deletions | additions       diff --git a/Theorem_maximum_soci.tex b/Theorem_maximum_soci.tex  index 2a6d076..05f907c 100644  --- a/Theorem_maximum_soci.tex  +++ b/Theorem_maximum_soci.tex 
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[[TODO: Define social welfare and best response]]  A line of previous work was devoted to the optimal variant of MAPF. In the optimal variant a solution which minimizes the summation of single agent paths is required.   Optimizing the summed utility over all agents is known as maximum social welfare. Many CA solvers guarntee maximum social welfare as long as agents use the myopic best response bidding strategy (Parkes 1999). According to this strategy, agents allways bid on the best bundle (according to thier evaluation) given the current prices.  This is a reasonable strategy for agents, and it has been  shown that myopic best response is the best strategy for an  agent given that other agents are acting based on this strategy  (Parkes 2001).  -this is guaranteed when each agent gives its best response