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The article deals with the development of mathematical sociology in Japan and introduces the articles featured in the 1989 issue of the Journal of Mathematical Sociology. A burgeoning of interest in mathematical sociology may well be traced back even to prewar Japan. A study of the structure of Japanese families by Teizo Toda in 1937 is such an example. In that study, Toda showed by examining census data that the distribution of types of families was determined by the age of first marriage of those involved, although he did not use a model building method explicitly. However, it was not until the mid-1960's that mathematical sociology was pursued as such. Around 1970, the Tokyo University Press published a set of sociology textbooks of eighteen volumes including one volume titled Mathematical Sociology edited by Yasuda. This was the first book in Japan which had the title of mathematical sociology as such. In the 1970's, there emerged more than a few semi-formal societies scattered within the nation for the study of mathematical sociology, which were unified into a nationwide semi-formal society formed in 1980. A dozen of active core members and about two more dozens of scholars and students had regular meetings twice a year by coming together for a few nights. Mathematical sociology in Japan has plunged into a specialty stage in the sense that a formal society, the Japanese Association for Mathematical Sociology, was set up and an official journal was newly published.

The puzzle of origins and future of government and social complexity in human and social dynamics, arguably a characteristic feature of the emergence and long-term evolution of hierarchy and power in the history of civilizations, is an enduring topic that has challenged political scientists, anthropological archaeologists, and other social scientists and historians. This paper proposes a new computational theory for the emergence of social complexity that accounts for the earliest formation of systems of government (pristine polities) in prehistory and early antiquity, as well as present and future political development. This general social theory is based on a “fast process” of crisis and opportunistic decision-making through collective action, which feeds a “slow” process of political development or decay. The “fast” core iterative process is “canonical” in the sense that it undergoes variations on a recurring theme of signal detection, information-processing, problem-solving, successful adaptation and occasional failure. When a group is successful in managing or overcoming serious situational changes (stresses or opportunities, endogenous or exogenous, social or physical) a probabilistic phase transition may occur, under a specified set of conditions, yielding a long-term (slow) probabilistic accrual process of emergent sociopolitical complexity and development. A reverse process may account for decay. The canonical theory is being formally implemented through the “PoliGen” agent-based model (ABM), based on the new Multi-Agent Simulator of Networks and Neighborhoods (MASON). Empirically, the theory is testable with the datasets on polities developed by the Long-Range Analysis of War (LORANOW) Project. This paper focuses on the concepts, mechanisms, and basic formal structure that constitute the canonical theory and inform the subsequent simulation model. [ABSTRACT FROM AUTHOR]

This paper examines Dawes (1975) model on commons dilemma (CD) situation and proposes an alternative model which formulates CD. Firstly, it makes clear that Dawes model does not have the characteristics of CD. Secondly, it specifies resource unit condition which models of commons dilemma must satisfy. Thirdly, it presents CD model, which is obtained by setting the condition in Dawes model. And lastly, it examines some nature of the proposed model and find that in CD situation, fine is distributed proportionally to each players property. [ABSTRACT FROM AUTHOR]

The theory of regular equivalence has advanced over the last 15 years on a number of different fronts. Notation and terminology have developed often making it difficult to obtain a coherent view of the area as a whole. This paper attempts to provide a framework in which to develop and explore the general mathematical theory of regular equivalence and to place a number of the more important results into that framework. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to data analysis that assists the investigator in discriminating among specific relations corresponding to alternative scientific predictions about qualitative variates. [ABSTRACT FROM AUTHOR]

Mathematical demography traditionally has been concerned with the dynamics of the growth and structure of a population that is undisturbed by migration. Recently, however, increasing attention has been directed at the relationships between interregional migration flows and the growth and structure of multiregional population systems that are open to internal migration. This paper contributes to that emerging body of knowledge by generalizing the notion of a life table to the multiregional case and showing how such a generalization leads to a mathematical theory of multiregional population growth that is consistent with the currently accepted single-region theory. [ABSTRACT FROM AUTHOR]

