G. van der Laan

Bio: G. van der Laan is an academic researcher from VU University Amsterdam. The author has contributed to research in topics: Stochastic game & Corporate governance. The author has an hindex of 14, co-authored 47 publications receiving 625 citations. Previous affiliations of G. van der Laan include Tinbergen Institute.

Simplicial variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using a general labelling

Abstract: This paper deals with the nonlinear complementarity problem on the product space of unit simplices, S. A simplicial variable dimension algorithm developed by van der Laan and Talman for proper labellings of S is extended to the case of general labellings. General labellings allow a more natural description of the complementarity problem on the boundary of S. A distinctive feature of the new algorithm is that lower dimensional simplicial movement can occur both on the boundary and in the interior of S. In contrast, the van der Laan and Talman algorithm for proper labellings of S allows lower dimensional simplicial movement only in the interior of S. Computational experiments confirm the usefulness of general labellings for solving nonlinear complementarity problems.

A class of simplicial restart fixed point algorithms without an extra dimension

Abstract: In an earlier paper we introduced an algorithm for approximating a fixed point of a mapping on the product space of unit simplices. Ideas of that paper are used to construct a class of triangulations ofR n. More precisely, for somek, 1 ≤k ≤ n, and positive integersm 1 ⋯ , mk with sumn, a triangulation ofR n is obtained by triangulating the cells which are formed by taking the product of given triangulations ofR mj, j = 1, ⋯ ,k. The triangulation of each cell will be defined in relation to an arbitrarily chosen pointv inR n, being the starting point of the algorithm. Fork = n we obtain theK′ triangulation originally due to Todd. Each element of the class can be used to find a simplex which approximates a fixed point of a mapping onR n by generating a unique path of adjacent simplices of variable dimension starting with the pointv. We also give convergence conditions. It is indicated how in casek = n a connected set of fixed points can be generated. Moreover, we give some computational experience.

On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games

Abstract: In this paper an algorithm based on the principle of simplicial approximation is introduced to compute fixed points of upper semicontinuous point to set mappings from the product space S of unit simplices into itself. The algorithm is a modification of an algorithm, introduced in an earlier paper. The main feature is that it starts with an arbitrary chosen point in S and that the triangulation of S depends on the starting point. Moreover, the algorithm can terminate with a non-full-dimensional subsimplex, yielding a good approximation. An application is given for non cooperative n person games, where S is the strategy space. Some computational experiences are given.

The Theory of Markets

Abstract: On the dynamics of supply-constrained equilibria, J.H. Dreze price-quantity adjustment in a Keynesian economy, P.J.-J. Herings, et al core equivalence in a mixed economy, V.A. Vasil'ev do we model the correct market information?, D.G. Saari rational animal spirits, W.A. Brock, C.H. Hommes an evolutionary model of market structure, C. Alos-Ferrer, et al on multiplicity of competitive equilibria when financial markets are incomplete, T. Hens, et al the impact of portfolio constraints in infinite-horizon incomplete-markets models, K.L. Judd, et al risk sharing and market incompleteness, D.K. Levine, W.R. Zame a note on the convergence to competitive equilibria in economies with moral hazard, A. Bisin, et al macroeconomic equilibrium in a monetary economy H. Polemarchakis, J.-P. Vidal positional abilities and rents on equilibrium wages, P.H.M. Ruys, R. van den Brink modelling producer decisions in a spatial continuum, M. Keyzer, Y. Ermoliev carbon abatement, revenue Recycling and intergenerational burden sharing, T.F. Rutherford, et al.

Evolution and the Theory of Games

Abstract: In the Hamadryas baboon, males are substantially larger than females. A troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young. The male prevents any of ‘his’ females from moving too far from him. Kummer (1971) performed the following experiment. Two males, A and B, previously unknown to each other, were placed in a large enclosure. Male A was free to move about the enclosure, but male B was shut in a small cage, from which he could observe A but not interfere. A female, unknown to both males, was then placed in the enclosure. Within 20 minutes male A had persuaded the female to accept his ownership. Male B was then released into the open enclosure. Instead of challenging male A , B avoided any contact, accepting A’s ownership.

The iron cage revisited: Institutional isomorphism and collective rationality in organizational fields (Chinese Translation)

Abstract: What makes organizations so similar? We contend that the engine of rationalization and bureaucratization has moved from the competitive marketplace to the state and the professions. Once a set of organizations emerges as a field, a paradox arises: rational actors make their organizations increasingly similar as they try to change them. We describe three isomorphic processes-coercive, mimetic, and normative—leading to this outcome. We then specify hypotheses about the impact of resource centralization and dependency, goal ambiguity and technical uncertainty, and professionalization and structuration on isomorphic change. Finally, we suggest implications for theories of organizations and social change.

Heterogeneous Agent Models in Economics and Finance

Abstract: This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

Coalitional game theory for communication networks

Abstract: In this tutorial, we provided a comprehensive overview of coalitional game theory, and its usage in wireless and communication networks. For this purpose, we introduced a novel classification of coalitional games by grouping the sparse literature into three distinct classes of games: canonical coalitional games, coalition formation games, and coalitional graph games. For each class, we explained in details the fundamental properties, discussed the main solution concepts, and provided an in-depth analysis of the methodologies and approaches for using these games in both game theory and communication applications. The presented applications have been carefully selected from a broad range of areas spanning a diverse number of research problems. The tutorial also sheds light on future opportunities for using the strong analytical tool of coalitional games in a number of applications. In a nutshell, this article fills a void in existing communications literature, by providing a novel tutorial on applying coalitional game theory in communication networks through comprehensive theory and technical details as well as through practical examples drawn from both game theory and communication application.