A Note on the Shapley Value for Characteristic Functions on Bipartitions
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 Discussion Paper Series|
|Discussion paper / Tinbergen Institute|
|Organisation||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