A Fun Look at Negotiating and Game Theory: The Golden Balls Game

Game theory has been a working subfield of microeconomics since its inception formally in the early 1800’s; however, it has only really taken off in research and literature since the 1970’s with the advent of computer modeling and data aggregation. Some useful insights from game theory can be applied to how businesses function and synergies, how suppliers respond to negative leverage, and how using asymmetric information may be more beneficial that using the whole picture. Some of these topics appear to be unrelated, but they have a few important factors in common. They are all part of a game. Not in the “Let’s play monopoly” sense, but in these types of interactions there are risks, odds, payoffs, winners, and losers. From these topics some interesting findings involving business transactions, cooperation, and negotiating leverage can emerge. One such finding can be seen in the British gameshow, Golden Balls Game.

The intellectually testing gameshow, challenges contestants to work cooperatively, playing the odds and taking risks. However, the contestants’ biggest risk isn’t even the game’s mechanics, rather the other players. Contestants work together to accumulate a large sum of money but vote one player off each round. In the final round, the two players remaining must each decide if they want to “split” or “steal” the money.

For anyone familiar with the prisoner’s dilemma, this should sound relatively familiar. There are two players who both have two options placed in front of them and a sum of money they have accrued over the course of the game. Players can choose to “split”, meaning they agree to split the money 50/50 with the other contestant. Or they can choose to “steal”, meaning they choose to take the whole sum of money and leave the other contestant with nothing. There are four potential outcomes that can occur:

1)       Player 1 and Player 2 chooses split; they both split the money 50/50
 

2)       Player 1 chooses split, Player 2 chooses steal; Player 2 steals all the money and Player 1 gets nothing

3)      Player 1 chooses steal, Player 2 chooses split; Player 1 steals all the money and Player 2 gets nothing

4)      Player 1 and Player 2 both choose steal;  both players get nothing.

It is important to emphasize, if both players choose steal, neither of them win the money. With these rules in place, the gameshow host prompts each player to say a few words to make their case to the other player regarding the decision they should make. Usually this culminates with both players agreeing to split the money after having some heart felt conversation and boasting about being better than the unsuccessful temptation of greed. While this may be a “feel good exercise in human behavior” this does usually end with at least one of the players feeling cheated, resulting in one, or both, going against their word and choosing steal. While on face value, this may be what you would expect, looking at the players’ incentives actually offers valuable insights.

The following link shows the specific situation I am describing and look to expand upon: https://www.youtube.com/watch?v=S0qjK3TWZE8

If you believe the opposing players’ heart wrenching testimony and are 100% certain they’ll split the money with you, you would be silly not to take advantage of the situation and choose to steal and take all of the money. Otherwise, there may be some moral compass guiding your decision, inclining you to split the money. If you’re a great negotiator and aware that you’re leaning towards split, you recognize the opposing player’s incentive to then choose steal. They know you’re falling for their plea and now have the opportunity to take all of the money for themselves.  More often than not, this leads to either one person choosing to steal and the other getting nothing, or both players trying to take advantage of the situation and deciding to steal resulting in neither of them taking home the money.

Believe it or not, there is a correct strategy for aligning incentives and goals in a zero-sum cooperation game. To fully incentivize the other player to commit to splitting the money, you need to give them no other option. In this situation, this means convincing them that you are going to steal, giving them no hope of obtaining the money unless they choose to split. Forcing the other player to make the decision, rather than try to convince you of their good intentions, is the only way to align incentives and make them cooperate. This strategy can be carried over to negotiating. 

Have you ever needed to take a hard line stance in a negotiation with a supplier, knowing all well they have become familiar with the process and can guess at outcomes in the bidding for packages? 

Have you ever gone into a negotiation with little to no leverage and nothing but your persuasion? While it may not be true all of the time and using your best judgement is important, representing strength and going against cooperative pleasantries may be the best strategy. By eliminating personal ambiguity, you make the other party’s decision clear cut. Making all of the information available and leaving the other player with their only other option to negotiating with you because not negotiating is potentially harmful to their business then establishes a logical rational of authentic cooperation.  As a result, you may walk away from negotiations with a more beneficial outcome than showing “cooperation” from the beginning.