Shapley value is a popular way to compute payoffs in cooperative games where the agents are assumed to have deterministic, risk-neutral (linear) utilities.This paper explores a class of Multi-agent constantsum cooperative games where the payoffs are random variables. We introduce a new model based on Borch’s Theorem from the actuarial world of re-insurance, to obtain a Pareto optimal allocation...

Diagrams can be represented by graphs, and the animation and transformation of diagrams can be modeled by graph transformation. This paper studies extensions of graphs and graph transformation that are important for programming with graphs: We extend graphs by a notion of hierarchy that supports value composition, and define hierarchical graph transformation in an intuitive way that resembles t...

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be implementations of matrix multiplication and the Cartesian product of two lists. The type system is proved to be sound w.r.t...

In mathematics and computer science, we often encounter structures which are faithfully encoded by a graphical calculus of the following sort. The basic data of the structure are depicted as certain diagrams; the basic operations of the structure act by glueing together these diagrams along certain parts of their boundaries; and the axioms of the structure are just those necessary to ensure tha...

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be implementations of matrix multiplication and the Cartesian product of two lists. The type system is proved to be sound w.r.t...

Vehicular Ad Hoc Network (VANET) is an appearing new technology integrating ad hoc network and improve road traffic safety. The main challenges in VANET is searching, maintaining an effective route for transporting data information. Today some kind of routing protocols used in VANET Hence, an analysis on routing protocols based on number of parameters of VANET i.e. a required issue in communica...