Quantitative sociology has grown by burrowing methods from the experimental sciences even though. for the most part, our data are observational. Where the procedures of experimental science can he applied, data analysis can exploit simplifying assumptions because good experimental design removes correlations among independent variables that exist nature, outside the experiment, as well as effects or unmeasured variables. Where the science is of necessity, observational, these simplifications can not be guaranteed and, as a result, the analyses reached through by use of some of the standard "workhorse" techniques of the statistical repertoire may not be valid and conclusions reached by the application of these techniques are in doubt, This paper explores an alternative framework for data analysis in quantitative sociology, bypassing the statistics associated with experimental methods. Specifically, it explores generalizations of the method and quantitative theory used by physical surveyors, generalizing them to the needs of observational data. Application of this framework to text, including editorials and free answers to questionnaires as well as application to (social) survey data, supports their its for these purposes and the cartographic methods suggest that micro theories embedded in these methods reduce the load of a priori assumptions "normally" required for both text analysis and survey analysis. The applications suggest a research path applicable to "ordinary" sociological variables, including education, income, occupation, and gender. that shifts the burden of argument away from variance explained criteria and toward an integration of theory and method, guided by principles of parsimony and consistency. [ABSTRACT FROM AUTHOR]

This paper extends a recently proposed model of dynamical interactions between the macro structures of a society to hierarchically ordered societies. The so extended model helps interpreting some social and political phenomena such as coalitions, their hierarchical level and the degree of anarchy on a certain hierarchical level. The surprising property of the underlined model that stability is certain in the constant parameter case strikingly extends to this model. One of the main results of the paper is that the system has a unique equilibrium exactly when there is no anarchy on the highest hierarchical level. These results apply to a study of changes in the equilibria as determined by the changes in the system parameters [ABSTRACT FROM AUTHOR]

The major achievement of most current qualitative data analysis software systems in social sciences has been the efficient code-and-retrieve abilities. Although such abilities greatly strengthen and assist the handling of qualitative data, they do not address the crucial tasks of theory construction as traditionally understood in qualitative research. Application of knowledge-based systems has been recognised as an important approach to theory construction in qualitative data analysis. This approach heavily depends on a suitable way of knowledge representation. This paper describes a knowledge representation method for representing grounded theory construction, in which a hybrid approach of fuzzy set theory and semantic networks is applied. [ABSTRACT FROM AUTHOR]

In the paper four semirings for solving social networks problems are constructed. The closures of the matrix of a given signed graph over balance and cluster semirings can be used to decide whether the graph is balanced or clusterable. The closure of relational matrix over geodetic semirings contains for every pair of vertices u and v the length and the number of u - v geodesics; and for geosetic semiring the length and the set of vertices on u - v geodesics. The algorithms for computing the geodetic and the geosetic closure matrix are also given. [ABSTRACT FROM AUTHOR]

The present paper deals with the identification and maximum likelihood estimation of systems of linear stochastic differential equations using panel data. So we only have a sample of discrete observations over time of the relevant variables for each individual. A popular approach in the social sciences advocates the estimation of the exact discrete model after a reparameterization with LISREL or similar programs for structural equations models. The exact discrete model corresponds to the continuous time model in the sense that observations at equidistant points in time that are generated by the latter system also satisfy the former. In the LISREL approach the reparameterized discrete time model is estimated first without taking into account the nonlinear mapping from the continuous to the discrete time parameters. In a second step, using the inverse mapping, the fundamental system parameters of the continuous time system in which we are interested, are inferred. However, some severe problems arise with this indirect approach. First, an identification problem may arise in multiple equation systems, since the matrix exponential function defining some of the new parameters is in general not one-to-one, and hence the inverse mapping mentioned above does not exist. Second, usually some sort of approximation of the time paths of the exogenous variables is necessary before the structural parameters of the system can be estimated with discrete data. Two simple approximation methods are discussed. In both approximation methods the resulting new discrete time parameters are connected in a complicated way. So estimating the reparameterized discrete model by OLS without restrictions does not yield maximum likelihood estimates of the desired continuous time parameters as claimed by some authors. [ABSTRACT FROM AUTHOR]

This paper argues for a heuristic rather than a fundamental role for mathematics in the social sciences. The a priori argument for insisting on a natural-scientific and mathematical approach to the study of social phenomena is found to rest on an untenable assumption about the powers of standard logic. Further, the requirements of description in the natural sciences are found to conflict irreconcilably with the nature of social interaction and social organization. As an alternative to the natural-science model, it is proposed that the regularities described by mathematical models depend upon and reflect underlying institutional arrangements. Consequently, mathematical models represent the outcomes of basic social processes rather than those processes directly. Nevertheless, it is argued, mathematical models are extremely useful and, indeed, indispensable in attempting to unravel the complexities of social phenomena. [ABSTRACT FROM AUTHOR]

