Boundedly Rational Agents Playing the Social Actors Game

In any organizational setting, each of the participating actors adopts a quite steady behavior with respect to others. This behavior is not always in line with what might be expected given the role of the actor, although it is quite cooperative and most often contributes significantly to the proper operation of the organization. Within the framework of the SocLab approach for the modeling and analysis of organizations, we propose a model of the bounded rationality that social actors could implement in the process yielding the joint adaptation of their behaviors. Keywords— organizational behavior; cooperation; actors game; regulation; bounded rationality; organization; reinforcement learning; SocLab. I. WHY AND HOW TO COOPERATE? This article considers organizations, and more generally social systems of organized action, viewed as social constructs: • established for some purpose, and thus aimed at achieving some goal(s), • including individuals and resources, • provided with rules about the handling of the resources by the individuals, intended to serve the achievement of the organization’s goals, where each of these elements is more or less precisely determined and recognized. This encompasses well-structured organizations (firms, institutions, ...), collaborative contexts (citizens associations, family, ...) as well as diffuse systems of collective action (public policy arena, partnered relationships, ...). In such contexts, the members are found to exhibit a more or less steady behavior with respect to each other, and the occurrence of this well-established phenomenon – the regulation – is necessary for the existence of the organization: it allows each one to anticipate the behavior of others and so ensures the co-ordination required for the achievement of the organization's aims, and so preserves its raison d'être. According to the Sociology of Organized Action, also called Strategic Analysis [2], this regularity originates from the strategic nature of actors' behaviors: each one has some goals and his behavior is driven by his believes on the best way to achieve these goals. As the goals of an actor embeds personal aims into his organizational role(s), the latter do not fully explain his behavior, more so as the concrete application of any organizational rule involves a contextual interpretation, which is at the discretion of actors. Therefore, the behaviors of social actors most often deviate from the rules while being, as we shall see later, generally much oriented toward cooperation. Viewing the regulation of an organization as a phenomenon that emerges from interactions between individual processes, the concern of this article is how actors succeed in the stabilization of their respective behaviors and why they stabilize as the do. So, it proposes an algorithm intended to model the actors' rationality while accounting the facts that they must jointly adapt their behaviors to the ones of all others, they are greatly unaware of the objectives and means of others, and most social behaviors are not deliberate. From the organization point of view, it proposes a model of the regulation process as resulting from the interplay between the actors' rationality. This question is addressed within the framework of the SocLab approach for the analysis of social relationships within organizational settings, which is extensively presented in a companion paper [1]. This approach is supported by a software platform that allows the user to edit models of organizations, to study the properties of models with analytic tools, and to compute by simulation the behaviors that the members of an organization could adopt the ones with respect to others [24]. Focusing on the social dimension of organizations, the simulation algorithm considers rather the conduct of an actor vis-a-vis others, his attitude which is assessed in terms of cooperativity, than his substantive contribution to the realization of the organization's goals. As far as one agrees with its theoretical fundaments, the SocLab platform looks like a tool for organizational diagnoses and the analysis of scenarios regarding evolutions of organizations. It can be used also for the design and analysis of virtual organizations having no direct reference to reality, intended to the study of theoretical properties of organizational configurations featuring particular characteristics. The purpose of this article is to present the SocLab simulation algorithm. Section II outlines the SocLab modeling of the structure of organizations that leads to consider the interactions among actors as a specific game we call the social actors game. Two models of simple organizations are also presented. Section III states requirements for a simulation algorithm regarding the expected results (the emergence macro-level view) and the actors' competences (the micro-level view). Section IV presents the actors' bounded rationality algorithm while providing, as much as possible, its social science underpins, while section V gives an overview of results. The last section discusses the originality of the algorithm and related works. II. THE SOCLAB MODEL OF SOCIAL ORGANIZATIONS The SocLab framework aims at formalizing and slightly extends the Sociology of Organized Action [2]. For space limitation we just outline the SocLab model of the structure of organizations, especially the elements that found the social actors game. The reader will find in [1] a comprehensive presentation and discussion of this model and how to model and study a concrete organization. A. The Structure of Organizations The core of this meta-model is represented graphically as a UML Class Diagram in figure 1. Accordingly, the structure of an organization is constituted of a set of Actors and a set of social Relations linked by the Control and Depend associations. Figure 1. The meta-model of the structure of organizations A relation is the matter of the recurrent interactions between an actor who controls the availability of a specific resource and actors who need this resource to achieve their goals. Resources, as the media for interactions among actors, must be understood in a very general sense as something useful or necessary for actors' activities: material objects, factual, procedural or axiological believes and knowledge, or even personal attitudes. Considering the concept of role, a relation may also be viewed as the playing of a role, be it defined by the organization or caught by the actor. The state of a relation corresponds to the controller actor’s policy regarding the management of the resource; its range is the Space of behaviors of the relation and its value measures to what extent the actor is cooperative (positive values) or uncooperative (negative values). When an actor acts(), he moves() the states of the relations he controls toward more or less cooperation, and he is the only one to be able to do so. An actor depends on the relations regarding the resources he needs to achieve his goals. How much an actor depends on a relation is determined by the necessity of the resource for the achievement of his goals and the relative importance of these goals. This level of dependency is represented by the stake attribute of the depend association. Each actor has 10 points of stakes that he distributes on the relations he depends on, including the ones he controls. For each actor dependent on a relation, there is an effect() function that, depending on the relation's state (i.e. the controller actor behavior), determines how well the actor can make use of the underlying resource. Negative effects correspond to hampering or preventing the use of the resource while positive effects correspond easing its use. The impact of a relation upon an actor is the value of the effect() function applied to the state of the relation weighted by the actor's stake. The aggregation of the impacts that an actor receives from the relations he depends on determines his capability, or action capacity. The capability measures how much the actor has the means to achieve his goals, so that to obtain a high level of capability constitutes a meta-goal that drives his behavior. If impacts are aggregated by the sum operator, when the organization is in the state s = (sr1, ... , srm), where R = {r1, ..., rm} is the set of relations, the capability of actor a is defined as capability(a, s) = ∑r ∈ R stake(a, r) * effectr(a, sr) = ∑r ∈ R impact(r, a, sr). The aggregation (once again by the sum operator) of the actors' capabilities defines the global capability of the whole organization as capability(s) = ∑a ∈ A capability(a, s) The model of an organization includes others elements such as constraints between relations or solidarities between actors, allowing to deal with essential dimensions of organizations [1].