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Raub and Snijders (1997) show that, under the assumption of S-shaped utility, conditions for cooperation in social dilemmas are more restrictive if outcomes represent losses than if outcomes represent gains. They neglected two interesting issues in their paper: conditions for cooperation in social dilemmas with both losses and gains as outcomes, and the effect of probability weighing on these conditions. In this paper it is shown that, under assumptions of Prospect Theory, conditions for cooperation are best if dilemmas include both positive and negative outcomes, and that these conditions improve with increasing loss aversion. Furthermore, it is shown that probability weighing can effect conditions to cooperate as well. [ABSTRACT FROM AUTHOR]

In a Markov chain model of a social process, interest often centers on the distribution of the population by state. One question, the stability question, is whether this distribution converges to an equilibrium value. For an ordinary Markov chain (a chain with constant transition probabilities), complete answers are available. For an interactive Markov chain (a chain which allows the transition probabilities governing each individual to depend on the locations by state of the rest of the population), few stability results are available. This paper presents new results. Roughly, the main result is that an interactive Markov chain with unique equilibrium will be stable if the chain satisfies a certain monotonicity property. The property is a generalization to interactive Markov chains of the standard definition of monotonicity for ordinary Markov chains. [ABSTRACT FROM AUTHOR]

The paper presents a formal approach which may increase the realism and parsimony of higher-order Markov models applied to certain human behaviors. Often in behavioral applications, any improvements in fit available from increasing the order of a Markov model would be more than offset by interpretive problems caused by the very rapid increase in the number of independent parameters. The model proposed here for the higher-order process greatly reduces the number of independent parameters, replacing them with sociologically relevant effects of persistence in and reversion to previous conditions. The general model is called the "reversion model." In it, individuals are allowed to carry along some information about their pasts, for a number of periods corresponding to the order of the model. The parameters describing residence histories are constructed to give each individual an underlying set of first-order transition probabilities, which are modified by experience of the various states of the system. When an individual occupies a particular state, his relative probability of future residence there (vis-a-vis the other states as a group) is permitted to change. But occupation of a particular state is not permitted to affect the relative chances of residence among the other states. With suitable constraints, the number of parameters of this higher-order process no longer increases geometrically with the order, but only arithmetically. Maximum likelihood estimation formulas are derived for the reversion model, which is then applied to longitudinal data on the work activities of U.S. Ph.D. physicists and chemists in 1960-1966, and is found to fit well using likelihood ratio tests. [ABSTRACT FROM AUTHOR]