This paper examines Caplow's model of coalitions in the triad and identifies several shortcomings. Retaining the basic structure of Caplow's arguments, it recasts the problem as one of interdependent rational decision making. The reformulation allows increased generality in several directions, including a more general notion of strength, relaxation of the additivity assumption about strength, and the adoption of probabilistic choice to allow predictions about the relative frequencies of the various coalitions. [ABSTRACT FROM AUTHOR]

In their original exposition of the fundamental concepts of game theory, John von Neumann and Oskar Morgenstern followed a definitional procedure. That is, they defined the principal instruments of the theory and supplemented their definitions with what might be called plausible reasoning to support their choices of definitions. This paper presents postulates which are necessary and sufficient that a social decision process is cooperative game according to the formulation of von Neumann and Morgenstem. In the von Neumann-Morgenstern formulation of a cooperative game, and in its subsequent extensions, one has generally a set of individuals, certain subsets of which are called coalitions, and a set of possible outcomes for which the individuals' preferences are given. The object of the formulation is to establish a relation of social preference among the outcomes through consideration of the powers and preferences of the coalitions. The definitional procedure consists of three suppositions: first, that there are given exogenously certain rules of the game which specify the powers of the coalitions; second, that the preferences of a coalition are determined by the rule of unanimity among its members; and third, that social preference coincides with the conjunction of power and preference for some coalition.

This article presents information on various theories which apply the "baseline model" logic to solve several major theoretical problems. In Bruce H. Mayhew's earlier works on the above mentioned subject, he adopted a notion of a baseline model that saw such models in a considerably more theoretical and explanatory role, but not as strong as the role advocated in the article in question. In "Baseline Models of Sociological Phenomena," Mayhew offers a rather different interpretation of baselines, although the types of models used as examples of baseline theories are logically the same as in earlier works. In the current work Mayhew proposes that baseline models are not merely "standards of comparison" nor even the more elegant "probabilistic null hypothesis." Rather, in this article, the baseline models have emerged as full-fledged theories that are proposed to explain variability. In pursuing a baseline strategy, Mayhew makes a strong case for sociology as a scientific enterprise. In all science, the ultimate goal of intellectual activity is theory. Mayhew is certainly correct in his emphasis on the fact that all science, including sociology, should be abstract, simple, parsimonious and should be unconcerned with tracing causal chains.

The research tested Laing and Morrison's myopic and hyperopic models for sequential, three-person coalition games when the goal is maximizing rank position. The myopic model assumes that people behave as if the present trial were the last, while the hyperopic model assumes that people behave as if the coalition formed on the present trial will continue forever. The experiment involved three different planning horizon conditions: an indefinite number of trials (the condition specified by Laing and Morrison for their models), one trial remaining, and eight trials remaining. Four different accumulated point totals were used: 300-250-50, 350-150-100, 250-200-150, and 225-200-175. In general, the myopic model was more successful than the hyperopic model, though neither model was especially accurate. Changes in the myopic model were proposed, and the difficulties in developing a theory of social decision making involving long range planning were discussed. [ABSTRACT FROM AUTHOR]

The article focuses on empirical evaluation of formal theory. In the paper by researchers D.K. Hildebrand, J.D. Laing and H.L. Rosenthal, henceforth HLR, proposed an index to measure the adequacy of a particular kind of theory when confronted with harsh facts. The authors L.A. Goodman and W.H. Kruskal, henceforth GK, presented a critical analysis, together with constructive proposals towards partial mitigation of the flaws and gaps they found in HLR. The authors do not agree with the rationales given in HLR for the independence like denominator of the proposed index. One can, however, take the index as given and ask how it performs. It was noted in GK that the HLR index compares the theoretically empty cells with the multiplicative yardstick probabilities for those cells, and no adequate justification for this comparison was found. This is so for both the unweighted and weighted forms of the index. In GK, some modest ways around this problem was suggested without claiming necessarily wide applicability for the suggestions.

