A and B are playing a simultaneous moves game. A can choose either High or Low and B can choose either Near or Far. If A chooses High and B chooses Near, A receives 5 and B receives 5. If A chooses High and B chooses Far A receives 3 and B receives 7. If A chooses Low and B chooses Near A receives 7 and B receives 3. If A chooses Low and B chooses Far, both receive 2.
(a) Write out a table representing each player¡¦s strategies and payoffs.
(c)What is/are the Nash equilibrium of this game?
(a) The table representing each player's strategies and payoffs can be written as follows:
| | Near | Far |
|-------|--------|--------|
| High | (5, 5) | (3, 7) |
| Low | (7, 3) | (2, 2) |
In this table, the first value represents the payoff of Player A, and the second value represents the payoff of Player B.
(c) To find the Nash equilibrium of this game, we need to find a strategy profile where neither player has an incentive to unilaterally deviate from their chosen strategy.
Looking at the table, we can see that (High, Near) is a Nash equilibrium because neither player can improve their payoff by deviating. If A switches to Low, they would receive a lower payoff of 7 instead of 5. If B switches to Far, they would receive a lower payoff of 7 instead of 5.
Similarly, (Low, Far) is also a Nash equilibrium because neither player can improve their payoff by deviating. If A switches to High, they would receive a lower payoff of 3 instead of 2. If B switches to Near, they would receive a lower payoff of 3 instead of 2.
Therefore, the Nash equilibria of this game are (High, Near) and (Low, Far).