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)
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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![Problem 13.3 (H) A team game is a cost-minimization game in
which all agents have the same cost function: C1(s)
for every outcome s. In a dummy game, the cost of every agent i is
independent of her strategy: C;(8i,s-i) =
and every s;, s; E S;.
Prove that a cost-minimization game with agent cost functions
C1,..., Ck is a potential game if and only if
Ck(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,..., C
is a dummy game.
•.• )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6160dc10-b619-4dba-93d8-e8a5de35ac97%2F1ea8d73b-4d8a-4889-a56d-fc2f9c76b2fa%2Fn31frvl_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 13.3 (H) A team game is a cost-minimization game in
which all agents have the same cost function: C1(s)
for every outcome s. In a dummy game, the cost of every agent i is
independent of her strategy: C;(8i,s-i) =
and every s;, s; E S;.
Prove that a cost-minimization game with agent cost functions
C1,..., Ck is a potential game if and only if
Ck(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,..., C
is a dummy game.
•.• )
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