Population biologists and comparative animal behaviorists assume that competition between members of the same species allocates resource utility, but they cannot validate that assumption without a unidimensional measure of resource utility such as money, which they do not have since they leave humans to the social sciences. One of the social sciences, economics takes the point of view that pervasive zero-sum competition between people does not determine wage and salary incomes. The present article validates the assumption of population biology and comparative animal behavior that competition within a species allocates resource utility by finding the statistical signature of pervasive zero-sum competition in longitudinal data on individual wage and salary incomes. [ABSTRACT FROM AUTHOR]

Despite the recent wave of interest in the social and physical sciences regarding "complexity," relatively title attention has been given to the logical foundation of complexity measurement. With this in mind, a number of fairly simple, "reasonable" axioms for the measurement of network complexity are here presented, and some of the implications of these axioms are considered. It is shown that the only family of graph complexity measures satisfying the "reasonable" axioms is of limited theoretical utility, and hence that those seeking more interesting measures of complexity must be willing to sacrifice at least one intuitively reasonable constraint. Several existing complexity measures are also described, and are differentiated from one another on an axiomatic basis. Finally, some suggestions are offered regarding future efforts at measuring graph complexity. [ABSTRACT FROM AUTHOR]

We argue that computer simulation can serve as a functional equivalent for the experimental method in sociology, with respect to theory development. To this end we present accounts of experimentation and simulation by experimenting/simulating scientists and sociologists of science. From these analyses we conclude desirable features of a simulation method: generality, surprisability and power to separate. That means that Ii. should be widely applicable, capable of surprising the researcher, and capable of separating surprising results that originate from sociological features of the model from those that stem from technical features. We demonstrate three methods that may provide these features: emergence, fixing points of reference, and comparative response testing. We develop the latter method in greater depth by discussing an exemplary simulation study. [ABSTRACT FROM AUTHOR]

Relationships between size and structural differentiation arc basic points of analysis by organizational sociologists. Building upon Blau's1970 theory of size and structure in organizations, we present a thermodynamic model of these relationships that offers a new theoretical perspective on processes central to understanding organizations: structural stability, equilibrium and change. Our method is to adapt Blau's theory to thermodynamic principles that specify relationships between organizational parameters such as size and differentiation and thereby explain stability. The underlying question for analysis, we propose, is the nature of organizational stability rather than temporal direct or indirect relationships between organizational size and structural differentiation. Starting with Blau's formal theory of size and differentiation, we use the model to logically justify and clarify interpretations in his generalizations and the more recent work of others. We start with Blau's theory because of its focus on stability and equilibrium in organizations and derive stability conditions in organizational structures by using a thermodynamic theory of physical systems. [ABSTRACT FROM AUTHOR]

We pose the question, What is necessary to build an artificial social agent? Current theories of cognition provide an analytical tool for peeling away what is understood about individual cognition so as to reveal wherein lies the social. We fractionate a set of agent characteristics to describe a Model Social Agent. The fractionation matrix is, itself, a set of increasingly inclusive models, each one a more adequate description of the social agent required by the social sciences. The fractionation reflects limits to the agent's information-processing capabilities and enrichment of the mental models used by the agent. Together, limited capabilities and enriched models, enable the agent to be sociaL The resulting fractionation matrix can be used for analytic purposes. We use it to examine two social theories—Festinger's Social Comparison Theory and Turner's Social interaction Theory—to determine how social such theories are and from where they derive their social action. [ABSTRACT FROM AUTHOR]

A generalized version of Coleman's rational choice model for pure exhange in a perfectly competitive setting is extended by introducing the possibility of imperfect access between actors. Imperfect access is assumed to affect the individual opportunity set for purchasing control over more interesting resources. Starting from this conceptualization, the effects of restricted access on the central outcomes of exchange are studied without leaving the general equilibrium framework. Structural variables such as actor dependency, prestige, centrality, and status are specified for exchange situations with imperfect access between competing market participants. [ABSTRACT FROM AUTHOR]

The term structure is one of the most common words in the vocabulary of the social sciences. Yet, even a cursory glance at the literature reveals that a clear conception of what it means and does, is quite generally lacking. In this contribution we try and develop just such a conception, and show that, and how, it is essential to understanding the mechanics and dynamics of social systems at any level of inquiry. In particular, it will appear that both individuals and social groups of any kind or size represent nonlinear dynamical systems, something which is not without important consequences for behavioral or sociological research. Moreover, the structure of these several systems turns out to have precisely the same form. As a consequence, too, the common distinction between micro- and macrosociology loses much of its dogmatic or theoretical meaning. [ABSTRACT FROM AUTHOR]

