An Algorithm for the Myerson Value in Probabilistic Graphs with an Application to Weighted Voting

Abstract

Myerson's graph-restricted games are a well-known formalism for modeling cooperation that's subject to restrictions. In particular, Myerson considered a coalitional game in which cooperation is possible only through an underlying network of links between agents. A unique fair solution concept for graph-restricted games is called the Myerson value. One study generalized these results by considering probabilistic graphs in which agents can cooperate via links only to some extent, that is, with some probability. The authors' algorithm is based on the enumeration of all connected subgraphs in the graph. As a sample application of the new algorithm, they consider a probabilistic graph that represents likelihood of pairwise collaboration between political parties before the 2015 general elections in the UK.