Econ546MCLec2

# I more output produced by others reduces the amount a

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Unformatted text preview: 0, 5 2, 7 0, 6 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, @ u1 (x) = 1 2x1 x2 x3 = 0 @ x1 Solve for similar conditions for players 2 and 3 to get three equations in three unknowns. x1 = x2 = x3 = 1 4 The\$production\$output\$would\$be\$half\$if\$they\$colluded\$together\$into\$one...
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## This document was uploaded on 03/23/2014.

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