32,941 research outputs found

    Homo Socionicus: a Case Study of Simulation Models of Norms

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    This paper describes a survey of normative agent-based social simulation models. These models are examined from the perspective of the foundations of social theory. Agent-based modelling contributes to the research program of methodological individualism. Norms are a central concept in the role theoretic concept of action in the tradition of Durkheim and Parsons. This paper investigates to what extend normative agent-based models are able to capture the role theoretic concept of norms. Three methodological core problems are identified: the question of norm transmission, normative transformation of agents and what kind of analysis the models contribute. It can be shown that initially the models appeared only to address some of these problems rather than all of them simultaneously. More recent developments, however, show progress in that direction. However, the degree of resolution of intra agent processes remains too low for a comprehensive understanding of normative behaviour regulation.Norms, Normative Agent-Based Social Simulation, Role Theory, Methodological Individualism

    Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras

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    CC^*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of CC^*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine CC^*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general) infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter \hbar. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation.Comment: This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

    How groups can foster consensus: The case of local cultures

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    A local culture denotes a commonly shared behaviour within a cluster of firms. Similar to social norms or conventions, it is an emergent feature resulting from the firms' interaction in an economic network. To model these dynamics, we consider a distributed agent population, representing e.g. firms or individuals. Further, we build on a continuous opinion dynamics model with bounded confidence (ϵ\epsilon), which assumes that two agents only interact if differences in their behaviour are less than ϵ\epsilon. Interaction results in more similarity of behaviour, i.e. convergence towards a common mean. This framework is extended by two major concepts: (i) The agent's in-group consisting of acquainted interaction partners is explicitly taken into account. This leads to an effective agent behaviour reflecting that agents try to continue to interact with past partners and thus to keep sufficiently close to them. (ii) The in-group network structure changes over time, as agents can form new links to other agents with sufficiently close effective behaviour or delete links to agents no longer close in behaviour. Thus, our model provides a feedback mechanism between the agents' behaviour and their in-group structure. Studying its consequences by means of agent-based computer simulations, we find that for narrow-minded agents (low ϵ\epsilon) the additional feedback helps to find consensus more often, whereas for open-minded agents (high ϵ\epsilon) this does not hold. This counterintuitive result is explained by simulations of the network evolution

    Evolutionary Game Theory

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    Group-theoretic compactification of Bruhat-Tits buildings

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    Let GF denote the rational points of a semisimple group G over a non-archimedean local field F, with Bruhat-Tits building X. This paper contains five main results. We prove a convergence theorem for sequences of parahoric subgroups of GF in the Chabauty topology, which enables to compactify the vertices of X. We obtain a structure theorem showing that the Bruhat-Tits buildings of the Levi factors all lie in the boundary of the compactification. Then we obtain an identification theorem with the polyhedral compactification (previously defined in analogy with the case of symmetric spaces). We finally prove two parametrization theorems extending the BruhatTits dictionary between maximal compact subgroups and vertices of X: one is about Zariski connected amenable subgroups, and the other is about subgroups with distal adjoint action

    Limits of kernel operators and the spectral regularity lemma

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    We study the spectral aspects of the graph limit theory. We give a description of graphon convergence in terms of converegnce of eigenvalues and eigenspaces. Along these lines we prove a spectral version of the strong regularity lemma. Using spectral methods we investigate group actions on graphons. As an application we show that the set of isometry invariant graphons on the sphere is closed in terms of graph convergence however the analogous statement does not hold for the circle. This fact is rooted in the representation theory of the orthogonal group

    Mechanisms of Endogenous Institutional Change

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    This paper proposes an analytical-cum-conceptual framework for understanding the nature of institutions as well as their changes. In doing so, it attempts to achieve two things: First, it proposes a way to reconcile an equilibrium (endogenous) view of institutions with the notion of agents’ bounded rationality by introducing such concepts as a summary representation of equilibrium as common knowledge of agents. Second, it specifies some generic mechanisms of institutional coherence and change -- overlapping social embededdness, Schumpeterian innovation in bundling games and dynamic institutional complementarities -- useful for understanding the dynamic interactions of economic, political, social and organizational factors.
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