Take-and-guess games

This paper studies two classes of two-person zero-sum games in which the strategies of both players are of a special type. Each strategy can be split into two parts, a taking and a guessing part. In these games two types of asymmetry between the players can occur. In the first place, the number of objects available for taking does not need to be the same for both players. In the second place, the players can be guessing sequentially instead of simultaneously; the result is asymmetric information. The paper studies the value and equilibria of these games, for all possible numbers of objects available to the players, for the case with simultaneous guessing as well as for the variant with sequential guessing.      

Relations between game parameters,value, and optimal strategy spaces in stochastic games and construction of games with given solution

Results of Bohnenblust, Karlin, and Shapley and results of Shapley and Snow, concerning solutions of matrix games, are extended to the class of discounted stochastic games. Prior to these extensions, relations between the game parameters, value, and optimal stationary strategy spaces are established. Then, the inverse problem of constructing stochastic games, given the solution, is considered.     

OnS-equivalence and isomorphism of games in characteristic function form

In this note an example is given of two superadditive games which are isomorphic and notS-equivalent.     

On three Shapley-like solutions for cooperative games with random payoffs

Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided.2000 Mathematics Subject Classification Number: 91A12.The authors thank two anonymous referees and an associate editor for their helpful comments.This author acknowledges financial support from the Netherlands Organization for Scientific Research (NWO) through project 613-304-059.Received: October 2000     

Cores and related solution concepts for multi-choice games

A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. Cooperative games form a subclass of the class of multi-choice games.This paper extends some solution concepts for cooperative games to multi-choice games. In particular, the notions of core, dominance core and Weber set are extended. Relations between cores and dominance cores and between cores and Weber sets are extensively studied. A class of flow games is introduced and relations with non-negative games with non-empty cores are investigated.     

On the Cores of cooperative games and the stability of the Weber set

In this paper conditions are given guaranteeing that the Core equals the D-core (the set of unDominated imputations). Under these conditions, we prove the non-emptiness of the intersection of the Weber set with the imputation set. This intersection has a special stability property: it is externally stable. As a consequence we can give a new characterization (th. 3.2) for the convexity of a cooperative game in terms of its stability (von Neumann-Morgenstern solutions) using the Weber set.     

Gentle immobilization of nonionic polymersomes on solid substrates

Vesicles from Pluronic L121 (PEO5-PPO68-PEO5) triblock copolymers were first stabilized by a permanent interpenetrating polymer network and then gently immobilized onto a glass or mica surface. Fluorescence-labeled micrometer-sized vesicles were visualized with confocal laser scanning microscopy, and smaller sized capsules, around 100 nm, were probed by liquid atomic force microscopy. The immobilized vesicles were weakly attached to a negatively charged surface via negatively charged polyelectrolytes in combination with Mg2+ ions and can be reversibly detached from the surface by slightly elevated temperatures. To illustrate that the immobilized vesicles remain responsive to external stimuli, we show that it is possible to transform their shape from spherical to cylindrical by introducing a second Pluronic, namely, P123 (PEO20-PPO70-PEO20). The detailed transition process has been recorded in real time by confocal laser scanning microscopy. Electron microscopy studies confirmed that a similar morphology change also occurs in the bulk.     

New Biosilified Pd-lipase hybrid biocatalysts for dynamic resolution of amines

In this work lipase CaLB was immobilized on functionalized Pd-SiO₂ nanoparticles in order to simplify the DKR of α-methylbenzylamine. Hybrid biocatalysts showed immobilization efficiencies of 82%, 80% and 76% when containing 1, 5 and 10% of Pd respectively. On DKR reaction values of ee?>?99% and conversion of 82% were found with only 1% of Pd, generating a productivity of 2.21?mg of product h^?1?mg of support^?1 against 0.76 found by N435®. Compared to commercial N435®, the novel biocatalysts showed protein loads about 15-fold lower and higher activity, demonstrating competitive performances and high industrial applications.     

Spectral Dimension of Trees with a Unique Infinite Spine

Using generating functions techniques we develop a relation between the Hausdorff and spectral dimension of trees with a unique infinite spine. Furthermore, it is shown that if the outgrowths along the spine are independent and identically distributed, then both the Hausdorff and spectral dimension can easily be determined from the probability generating function of the random variable describing the size of the outgrowths at a given vertex, provided that the probability of the height of the outgrowths exceeding n falls off as the inverse of n. We apply this new method to both critical non-generic trees and the attachment and grafting model, which is a special case of the vertex splitting model, resulting in a simplified proof for the values of the Hausdorff and spectral dimension for the former and novel results for the latter.