A doubt about Game Theory(Gibbons, Game Theory for Applied Economists) - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-19T23:04:22Z http://mathoverflow.net/feeds/question/30152 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/30152/a-doubt-about-game-theorygibbons-game-theory-for-applied-economists A doubt about Game Theory(Gibbons, Game Theory for Applied Economists) Survivor 2010-07-01T07:41:18Z 2010-07-01T08:17:56Z <p>When I read the book write by Robert Gibbons . In the first chapter, they discussed "The Problem of the Commons" I can't understand why</p> <p>$v^{'} \left(g_i + g_{-i}^{*}\right)$ (page 27)</p> <p>represent the damage of the price of the original price of the sheep.</p> <p>I think the damage of the price of the original price should be:</p> <p>$v \left(G\right) - v\left(g_i + g_{-i}^{*}\right)$</p> <p>where $G$ means the original number of sheep . the price function $V$ has the relationship with the number of the sheep.</p> <p>Also in the page 27, the author say the first order condition for this optimization problem </p> <p>is $v \left(g_i + g_{-i}^{*}\right) + g_iv^{'} \left(g_i + g_{-i}^{*}\right) -c =0$</p> <p>I can't understand the author want to say......Perhaps he means we should find $g_i$ as bigger as possible until we can't earn more money when we add more sheep. </p>