“…For convenience and simplify the problem behind in this paper, we assume that the third derivative of ( ) is positive, i.e., ′′′ ( ) > 0. (Notes : we review the demand function related to cooperative advertising and game, we find that the most literatures either adopt a square root function ( [19]- [24]) or a power function ( [5], [19], [25], [26]) to describe the form of the market demand related to advertising expenditures, while only few literature [27], [28] use the linear demand function. So, we do not consider the linear demand, after computing the third order derivative of the other demand function(i.e., the square root function and the power function)with respect to advertising expenditures, we give the assumptions above).…”