of confidential information as a single purpose instrument amid conflicting objectives, and an approach to a selective protection of confidentiality is suggested which achieves both economic efficiency and distributional justice by varying the assignments of rights and burden of proof to different parties depending on their relative gains/losses and relative strength.
Abstract: This article concerns confidentiality of information in social systems at the levels of the group, organization, society, and supranational system. It analyses the benefits and costs of confidentiality in terms of actual and potential Pareto optimality. A systems perspective based on the ecological concepts of successional and climax communities is used to analyze both the power and limit of confidential information as a single purpose instrument amid conflicting objectives. A cusp catastrophe is employed to model discontinuity in confidential behavior, which tends to reduce the quality and availability of confidential information and, therefore, increase the cost of obtaining it when confidentiality is violated. Finally, an approach to a selective protection of confidentiality is suggested which achieves both economic efficiency and distributional justice by varying the assignments of rights and burden of proof to different parties depending on their relative gains/losses and relative strength.

Journal ArticleDOI
TL;DR: A unique modification of the entropy level measure is proposed to explain switching patterns of loyalty such as: one choice alternative is repeatedly selected, but the consistency is punctuated by occasional switching to others, and the best description of a variety-seeking system over time is not measured by the net change in its entropy but by the absolute change.
Abstract: This article deals with living systems at the organism level. Through aggregation we obtain the behavior of groups or classes of persons as they exercise choice perogatives within society. The study focuses on subsystems which process information with major emphasis on the associator, the memory, and the decider. Fundamental advances in modeling human choice behavior (at the level of an individual human being) have occurred as a result of computer simulation capabilities for testing various hypotheses about sustained loyalty over a sequence of decisions, e.g., repeating brand choice. The models reflect the fact that choice behavior can be viewed as an information process. One of the prime descriptions of information sequences is the Shannon entropy measure which has been used by social scientists for about the same length of time as computers have existed. This paper proposes a unique modification of the entropy level measure to explain switching patterns of loyalty such as: one choice alternative is repeatedly selected, but the consistency is punctuated by occasional switching to others. The modified measure relates to changes in entropy. Specifically, the most successful hypothesis for explaining observed loyalty is that the individual strives to maximize the cumulative absolute change of entropy, i.e., max Σ ‖ ΔHt ‖ = max Σ ‖ Ht − Ht−1 ‖. This dynamic viewpoint necessitates consideration of the effects of planning horizons (how far in the future is T?) and experience horizons (how far back does memory extend?). The latter is reflected in the calculation of Ho. Unequal costs of alternatives (such as brands) are shown to produce stronger loyalty effects for the less expensive choices. This leads to the postulate that individuals perceive lower costs for choices that change entropy and higher costs for choices that provide minimal changes. Thus the best description of a variety-seeking system over time is not measured by the net change in its entropy (Σt ΔHt), but by the absolute change (Σt ‖ ΔHt ‖). Zipf's empirical studies (e.g., concerning word lengths) are cited in support of these notions. The aggregation of simulations of choices by individual human beings based on the max Σ ‖ H ‖ hypothesis presents challenging opportunities to study and explain social behavior.

Journal ArticleDOI
TL;DR: A further equivalence relation, extended threshold, is introduced, and it is suggested that this may be interpreted as management by consensus level, and the notion of extended threshold is examined in detail.
Abstract: This article deals with decision making at the organization level of living systems. It develops concepts presented in a previous article (Walker & Gelfand, 1979), which discusses a modeling technique for control systems that attempts to accommodate a manager's limited scope of rational action in the face of organizational and control system complexity. The modeling context used also provides a setting in which some management strategies may be formalized as equivalence relations. In particular, the previous article interprets the formal concepts of internal homogeneity, forcibility, and input span as managerial control strategies: management by exception, management by priority, and management by input span, respectively. This present article introduces a further equivalence relation, extended threshold, and suggests that this may be interpreted as management by consensus level. This notion of extended threshold is examined in detail, together with its interactions with internal homogeneity and forcibility. It is shown that systemwide control may be effected by manipulating levels of each of the three managerial strategies.



Journal ArticleDOI
TL;DR: A dynamic model of a military base-local community system is presented in this paper, which relates to decision making in living systems at the organization level and is designed for use in assessing policy for military installation closures and realignments.
Abstract: A dynamic model of a military base-local community system is presented in this paper. It relates to decision making in living systems at the organization level. The model is designed for use in assessing policy for military installation closures and realignments. The model is of a typical base-community economic system. It is used to illustrate the interdependence of national and local concerns and the link between national policy and community well-being. It focuses upon population, community business activity, and labor force movement.

Journal ArticleDOI
TL;DR: In this paper, the authors deal with decision making at the organization level, but it is perhaps applicable to all other levels, and they use the nesting method of Lagrangian multipliers to bridge the gap between both phases of decision-making processes.
Abstract: This article deals with decision making at the organization level, but it is perhaps applicable to all other levels. Decision-making processes generally have multiple purposes and are made with uncertainty. The objectives are usually on commensurate and in conflict with one another. The processes involve two phases: analytical and judgmental. For the analytical phase, mathematical optimization methods such as mathematical programming are efficiently applied. The nesting method of Lagrangian multipliers is one device intended to bridge the gap between both phases of decision-making processes. The System and Decision Sciences Area of the International Institute for Applied Systems Analysis has been very involved with multiobjective decision problems. This study is one of several works on methodological development for a multicriteria decision-making process.

