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4, 1 C OMMON R ESOURCE P ROBLEM I There are three players who use a common resource to produce output.
I More output produced by others reduces the amount a given player can produce. I Resource used by player i is denoted by xi .
I Player i’s output given the resource usage choices of others is xi (1 x1 x2 x3 ) if x1 + x2 + x3 1 and 0 otherwise. I Each ﬁrm wishes to maximize their output.
I Nash Equilibria? C OMMON R ESOURCE P ROBLEM
Figure out what the best response function for each player looks like.
ui (x) = xi (1 x1 x2 x3 ) To maximize this output, we compute the derivative with respect to xi and
set it equal to 0.
So for player 1,
(x) = 1 2x1 x2 x3 = 0
Solve for similar conditions for players 2 and 3 to get three equations in three
x1 = x2 = x3 = 1
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This document was uploaded on 03/23/2014.
- Spring '14
- Game Theory