Consider the partnership game analyzed in this chapter, but assume that c < 0. Graph the players' best-response functions for this case, and explain

how they differ from those in the original model. If you can, find the rationalizable strategies for the players. Use the graph to find them. Repeat the

analysis under the assumption that c > 1/4

The game is represented as follows.

Two partners, PX and PY, share profit given by

4(x+y+cxy) where 0

x: the level of effort by Player X(PX) and 0 x 4

y: the level of effort by Player Y(PY) and 0 y 4.

The cost of effort is given by X² for x and y² for y.

Hence the payoffs are given by

1/2[4(x+y+cxy)]- X²

for PX and 1/2[4(x+y+cxy )] - y²

for PY

Two players: PX and PY Strategies: x or y in [0,4] for both PX and PY Pay-off functions: Ux (x,y)=1/2[4(x+y+cxy)]- X² for PX and Uy (x,y)=1/2[4(x+y+cxy )]- y² for PY

{x=1/(1-c)} for PX and {y=1/(1-c)} for PY are the pair of rationalizable strategies.