(Solved): Consider the following game, between a criminal and the government. The criminal selects a level of ...

Consider the following game, between a criminal and the government. The criminal selects a level of crime, y >= 0, and the government chooses a level of law enforcement x >= 0. Both choices are simultaneous and independent, and utility functions of the government (G) and the criminal (C) are, respectively U_(G)=-(y^(2))/(x)-xc^(4);" and "U_(C)=(1)/(1+xy)sqrty Intuitively, the government takes into account that crime, y, is harmful for society (i.e., y enters negatively into the government's utility function U_(G) ), and that each unit of law enforcement, x, is costly to implement, at a cost of c^(4) per unit. In contrast, the criminal enjoys sqrty if he is not caught, which definitely occurs when x=0 (i.e., his utility becomes U_(C)= sqrty when