Question

1. Consider the following game:

	L	R
L	2,1	0,0
R	1,0	3,2

a)Find all Nash equilibria and derive the players’ expected payoffs in each of the Nash equilibria.

b)Now change the payoffs slightly so that

	L	R
L	2,1	2,0
R	1,0	3,2

i.Derive all Nash equilibria for this modified game.

ii.Have any of the Nash equilibria changed? If so, for each player explain why the player has or has not changed her strategy.

c) Do the players in these games have good reasons for wanting to be unpredictable? Explain

Answer 1

Nash equillibrium is a strategy from which no one wants to deviate.

• Nash equilibrium : (2,1) and (3,2) because
  • If A chose L --> B choose L (see table)

and if B chose L --> A choose L

=> L,L =(2,1) is Nash equilibrium

• If A chose R --> B choose R

and if B chose R --> A choose R

=> R,R = (3,2) is also Nash equilibrium

• Expected payoff for player A (note : probability is written in brackets)

Expected payoff for player B;

Putting values of a and b in expected value equations we get,

Expected value of player A = 1.5

Expected value of player B = 0.67

• Nash equilibrium
  • If A chose L --> B choose L

Now, If B choose L --> A choose L

=> L,L (2,1) is Nash equilibrium

• If A chose R --> B choose R

Now if B choose R --> A choose R

=> R,R (3,2) is Nash equillibrium

• The players have not changed their startegy.