
202 Supply Chain Management and Logistics
8.2 The Overcapacity Effect
8.2.1 Setup
Our investment game involves n identical rms. These rms compete in
utilizing costly capital to build capacities with hopes of generating future
returns. Each rm’s cost for capital follows a function c: R
+
→ R
+
, where R
+
stands for [0 + ∞). The return to an individual rm is not solely determined
by its own investment level. Rather, the total return to all rms is governed
by a function r: R
+
→ R
+
of these rms’ total investment level. The return to
each rm i is proportional to its investment level x
i
∈ R
+
. Therefore, when the
prole of other rms’ investment ...