George and Gina: A
Match Made in Heaven? 
George and Gina are sweethearts. After dating for a mere ten years, George must decide on a location for his anniversary dinner with Gina. Once the choice is made it is known to both of them. The choices are Perrier, a very upscale restaurant in Philadelphia, and the local McDonald's.
Being a very deliberate fellow, George must also decide beforehand on appropriate dinner conversation for each venue. If he takes Gina to Perrier then George feels that he must either formally propose, or prevaricate and postpone the big announcement for another year. If he takes Gina to McDonald's then George can still propose, but if he chooses not to propose then he better have something of interest to Gina that he can talk about, namely stocks. George's topic of conversation will not be known to Gina until they are in the restaurant.
Gina thinks it is about time that she and George settle on a future for their relationship. Indeed, she has decided that she will preempt George's chosen topic and either accept or refuse his offer of marriage should she find herself dining at Perrier. It is so inconceivable to her that George would be so crass as to propose in McDonald's that she will prepare herself to discuss either football or bonds should she find herself there.
The payoffs to George and Gina are shown in the following game tree.
What are the subgames in this marriage game between George and Gina? There is one at the node labeled P&P. Fill in the payoffs and find the Nash equilibria.
Subgame at Propose and Prevaricate (P & P) 


Gina 

Accept 
Refuse 

George 
Propose 


Prevaricate 


There is another subgame at the node labeled P & S. Fill in the payoffs and find the Nash equilibria.
Subgame at Propose and Stocks (P & S) 


Gina 

Football 
Bonds 

George 
Propose 


Prevaricate 


The entire game is also a subgame. Fill in the remaining payoffs and find the Nash equilibria. In working with the following normal form game recall that a strategy is a complete contingent plan. This means that George must have a plan of action in the event that he finds himself at any node in the game. Therefore each of his strategies consists of three possible moves.
The Normal Form of George's and Gina's Mating Dance 


Gina 

Strategy 1 
Strategy 2 
Strategy 3 
Strategy 4 

At P&P 
At P&S 
At P&P 
At P&S 
At P&P 
At P&S 
At P&P 
At P&S 

Accept 
Foot 
Refuse 
Foot 
Accept 
Bonds 
Refuse 
Bonds 

George 
Perrier 
Propose 
Propose 
3, 8 


1, 2 

Perrier 
Prevar 
Propose 
7, 9 




Perrier 
Propose 
Stocks 
3, 8 




Perrier 
Prevar 
Stocks 
7, 9 




McD 
Propose 
Propose 
10, 4 
10, 4 
8, 3 
8, 3 

McD 
Prevar 
Propose 
10, 4 




McD 
Propose 
Stocks 
0, 5 




McD 
Prevar 
Stocks 
0, 5 


4, 0 


At Rest 
At P&P 
At P&S 

You should have found a Nash equilibrium in each of the two subgames. In the normal form of the entire game there is only one subgame perfect equilibrium. Explain why one of the subgame Nash equilibria is not a subgame perfect equilibrium.