S ONE | DOI:10.1371/journal.pone.0120882 March 31,12 /A Generic Model of Dyadic

S ONE | DOI:10.1371/journal.pone.0120882 March 31,12 /A Generic Model of Dyadic Social Relationshipsas well as between A and C. If however one knows of the groups and applies our model to the X high-level agents G1 and G2, one observes G1 ! G2 and interprets it as an EM relationshipXbetween the two groups. This example motivates to identify the relevant social units in the data set under study. This may be achieved by measuring the number and/or duration of interactions between all pairs of individuals and thus creating a weighted graph. By choosing a threshold for the weight of the links, one may be able to isolate social units. Our model would then apply to pairs of members of the same social unit, as well as to pairs of social units.Valuing the action fluxesOur fluxes representation reflects only the presence or absence of fluxes, without saying anything about the quantities involved. The amount carried by an action flux can be readily measured when the action consists in the transfer of a physical item for which a unit of measure can easily be agreed upon. Valuing an action in general is not straightforward. The average time or physical effort necessary to perform the action can be measured (or simply intuitively approximated), but it is naturally much harder to quantitatively agree on a possible emotional or intellectual value. We propose that a value function does not need to be identical for each agent, and each agent does not need to possess a fixed, deterministic value function. For our present needs, it is sufficient for each agent to have personal notions of the value of the social actions performed by herself and others. These personal scales may be probabilistic, in the sense that the value they return may follow probability distributions. Correspondingly, decisions may be probabilistic, as suggested by Quantum Decision Theory [29, 30]. Alternatively, a value function could be a von Neumann-Morgenstern utility [31], a subjective cumulative prospect utility [32], or any other value function order Actinomycin IV capturing different forms of happiness or contentment, as in the theory of utilitarianism [33]. We hypothesize that, in a population of interacting agents evolving under selective pressure, the action fluxes of our model converge toward equilibria characterized by an equality in value between opposite fluxes. This proposition rests on the idea that unequal fluxes disadvantage at least one party. They are thus likely to jeopardize the (-)-Blebbistatin site relationship in the short term (in case of inequity aversion), and hinder the survival or reproductive success of the disadvantaged party in the long run. Hence, both individual optimization and selection pressure from external forces in the environment should drive interactions toward stable equilibria characterized by value equalities. We expect these equilibria to depend upon initial conditions and previous states. In other words, different societies would estimate that different things or actions have equal values. Let us now examine this suggestion in relation to RMT. MP requires a formal matching agreement stating the respective values of what is exchanged, whether actions (such as work), commodities or symbolic items (e.g. money). In EM, the things exchanged are not only of the same nature, but also of the same value. Thus, the idea of value equalities is already embedded into the definitions of these two RMs. RMT keeps CS and AR apart by stating that these RMs are not supposed to necessitate any kind.S ONE | DOI:10.1371/journal.pone.0120882 March 31,12 /A Generic Model of Dyadic Social Relationshipsas well as between A and C. If however one knows of the groups and applies our model to the X high-level agents G1 and G2, one observes G1 ! G2 and interprets it as an EM relationshipXbetween the two groups. This example motivates to identify the relevant social units in the data set under study. This may be achieved by measuring the number and/or duration of interactions between all pairs of individuals and thus creating a weighted graph. By choosing a threshold for the weight of the links, one may be able to isolate social units. Our model would then apply to pairs of members of the same social unit, as well as to pairs of social units.Valuing the action fluxesOur fluxes representation reflects only the presence or absence of fluxes, without saying anything about the quantities involved. The amount carried by an action flux can be readily measured when the action consists in the transfer of a physical item for which a unit of measure can easily be agreed upon. Valuing an action in general is not straightforward. The average time or physical effort necessary to perform the action can be measured (or simply intuitively approximated), but it is naturally much harder to quantitatively agree on a possible emotional or intellectual value. We propose that a value function does not need to be identical for each agent, and each agent does not need to possess a fixed, deterministic value function. For our present needs, it is sufficient for each agent to have personal notions of the value of the social actions performed by herself and others. These personal scales may be probabilistic, in the sense that the value they return may follow probability distributions. Correspondingly, decisions may be probabilistic, as suggested by Quantum Decision Theory [29, 30]. Alternatively, a value function could be a von Neumann-Morgenstern utility [31], a subjective cumulative prospect utility [32], or any other value function capturing different forms of happiness or contentment, as in the theory of utilitarianism [33]. We hypothesize that, in a population of interacting agents evolving under selective pressure, the action fluxes of our model converge toward equilibria characterized by an equality in value between opposite fluxes. This proposition rests on the idea that unequal fluxes disadvantage at least one party. They are thus likely to jeopardize the relationship in the short term (in case of inequity aversion), and hinder the survival or reproductive success of the disadvantaged party in the long run. Hence, both individual optimization and selection pressure from external forces in the environment should drive interactions toward stable equilibria characterized by value equalities. We expect these equilibria to depend upon initial conditions and previous states. In other words, different societies would estimate that different things or actions have equal values. Let us now examine this suggestion in relation to RMT. MP requires a formal matching agreement stating the respective values of what is exchanged, whether actions (such as work), commodities or symbolic items (e.g. money). In EM, the things exchanged are not only of the same nature, but also of the same value. Thus, the idea of value equalities is already embedded into the definitions of these two RMs. RMT keeps CS and AR apart by stating that these RMs are not supposed to necessitate any kind.