The idea of partitioning a network in terms of a specific conceptualization of equivalence has taken a powerful hold on the imagination of network analysts. Frequently, an empirically established blockmodel is assessed in terms of its consistency with a particular visualization of a network. We demonstrate that, while a visual representation of a network can be helpful, this also constrains powerfully our image of the structure of that network. This implies that a particular picture of a network is not sufficient for establishing the adequacy of a blockmodel. We argue that once committed to a specific form of equivalence, a network analyst must be committed also to an explicit method of assessing the extent to which a blockmodel is consistent with the selected form of equivalence. We provide a method for doing this. Additionally, and perhaps more importantly, efforts to measure the fit of a blockmodel in terms of a sin- Sic form of equivalence reveal a serious weakness in the idea of using only a single form of equivalence to partition a network. It follows that this idea must be reconsidered. An appropriate generalization of the equivalence idea is one where each block, of a particular image in a blockmodel, is free to conform to a different form of equivalence. We provide a general criterion function, together with a local optimization procedure, for establishing such a generalized blockmodel. This criterion function also provides an appropriate measure of fit. Finally, we propose partitioning a network into a generalized blockmodel where each block, again in an image, can also have a particular pattern within which each equivalence type is a special case. Again, we provide a method for establishing such a model and assessing its fit. [ABSTRACT FROM AUTHOR]

Analyses of likelihood judgments for 515 events support the idea that the perceived likelihood of an event is partly a function of affective processes. Production of affective disturbances makes events seem unlikely. Event likelihoods also are influenced by specific kinds of people and behaviors which are involved in the events. Affective determination of likelihood is stronger when actors have institutionally-clear identities rather than institutionally-vague identities; indeed, affect accounts for more than half of the variance in likelihoods of events within clear institutional contexts. [ABSTRACT FROM AUTHOR]

Let Q,I,J be sets of social goods, aspects and individuals, respectively, and consider the functions v: Q×I×J → {-1,1} and w: Q×J → {-1,1}. We study two 2-stage methods for ordering Q characterized by majority vote and, respectively, amalgamating v first over I and then over J (method IP) or vice versa (method PI). An Ostrogorski paradox occurs when IP and PI give different outcomes. Conditions for this paradox and its relations to Condorcet's paradox are investigated, particularly via a scalogram structure of w. While PI seems more like direct democracy than IP, for decisions on k ⩽ 3 social goods PI is transitive whereas IP may give a cyclic outcome. Extensions to richer than binary data and to decision systems different from majority vote are explored. [ABSTRACT FROM AUTHOR]

The author's fully agree with Bruce H. Mayhew's approach, his emphasis on baseline models, and much of his analysis. It is opined that a theory is a systematic explanation of observable events. It explains these events in general terms, that is, on the basis of general principles that are contingent propositions about the way two or more concepts are related. It has been opined that the objective of sociology, is to analyze social facts, that is, the external constraints that conditions in the social environment exert upon people. Most sociologists do not confine the task of sociology so narrowly, but Mayhew does, and the authors are in full accord with him on this structural definition of sociology. Opportunities are chances. Baseline models indicate the chance occurrences of events. Baseline models are important as they help to make specific predictions about variations in many social phenomenon, predictions concerning the influences of opportunities which have been largely neglected in past social research.

This article reports a test of theories of payoff allocation in n-person game--theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4person, 2-strategy non-sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α-effectiveness (von Neumann--Morgenstern) and β-effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the β-imputation set was more accurate than the α-imputation set, the β-stable set was more accurate than the α-stable set, and the β-core was more accurate than the α-core; in other words, for each of the solutions tested, the prediction from any solution concept based on β-effectiveness was more accurate than the prediction from the same solution based on α-effectiveness. Second, the β-core was the most accurate of the six theories tested. Results are interpreted as showing that β-effectiveness is superior to α-effectiveness as a basis for payoff predictions in cooperative non-sidepayment games. [ABSTRACT FROM AUTHOR]

The development of the field of mathematical sociology is analyzed as a process of balancing three competing objectives—analytic power, scope, and descriptive accuracy—with a particular focus upon means for increasing each without compromising the others. It is argued that recent developments in the fields of artificial intelligence and mathematical decision theory appear to be particularly promising. [ABSTRACT FROM AUTHOR]

The article presents a discussion on the relationship between mathematics and social networks analysis. The latter is recognized as one of the fastest growing specialties in social science. Social networks analysis is based on traditions of different branches of subjects including anthropology, communications science, human geography, and information science. Mathematics has proved to be successful in research work in all the fields particularly physics. The subject focuses on the abstract structure or form of an argument. There are number of mathematicians who are well acquainted with the social networks area. There are several social scientists who are working in the networks area who know mathematics well.

