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Package ‘CoopGame’
(2019)
The theory of cooperative games with transferable utility offers useful insights into the way parties can share gains from cooperation and secure sustainable agreements, see e.g. one of the books by Chakravarty,Mitra and Sarkar (2015, ISBN:978-1107058798) or by Driessen (1988,ISBN:978-9027727299) for more details. A comprehensive set of tools for cooperative game theory with transferable utility is provided. Users can create special families of cooperative games, like e.g. bankruptcy games,cost sharing games and weighted voting games. There are functions to check various game properties and to compute five different set-valued solution concepts for cooperative games. A large number of point-valued solution concepts is available reflecting the diverse application areas of cooperative game theory. Some of these point-valued solution concepts can be used to analyze weighted voting games and measure the influence of individual voters within a voting body. There are routines for visualizing both set-valued and point-valued solutions in the case of three or four players.
This document gives a brief and concise overview of the various functionalities of the package CoopGame and presents a few use cases. In particular, we introduce the capabilities of CoopGame to create special families of cooperative games, to check game properties and to compute set-valued and point-valued solutions. We also introduce the usage of CoopGame for visualizing set-valued and point-valued solutions in the caseof three or four players. We end with a brief outlook to future developments. This vignette accompanies version 0.2.1 of the package CoopGame.
We are studying the Gately point, an established solution concept for cooperative games. We point out that there are superadditive games for which the Gately point is not unique, i.e. in general the concept is rather set-valued than an actual point. We derive conditions under which the Gately point is guaranteed to be a unique imputation and provide a geometric interpretation. The Gately point can be understood as the intersection of a line defined by two points with the set of imputations. Our uniqueness conditions guarantee that these two points do not coincide. We provide demonstrative interpretations for negative propensities to disrupt. We briefly show that our uniqueness conditions for the Gately point include quasibalanced games and discuss the relation of the Gately point to the τ-value in this context. Finally, we point out relations to cost games and the ACA method and end upon a few remarks on the implementation of the Gately point and an upcoming software package for cooperative game theory.