6. Consider the following production coordination game: each agent i = 1, 2 has capital kli > 0, with current output yli = f(kli) with intertemporal preferences u(C1i)+Bu(czi), where 3 (0,1), u(e) is strictly concave, continuous, and strictly increasing with Inada conditions at c-0. The household can save or eat date 1 output, where savings is Ili, and tomorrow capital stock for household i is just k2i = I1i. Each household has a production technology that produces output "tomorrow" as y2i = fi(21i& 1 - i) where x1-i is the investment by the other agent than i. So payoffs in the game are given by u(f(kit) - x;) + Bu( f('li, 11-1)) Assume finally that u( f (311, 21-1)) is supermodular on (0,00) x (0,0). (a). Show that the best reply maps for both players are (i) strong set order ascending in the other player's investment, with least and greatest selections isotone; (ii) that both players best replies are increasing in (k,3), (iii) That least and greatest pure strategy Nash equilibrium exist for fixed (k,8), and (iv) the least and greatest Nash equilibria are increasing in (k, 8). (b) Discuss when the least and greatest Nash equilibrium can be computed. 6. Consider the following production coordination game: each agent i = 1, 2 has capital kli > 0, with current output yli = f(kli) with intertemporal preferences u(C1i)+Bu(czi), where 3 (0,1), u(e) is strictly concave, continuous, and strictly increasing with Inada conditions at c-0. The household can save or eat date 1 output, where savings is Ili, and tomorrow capital stock for household i is just k2i = I1i. Each household has a production technology that produces output "tomorrow" as y2i = fi(21i& 1 - i) where x1-i is the investment by the other agent than i. So payoffs in the game are given by u(f(kit) - x;) + Bu( f('li, 11-1)) Assume finally that u( f (311, 21-1)) is supermodular on (0,00) x (0,0). (a). Show that the best reply maps for both players are (i) strong set order ascending in the other player's investment, with least and greatest selections isotone; (ii) that both players best replies are increasing in (k,3), (iii) That least and greatest pure strategy Nash equilibrium exist for fixed (k,8), and (iv) the least and greatest Nash equilibria are increasing in (k, 8). (b) Discuss when the least and greatest Nash equilibrium can be computed