AbstractsBusiness Management & Administration

This thesis is concerned with the formal description (Part I) and metastability analysis (Part II) of agent-based evolutionary models. Part I discusses the need for specifations as an intermediate layer between implementations and narrative descriptions of computer-based models. We present the basic structure of a functional framework for the specification of agent-based models of exchange. The focus is to expose the relationship of agent-based models of exchange with existing economic theory. We represent the models as discrete-time Markov processes and show that they differ from stochastic evolutionary games only in that their fitness function is in general not deterministic. We apply the framework to demonstrate how to formulate the research question behind agent-based models of exchange precisely, which establishes a direct relationship with general equilibrium theory. Moreover, we discuss how it constitutes a starting point for formal model analysis and further numerical investigations. Part II presents a novel approach to the analysis of stochastic evolutionary games, which are simple agent-based models. We motivate this approach by the observation that stochastic evolutionary games often exhibit metastable dynamics but the existing approaches to their analysis are not able to capture this behavior. We derive the aggregated strategy updating process for general stochastic evolutionary games as a discrete-time Markov chain on a finite state space. We present two characterizations of metastability and investigate both of these characterizations for stochastic evolutionary games. In particular, we show that every decomposition of state space into limit sets of the unperturbed Markov chain of the stochastic evolutionary game is metastable according to both characterizations. We furthermore consider for stochastic evolutionary games the core set Markov state modeling approach to the construction of Markov models that capture the essential, metastable dynamics on a considerably smaller state space and that are thus of reduced complexity. The underlying idea is the best approximation and thus orthogonal projection of a transfer operator of the evolutionary game onto the subspace spanned by the committor functions on given disjoint subsets of population state, the so-called core sets. The matrix representation of this projected transfer operator represents the transition matrix of the reduced Markov chain. We elaborate on the relationship between the original Markov chain and the core set Markov state model. We show that the construction preserves stochastic stability. Building on the analysis of the approximation error, we present an algorithmic strategy to the identification of core sets such that the resulting core set model represents well the dominant time scales and in this sense the metastable dynamic behavior of the evolutionary game. Both the core sets as well as the transition matrix can be estimated from simulated trajectory data. The approach is thus appealing in the context of agent-based modeling.…