The article presents an analysis of the neoclassical approach in sociological theory. Some central ideas of the classic sociological tradition associate with mathematical ideas. The author has also presented an analysis of the nature of formal theoretic methods that have been adopted to the requirements of advancing sociological theory. A significant unresolved problem of mathematical sociology is the combining of formalism with theory in such a manner that the former becomes essential to the latter.

The article focuses on various aspects of mathematical sociology. Mathematical sociology includes mathematical or formal models to expand the scope, precision and explanatory power of sociological theory. The enthusiasm of those who wanted a successful marriage between sociological theory and mathematics, was heightened by the rapid spread of computer technology. Today, the relationship between mathematics and sociological theory seems to be more ephemeral than ever. On the disciplinary landscape, mathematical sociology has now acquired the status of a struggling specialty.

The article refers to the theoretical aspects in mathematical sociology. Mathematical and sociology consider theory as a list of hypothetical statements. A variety of geometries have been used to make abstract objects and events in a physical theory. Both classical social and classical physical theory stand opposite one another. The contrast between the two is more if the focus in more on the end product of theory work. A social theory has to include general hypothesis about people and their actions and relationships if theory would have been a list of hypothesis.

Three components of indices of social mobility and social inheritance (immobility) are identified, resulting in a procedure which allows one to systematically construct indices incorporating particular social priorities. The procedure is also useful analytically, since the sociological point of view reflected by a given index is made more apparent when the index is decomposed into its constituent parts. [ABSTRACT FROM AUTHOR]

The Siegel-Of she two-component repetitive choice model, while demonstrating great predictive accuracy, is difficult to interpret and is very data-inefficient. Reasons for these shortcomings are analyzed in detail, and a modified model is suggested. The new model can be more easily interpreted, provides greater data-efficiency, and furthermore, holds up well when tested with available data. The importance of the new "discrimination" model for sociology lies mainly with two factors: first, it can explain deviations from gain maximization, and second, it demonstrates that individuals do not act directly on the basis of values (utility) but rather on the basis of marginal utility. A comparison of the discrimination model with the Camilleri-Berger model (a model in which marginal utility plays no role) favors the former. [ABSTRACT FROM AUTHOR]

The article focuses on empirical evaluation of formal theory. Researchers D.K. Hildebrand, J.D. Laing, and H.L. Rosenthal, henceforth H-L-R, propose an index to measure the adequacy of a theory that asserts or predicts emptiness of some cells in a two-way cross classification. There are two separate motivating arguments used by H-L-R to justify the independence-like products of marginals in the denominator of their index. The first argument establishes a kind of null or benchmark hypothesis for saying something about y in ignorance of both "x" and "y" to compare with statements of the theory. But that benchmark procedure seems to us arbitrary and inappropriate. The second argument for benchmark independence turns on arbitrary, tendentious definitions of the terms scope and precision for the theory. There have been many attempts to frame useful quantitative notions of degree of confirmation of a theory. H-L-R and also much of the literature mentioned treat highly simplified notions of theory. The very concept of a scientific theory is not simple, and in any case it seems to us confusing to deal with scientific theories as if they were reducible to cross-classifications with some cells asserted empty.

Examines the Bogart model and its potential application in social sciences. Derivation of a distance measure and computing devices by Bogart; Features of the model; Possible applications of the model.

Multi-person versions of Prisoner's Dilemma are widely applicable in the social sciences. Examination of two important classes of real-world situations reveals that although both can appropriately be called Prisoner's Dilemma, they have incompatible payoff structures. Thus Prisoner's Dilemma games constitute an important but apparently ambiguous set of models. We therefore undertake a taxonomy of multi-person Prisoner's Dilemma. Some aspects of the well-studied two-person case provide a useful beginning for the task. In the general multi-person form, however, some properties of the two-person game are found incompatible with others and so are dropped. Additional properties are suggested by strategic considerations and the associated social phenomena. We demonstrate interdependencies among the various properties and relate some of them to a simple graphical representation. [ABSTRACT FROM AUTHOR]