= - Five players must simultaneously choose a number from the interval [0, 9]. Let x; denote the number chosen by player i; x = (x1, ..., x5 ) all selected numbers; x_{ x\x; all selected numbers except the number chosen by player i. If player i chooses the number x; Є [0,9], while the others choose the numbers _, then the utility of player i is u; (xi, x_i) = 4(9 − xi) + 2-1 xj. Find the Nash equilibria of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game requiring them to choose the number 9?

The economic analysis division of Mapco Enterprises has estimated the demand function for its line of weed trimmers as QD=18,000+0.4N350PM+90Ps where N=numberofnewhomescompletedintheprimarymarketarea PM=priceoftheMapcotrimmerPS=priceofitscompetitorsSurefiretrimmer In 2010, 15,000 new homes are expected to be completed in the primary market area. Mapco plans to charge $50 for its trimmer. The Surefire trimmer is expected to sell for $55. What sales are forecasted for 2010 under these conditions? If its competitor cuts the price of the Surefire trimmer to $50, what effect will this have on Mapcos sales? What effect would a 30 percent reduction in the number of new homes completed have on Mapcos sales (ignore the impact of the price cut of the Surefire trimmer)?