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The usual assumption in models of asymmetric information is that I know my attributes and you do not. But sometimes the asymmetry seems to be reversed: You (a woman, a firm) know better than I (a man, a job applicant) my market value. This may result in a dilemma because equilibrium strategies may be described by the title of this paper. (Iff means: if and only if.) The result resembles the "No-Trade-Theorem" of Milgrom and Stokey (1982) but cannot be derived from it. [ABSTRACT FROM AUTHOR]

The article discusses a stability proof for an interactive Markov chain. An interactive Markov chain is one in which the transition probabilities applying to each individual of a population are functions of the frequencies by state of the rest of the population. This functional dependence allows social interaction among individuals, whereas conventional Markov chains assume away such interaction. Let P = [Pij] be the KXK transition matrix applying to each individual; where Pij is the probability of transition from state j to state i. The elements of P must be nonnegative, and all column sums must equal one. Throughout, when the symbols ≥ and > are used with an array, they will mean every element greater than or equal to and every element greater than, respectively. It is known from the theory of nonnegative matrices that A has a dominant eigenvalue which is real, positive and of multiplicity one. This dominant eigenvalue has a corresponding dominant eigenvector which has all elements positive and which is unique up to a scalar multiple. To put the primitivity assumption in perspective, it is useful to recall that, in the ordinary Markov chain case b = 0, primitivity is both necessary and sufficient for convergence.

In this paper, the equilibrium properties of Coleman's (1973) model of social exchange are explored as a prelude to making interpretations about the dynamics implicit in static models of exchange in general, this model in particular. The model is first presented in the conventional way--as an exchange condition embedded within more general equilibrium conditions, and the subsequent analysis of the model is enriched by examining its equilibrium at aggregate as well as disaggregate levels and by interpreting the model as a set of flows or networks. Its equilibrium properties are then described. First, it is shown how a model in which the exchange condition is a function of its equilibrium, defines an equilibrium which is reproducible and reversible in the stochastic sense. Tests for reversibility are given which show how the equilibrium conditions can be computed from inspection of the data set. Second, an underlying flow structure to the model is assumed, and it is shown how equilibrium in this structure is equivalent to the exchange condition being met. This produces symmetric flows or equal exchange at the aggregate level and a reversible equilibrium. The real interest in this analysis is on how near an actual system is to such equilibria and thus a set of accounts measuring such departures from equilibrium in terms of aggregate and disaggregate flows is presented. Finally, a test example based on the data used by Michener, Cohen and Sorensen (1977) is presented to illustrate the concepts of proximity to structural and reversible equilibria. [ABSTRACT FROM AUTHOR]

This paper presents a model of change in sociometric structure in an idealized "small" group where everyone is in constant, uniform interaction. After the model is discussed dynamically, the set of invariant sociograms for this model is defined and compared to those defined for other theories. The model is shown to include the strong forms of balance theory, clustering, transitivity, and positive balance. The model predicts that the weak forms become strong forms under constant contact. Equilibrium conditions are discussed in some detail, and specific examples are displayed, including examples which are not predicted by balance theory, clustering, or other theories. [ABSTRACT FROM AUTHOR]

Social exchange is modeled by Coleman in analogy to the theory of competitive equilibrium. Using this analogy, a dynamic stability analysis of the equilibrium is presented. Also, a comparative static analysis is provided with respect to the effects of a variation of certain exogenous variables. It is shown that the equilibrium is stable under weak conditions. A partial variation of exogenous conditions has the expected effects on endogenous parameters. [ABSTRACT FROM AUTHOR]

The purpose of this discussion is to transform the implicit equilibrium assumption endemic to network analysis into an explicit instrument for such analysis. I propose a formal model that brings together Coleman's restriction of Walras' general equilibrium model and recent developments in describing the "social topology" of a multiple network system of actors such that a class of relational equilibria is defined. The specific equilibrium expected in a system is a function of the previously existing stratification of actors in the system. Corresponding to multiple observed networks, the model generates multiple equilibrium networks. The structural analysis of the observed networks can therefore be repeated on the equilibrium networks so as to assess the extent to which the analysis would differ if the observed relations were actually in an equilibrium state. Numerical illustration is provided by an analysis of alternative relational equilibria in the system of elite experts in methodological and mathematical sociology as such a system existed in 1975. [ABSTRACT FROM AUTHOR]

Our object is to develop matrix formulas for measuring transitivity in digraphs and balance in signed graphs or digraphs. The transitivity ratio is introduced giving the probability that a 2-step path will be completed to a transitive triple. As it is not feasible to enumerate all cycles in a signed graph or digraph, restrictive degrees of balance are considered which involve only small cycles. [ABSTRACT FROM AUTHOR]