Question

1. The 31 members of the board of the Mega Coporation are about to take a secret ballot vote on whether to accept a merger proposal with SuperGiant, Inc. Each member can vote to ‘accept,’ ‘reject,’ or ‘abstain.’ For the proposal to be accepted, 16 board members must vote to accept it. All the 31 board members care about is being on the winning side. That is, if the proposal is accepted, each member would prefer to have voted to accept it, and if the proposal is rejected, each member would prefer to have voted to reject it. Find the two pure strategy Nash equilibria of this game. What do you predict the outcome will be? Why?

Answer 1

Nash equilibrium or the pure strategy of this game would be achieved if people either in totality accept the proposal of merger or reject or abstain from the voting process.

The nash equilibrium of the above game can be stated as below.

	accept	reject	abstain
accept	31,0	16,15	16,15
reject	16,15	31,0	16,15
abstain	16,15	16,15	31,0

From the above we can say that the nash equilibrium will be reached when all the members together reject, accept or abstain from the merger proposal. Given that no one wants to be on the losing side the members would adopt the pure strategy which would be beneficial to the entire board members.

The first pure strategy would be (Accept,Accept), all the 31 members would accept the proposal of merger as if 16 members accept and the remaining 15 reject or abstain, then those 15 wont be on the winning side as they want.

The strategy would be where all the members reject the proposal as then there will not be a n uncertainity of being on the losing side.

The most favorable outcome would be when all the members abstain from the voting process and hence the strategy outcome will be (31,0) with all the members voting to remain on the same side of the voting process.