Suppose two players, A and B, select from three different numbers, l, 2, and 3. Both players get dollar prizes if their choices match, as indicated in the following table.
|
|
B
|
|
1
|
2
|
3
|
|
A
|
1
|
10,10
|
0,0
|
0,0
|
|
2
|
0,0
|
15,15
|
0,0
|
|
3
|
0,0
|
0,0
|
15,15
|
(a) What are the Nash equilibria of this game? Which, if any, is likely to emerge as the (focal) outcome? Explain.
(b) Consider a slightly changed game in which the choices are again just n umbers bu t the two cells with (15, 15) in the table become (25, 25). What is the expected (average) payoff to each player if each flips a coin to decide whether to play 2 or 3? ls this better than focusing on both choosing l as a focal equilibrium? How should you account for the risk that A might do one thing while B does the other?