Question

1. Assume two players (ie. Florent and Bernard) compete in a one-shot simultaneous move game. Florent can choose up or down, whereas Bernard can choose left, middle or right. Assume the following payoff matrix Bernard Florent Up 6,8 3,2 Down 3.2 4.4 Payoff: (Florent, Bernard) a) Identify the dominant strategy equilibrium(s), if any. (3 marks)

Answer 1

ans1a)

In dominant strategy we consider the best possible outcome for both the parties, regardless of what the other person is doing.

Here for Bernard, Right is the dominant strategy as the expected utility drawn out of it is maximum in right

Heres how we calculate expected utility

Left : 8+2

Middle:2+4

Right:5+10= 15 (max among the three)

Similarly for Florent:

expected utilities:

UP:6+3+2

DOWN:3+4+9= 16 (max)

Hence the dominant strategy would be a combination of right and down.

1b) Nash equlibrium doesnot exist. because if Florent chooses UP, Bernard will choose left,

Whereas if Florent chooses DOWN, Bernard will choose right.

Hence we cant pinpoint any particular cell to serve as nash equilibrium.

This is a wierd case as in when the marix is a 2*2, the presence of a dominant strategy indicates nash equilibrium, not here.

1c) If one player is bound to make a particular choice, the other player would opt for maximising his utility constrained to the others choice.

Say, if Florent is bound to choose DOWN, Bernard will choose right, making that the nash equlibrium in this case.

Similarly, if Florent is bound to choose UP, Bernard will choose left, making that the nash equlibrium in that case.