Journal ArticleDOI
TL;DR: The theory is discussed as an explicit statement of multileveled relationships for the analysis of the vertebrate CNS and, therefore, as presenting a paradigm for, or a way of thinking about, local and global brain theories, brain dysfunction, and brain evolution.
Abstract: An holistic theory of the functional organization of the central nervous system, a system at the level of the organ, in vertebrate organisms is presented as an alternative to localization of function by using two sets of complementary rules for systems designation derived from systems theory. These rules reveal three types of systems according to levels of operation and the origins of goals. These are: (1) the teleogenic or primary systems (reproductive, food-water intake-use, thermoregulative, immune, oxygen intake-use); (2) the teleozetic or subsystems (internal sensory and motor, external motor, external sensory); (3) the teleonomic systems or echelons (field, local circuit, basic functional unit, basic excitation unit). The systems, subsystems, and echelons are discussed with regard to their hierarchical relationships, the nature of their goals, and the supporting experimental evidence. The theory is discussed as an explicit statement of multileveled relationships for the analysis of the vertebrate cns and, therefore, as presenting a paradigm for, or a way of thinking about, local and global brain theories, brain dysfunction, and brain evolution.

Journal ArticleDOI
TL;DR: This work provides a vehicle through which a number of existing models in mathematical psychology, and various as yet unmathematized processes in social psychology and psychiatry, can be brought together constructively and on a uniform mathematical basis.
Abstract: This article deals with information processing subsystems of the human organism and group. While a number of specific (but generally unrelated) mathematical models exist for various processes in the realm of social psychology and psychiatry, the predictive power of these models usually covers only a small range of phenomena. The overall objective of this work is to provide a vehicle through which a number of existing models in mathematical psychology, and various as yet unmathematized processes in social psychology and psychiatry, can be brought together constructively and on a uniform mathematical basis. Particular attention is given to impression formation, choice, and the psychotherapeutic interaction. A probabilistic and relativistic Directype state-vector formalism provides the overall framework. The ultimate goal of constructing such a system is to increase our knowledge of the dynamic laws governing human behavior. It is clear from our study that there is an essential similarity among the psychoanalytic, gestalt, and behavioral psychotherapies.

Journal ArticleDOI
TL;DR: Three experiments are reported which deal with the human's response to uncertainty in decisions varying in objective uncertainty as measured by the information theoretic metric, H, and results confirm earlier findings that mean uncertainty estimates increase linearly with H.
Abstract: The human organism functions as a decider in a variety of systems, particularly at the level of groups and organizations. Because of the importance of the human's decisions to the performance of these systems, it is desirable to understand how human decision makers respond to the uncertainty and handle the information within them. Three experiments are reported which deal with the human's response to uncertainty in decisions varying in objective uncertainty as measured by the information theoretic metric, H. Results confirm earlier findings that mean uncertainty estimates increase linearly with H from 0.2 to 2.8 bits where a discontinuity in the function occurs. The location of this discontinuity is shown to change with information processing load and to be as high as 3.8 bits under low load conditions. Uncertainty estimation proves to be rather robust under conditions of reduced supports for estimation, such as the elimination of anchors (sample stimuli). Finally, a shift also from uncertainty to probability estimation occurs at the discontinuity in the function and this shift is shown to be dependent on information processing load.

Journal ArticleDOI
TL;DR: In this article, the outcomes of a series of multiperson bargaining experiments reported by J. Keith Murningham are reanalyzed to assess their support for the game-theoretic competitive solution.
Abstract: The outcomes of a series of multiperson bargaining experiments reported by J. Keith Murningham are reanalyzed to assess their support for the game-theoretic competitive solution. This paper deals with decision-making processes in a group system. It is shown that the payoff predictions of this solution hypothesis do at least as well as the predictions of the several behavioral hypotheses Murningham considers. The conclusion, then, is that solutions based on traditional decision and game theoretic concepts can provide adequate explanations of multiperson cooperative action.

Journal ArticleDOI
TL;DR: This paper presents a mathematical model for all matter-energy processing subsystems at the level of the society, specifically India, and explores India's choices in the food and energy sectors over the coming decades.
Abstract: This paper presents a mathematical model for all matter-energy processing subsystems at the level of he society, specifically India. It explores India's choices in the food and energy sectors over the coming decades. Alternative land intnsive, irrigation energy intensive, and fertilizer intensive techniques of food production are identified using a nonlinear programming mdel. The land saved is devoted to growing firewood. The optimum combination of railway (steam, diesel, and electric traction) and road automobiles, diesel trucks, and diesel and gasoline buses) transport is determined. For the oil sector, two alternative sources of suply of crude oil and petroleum products are included, namely, domestic production and imports. The optimum choice is determined through a linear programming model. While the model is basically a satic one, designed to determine the optimal choice for the target year of 2000-2001, certain intertemporal detail is incorporated forelectricity generation. The model minimizes the costs of meeting the needs for food, transport in terms of passenger kilometers and goos per ton per kilometer, energy needs for domestic cooking and lighting, and the energy needs of the rest of the economy.

Journal ArticleDOI
TL;DR: The conditions are given under which the usual serve strategy (strong-weak) is optimal and it is shown that the last property does not carry over to the case of optimal strategy in a match.
Abstract: : The paper shows how the probability of winning a game, a set and a match, depend on the probability of winning a ball (from one's own and from the opponent's serve). The conditions are given under which the usual serve strategy (strong-weak) is optimal. It is also shown that a game is 'strategy-less in the sense that if the player has k( = 1, 2 or 3) balls which he can play with increased probability of winning, then all strategies of placing these balls during the game are equivalent. Finally, it is shown that the last property does not carry over to the case of optimal strategy in a match. (Author)