Question

In the following game, determine the maximum amount you would be willing to pay for the privilege of moving (a) first, (b) second, or (c) third: There are three players, you and two rivals. The player announcing the largest integer gets a payoff of $\cancel{\mathbf{S}}\mathbf{10}$, that announcing the second largest integer gets $\cancel{\mathbf{S}}\mathbf{0}$, and that announcing the third largest integer gets $\cancel{\mathbf{S}}\mathbf{5}$.

Short answer

The concerned player is player (c), and the maximum amount that this player pays is $10.

Step-by-step solution

Define Business strategy

The game theory is a mathematical concept used in business to decide business strategy. The purpose of using this technique is to create the best strategy for own and defeat competitors.

Evaluating the maximum amount willing to pay

When there are three players, they can pay for the pleasure of moving (a) first, (b) second and (c) third, with the player who states the greatest integer is receiving a prize of $10, the second larger $0, and the third $5.

The player a:

The incentive to be able to play first is $0. By observing the behavior of first player, the other two players will know how to say a number above and below to make a profit, and as a result, the first player will remain second, earning $0.

The player b:

For the whole number of the first player, the incentive to play second place will be up to $5. The most rational thing to do is to say a lower whole number to be third place.

The player c:

Finally, the third player's motivation will be up to $10. This player knows the first players' numbers and so, will select a whole number bigger than the other two players to earn the first place prize of $10.

Therefore, the player (c) is ready to pay the maximum amount of $10