# Game Theory - Strategy

Game Theory - Strategy. See attached file for full problem description.

Two major networks ABC and NBC are competing for viewer ratings in the 8-9 p.m. and

9-10 p.m. slots on a particular weeknight. Each has two shows to fill this time period and is juggling its lineup. Each can choose to put is "bigger" show first (8-9 p.m. slot) or to place it second (9-10 p.m. slot).

Suppose that the combination of decisions leads to the following "ratings points" results:

The networks want the highest "ratings points" they can get.

a. Does ABC have any dominant strategy? If so, what is it? If not, why not?

b. Does NBC have any dominant strategy? If so, what is it? If not, why not?

c. Does there exist any dominant strategy equilibrium in this game? If so, what is it? If not, why not?

d. Does there exist any Nash Equilibrium in the game? If so, what is it? If not, why not?

Now suppose that the combination of decisions leads to the following "ratings points" results:

e. Does ABC have any dominant strategy? If so, what is it? If not, why not?

f. Does NBC have any dominant strategy? If so, what is it? If not, why not?

g. Does there exist any dominant strategy equilibrium in this game? If so, what is it? If not, why not?

h. Does there exist any Nash Equilibrium in this game? If so, what is it? If not, why not?

#### Solution Preview

a. Does ABC have any dominant strategy? If so, what is it? If not, why not?

If NBC picks first, then ABC picks first (18) and if NBC picks second, then also ABC picks first (23). Thus ABC's dominant strategy is "First".

b. Does NBC have any dominant strategy? If so, what is it? If not, why not?

If ABC picks first, then NBC picks first (18), and if ABC picks second, then also NBC picks first (23). Thus NBC's dominant strategy is also "First".

c. Does there exist any dominant strategy equilibrium in this game? If so, what is it? If ...

#### Solution Summary

The solution provides excellent answer to the problem below.