Computability and Evolutionary Complexity: Markets As Complex Adaptive Systems (CAS)

The purpose of this Feature is to critically examine and to contribute to the burgeoning multi disciplinary literature on markets as complex adaptive systems (CAS). Three economists, Robert Axtell, Steven Durlauf and Arthur Robson who have distinguished themselves as pioneers in different aspects of how the thesis of evolutionary complexity pertains to market environments have contributed to this special issue. Axtell is concerned about the procedural aspects of attaining market equilibria in a decentralized setting and argues that principles on the complexity of feasible computation should rule in or out widely held models such as the Walrasian one. Robson puts forward the hypothesis called the Red Queen principle, well known from evolutionary biology, as a possible explanation for the evolution of complexity itself. Durlauf examines some of the claims that have been made in the name of complex systems theory to see whether these present testable hypothesis for economic models. My overview aims to use the wider literature on complex systems to provide a conceptual framework within which to discuss the issues raised for Economics in the above contributions and elsewhere. In particular, some assessment will be made on the extent to which modern complex systems theory and its application to markets as CAS constitutes a paradigm shift from more mainstream economic analysis

The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame

Efficient Markov perfect Nash equilibria: theory and application to dynamic fishery games

In this paper, we present a method for the characterization of Markov perfect Nash equilibria being Pareto efficient in non-linear differential games. For that purpose, we use a new method for computing Nash equilibria with Markov strategies by means of a system of quasilinear partial differential equations. We apply the necessary and sufficient conditions derived to characterize efficient Markov perfect Nash equilibria to dynamic fishery games.We are grateful to the editor Kenneth L. Judd and an anonymous referee for helpful comments. The research of the first author was supported by MCYT under project BEC2002-02361 and JCYL under project VA51/03, cofinanced by FEDER funds. The research of the second author was supported by MCYT under project BFM2002–00425 and JCYL under project VA099/04 cofinanced by FEDER funds.Publicad

GAME THEORETIC FLOW AND ROUTING CONTROL FOR COMMUNICATION NETWORKS

As the need to support high speed data exchange in modern communication networks grows rapidly, effective and fair sharing of the network resources becomes very important. Today's communication networks typically involve a large number of users that share the same network resources but may have different, and often competing, objectives. Advanced network protocols that are implemented to optimize the performance of such networks typically assume that the users are passive and are willing to accept compromising their own performance for the sake of optimizing the performance of the overall network. However, considering the trend towards more decentralization in the future, it is natural to assume that the users in a large network may take a more active approach and become more interested in optimizing their own individual performances without giving much consideration to the overall performance of the network. A similar situation occurs when the users are members of teams that are sharing the network resources. A user may find itself cooperating with other members of its team which itself is competing with the other teams in the network. Game theory appears to provide the necessary framework and mathematical tools for formulating and analyzing the strategic interactions among users, or teams of users, of such networks. In this thesis, we investigate networks in which users, or teams of users, either compete or cooperate for the same network resources. We considered two important network topologies and used many examples to illustrate the various solution concepts that we have investigated.. First we consider two-nodeiiiparallel link networks with non-cooperative users trying to optimally distribute their flows among the links. For these networks, we established a condition which guarantees the existence and uniqueness of a Nash equilibrium for the link flows. We derived an analytical expression for the Nash equilibrium and investigated its properties in terms of the network parameters and the users preferences. We showed that in a competitive environment users can achieve larger flow rates by properly emphasizing the corresponding term in their utility functions, but that this can only be done at the expense of an increase in the expected delay. Next, we considered a general network structure with multiple links, multiple nodes, and multiple competing users. We proved the existence of a unique Nash equilibrium. We also investigated many of its intuitive properties. We also extended the model to a network where multiple teams of users compete with each other while cooperating within the teams to optimize a team level performance. For this model, we studied the Noninferior Nash solution and compared its results with the standard Nash equilibrium solution