Problem 13.3 (H) A team game is a cost-minimization game inwhich all agents have the same cost function: C1(s)for every outcome s. In a dummy game, the cost of every agent i isindependent of her strategy: C;(8i,s-i) =and every s;, s; E S;.Prove that a cost-minimization game with agent cost functionsC1,..., Ck is a potential game if and only ifCk(s)...C:(s', s_i) for every s_¡C;(s) = C{(s) + C¢(s)for every i and s, where Cf,..., C is a team game and Cf,..., Cis a dummy game.•.• )

If:Suppose that a cost-minimization game with agent cost functions C1, ..., Ck is a potential game.…

Problem 13.3 (H) A team game is a cost-minimization game in which all agents have the same cost function: C₁(s) : = Ck(s) for every outcome s. In a dummy game, the cost of every agent i is =... - Ci(si, s_i) for every s_i independent of her strategy: Ci(si, s_i) and every si, s € Si. = Prove that a cost-minimization game with agent cost functions C₁,..., Ck is a potential game if and only if Ci(s) = C(s) + Cd (s)

Problem 13.3 (H) A team game is a cost-minimization game in which all agents have the same cost function: C₁(s) : = Ck(s) for every outcome s. In a dummy game, the cost of every agent i is =... - Ci(si, s_i) for every s_i independent of her strategy: Ci(si, s_i) and every si, s € Si. = Prove that a cost-minimization game with agent cost functions C₁,..., Ck is a potential game if and only if Ci(s) = C(s) + Cd (s)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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