We investigate group formation and strategic behaviors of wind power
producers in the electricity market. Currently, wind farms bid into the
day-ahead market in a conservative fashion to reduce the possible real-time
penalty of not meeting their bid amount. It has been suggested in the
literature that wind farms would bid less conservatively if they can form
large groups to take advantages of spatial diversity to reduce uncertainty
in their aggregate output.  We show that if this group acts strategically,
it would artificially lower the aggregate output because of market power: under a wide range of operating conditions, the power
production of a a grand coalition of wind producers is less than the total
wind production if each wind farm individually bid into the market.