This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two- player nice games, i.e., games with compact real intervals as strategy spaces...

It is well known since Owen (Management Science, 1968) that the weights in the weighted Shapley value cannot be interpreted as a measure of power (i.e. of the ability to bargain) of the players. This paper proposes a new weight scheme for the Shapley value. Weights in this framework have to be...