We consider a cooperative game with a bipartition that indicates which players are participating. This paper provides an analytical solution for the Shapley value when the worth of a coalition only depends on the number of participating coalition players. The computational complexity grows linearly in the number of players, which contrasts with the usual exponential increase. Our result remains true when we introduce (i) randomization of the bipartition, and (ii) randomly draw a characteristic function.

Shapley value, bipartition, computational complexity
Cooperative Games (jel C71)
Tinbergen Institute
hdl.handle.net/1765/26085
Tinbergen Institute Discussion Paper Series
Discussion paper / Tinbergen Institute
Erasmus School of Economics

Muns, S. (2011). A Note on the Shapley Value for Characteristic Functions on Bipartitions (No. TI 2011-124/2). Discussion paper / Tinbergen Institute (pp. 1–11). Tinbergen Institute. Retrieved from http://hdl.handle.net/1765/26085