Problem One5

Consider the following simultaneous moves game in normal form:

Player Two
t1 t2
Player One r1 -2,4 0,-2
r2 -4,5 0,1

(a)State the set of Nash equilibrium strategies.
(b)State the payoffs to each player in the Nash equilibrium.

To find the Nash equilibrium strategies and payoffs in this simultaneous moves game, we can follow these steps:

(a) Finding the Nash Equilibrium Strategies:

1. Evaluate the row player's best response to each of the column player's strategies.
- For Player One (Row player), their best response to t1 is choosing r1 since its payoff (-2) is higher than the alternative r2 (-4).
- For Player One (Row player), their best response to t2 is also choosing r1 since its payoff (0) is higher than the alternative r2 (1).

2. Evaluate the column player's best response to each of the row player's strategies.
- For Player Two (Column player), their best response to r1 is choosing t2 since its payoff (4) is higher than the alternative t1 (-2).
- For Player Two (Column player), their best response to r2 is choosing t2 since its payoff (5) is higher than the alternative t1 (0).

3. Identify the strategies where both players have a best response to each other.
- From the previous step, we can see that r1 and t2 are the strategies where Player One and Player Two have their best responses.

Therefore, the Nash equilibrium strategies are (r1, t2).

(b) Finding the Payoffs in Nash Equilibrium:
- In the Nash equilibrium, Player One plays r1 and Player Two plays t2.
- The payoffs corresponding to these strategies are -2 for Player One and 4 for Player Two.

So, in the Nash equilibrium, Player One receives a payoff of -2 and Player Two receives a payoff of 4.