Question

Is it possible that which player goes first in a sequential game can change what the Nash equilibrium outcome is?

In this particular game, why or why not?

a. It is possible, since one player will prefer the simultaneous-game Nash

b. It is possible, since the person going second will get to know what the other player did first, putting them in a better position

c. It is possible, since going first allows a player to commit to their action

d. It is not possible, since mathematically the games are the same whoever goes first

e. It is not possible, since the Nash comes from the best responses, and the best responses stay the same regardless of who goes first

f. It is not possible, since the player going second cannot make a credible threat/promise

Answer 1

When games are played sequentially instead of simultaneously, equilibrium is no longer a natural solution concept. Instead we use the equilibrium where first player calculates the second players response and goes accordingly to gain the highest. So in a sequential game, it can be advantageous to go first or second depending on the particular game.

So the answer must be - b. It is possible, because the person going second will get to know what the first player did, putting them in better position.

But actually the particular game is not given, so do check in the game.