Values for two-stage games: Another view of the Shapley axioms

This short study reports an application of the Shapley value axioms to a new concept of two-stage games. In these games, the formation of a coalition in the first stage entitles its members to play a prespecified cooperative game at the second stage. The original Shapley axioms have natural equivalents in the new framework, and we show the existence of (non-unique) values and semivalues for two stage games, analogous to those defined by the corresponding axioms for the conventional (one-stage) games. However, we also prove that all semivalues (hence, perforce, all values) must give patently unacceptable solutions for some two-stage majority games (where the members of a majority coalition play a conventional majority game). Our reservations about these prescribed values are related to Roth's (1980) criticism of Shapley's -transfer value for non-transferable utility (NTU) games. But our analysis has wider scope than Roth's example, and the argument that it offers appears to be more conclusive. The study also indicates how the values and semivalues for two-stage games can be naturally generalized to apply for multi-stage games.Earlier versions of this study were presented at the International Conference on Game Theory and its Applications, organized by Ohio State University in 1987, and at the Workshop on Mathematical Economics and Game Theory at Tel Aviv Unversity. We gratefully acknowledge the valuable comments received on both occasions, especially those of Robert J. Aumann, Roy Gardner, Sergiu Hart, Ehud Kalai, Michael Maschler, Alvin E. Roth, and Lloyd S. Shapley, and also those ofIJGT's anonymous referees. Of course, all responsibility lies with us.     

Sphere orders

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P _i } of ordered sets such that eachP _i is ann-sphere order only forni; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.Research supported by ONR grant N00014 85-K-0769.     

Primary processes in photochemistry of 2,3-bis(2,5-dimethylthiophen-3-yl)cyclopent-2-enone

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Radiation-induced grafting of vinyl benzyl trimethyl ammonium chloride onto nylon-6 fabric

Vinyl benzyl trimethyl ammonium chloride (VBTAC) was grafted onto nylon-6 fabric in the presence of 2- hydroxy ethyl methacrylate (HEMA) by the simultaneous irradiation method in the presence of air with ⁶⁰Co γ-radiations. An increase in grafting was observed with increasing dose. Fourier transform infrared (FTIR) and thermogravimetric analysis (TGA) confirmed the grafting of VBTAC. Morphological changes after grafting were confirmed by scanning electron microscopy (SEM). The X-ray diffraction (XRD) pattern showed changes in crystallinity on grafting. The initial studies carried out with grafted nylon fabric showed behavioural changes in the burning properties.     

Comparison between self-reinforced composites based on ultra-high molecular weight polyethylene fibers and isotropic UHMWPE

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Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains

Journal of Theoretical Probability - We present new criteria for geometric and algebraic transience for discrete-time transient Markov chains on general state spaces, based on the moment of the...     

Correction to: Idealness of k-wise intersecting families

Mathematical Programming - A Correction to this paper has been published: 10.1007/s10107-020-01587-x     

Idealness of k-wise intersecting families

Mathematical Programming - A clutter is k-wise intersecting if every k members have a common element, yet no element belongs to all members. We conjecture that, for some integer $$k\ge 4$$ , every...     

Robust risk-taking under a sustainable constraint

We consider a model in which the representative investor makes optimal portfolio and consumption choices robust to ambiguity with a sustainable constraint. We find that the influences of ambiguity on risk-taking are two ways. Those are gambling when the risk-free interest rate is less than a critical value, but derisk when the risk-free interest rate is greater than the critical value. Moreover, the erosion of ambiguity on consumption is more substantial in constrained cases, and ambiguity will magnify welfare losses.     

Global Asymptotic Stability in a Delay Differential Equation Model for Mosquito Population Suppression

Acta Mathematicae Applicatae Sinica, English Series - A bio-safe dengue control strategy is to use Wolbachia, which can induce incomplete cytoplasmic incompatibility (CI) and reduce the mating...