Two players, 1 and 2, simultaneously choose their consumption of a public good. Given the consumption choices, g1 and g2, player 1 derives a marginal benefit of MB1 = 10 - (g1 + g2), while player 2's marginal benefit is given by MB2 = 8 - (g1 + g2). The unit price of the public good is equal to 4.
The question asks to find a Nash Equilibrium of the game, then calculate the efficient level of public good provision and compare it to the NE.
I can understand the efficient provision of public good which will be nothing but the sum of marginal benefits set equal to the marginal cost. In this case, it turns out to be 7. What will be the Nash equilibrium?
An update with my attempt:
Player 1's best response function: g1 = 6 - g2 Player 2's best response function: g2 = 4 - g1
Added these two to get the total level of public good - it comes to 5.
Then I equated the two response function to get: g1 = g2 - 2
Substituted it in g1 + g2 = 5 equation with getting g2 = 3.5 and g1 = 1.5
I don't know if this is correct.