Nobel Laureate Aumann talks game theory

Photo courtesy of GT Chabad

Some people cannot play a game without their lucky socks, while some people insist on listening to their lucky song before a game. Some even search for symbols or omens like ladybugs or clovers. Others turn to game theory. Professor Robert Aumann is one such person. In fact, Aumann has received the Nobel Memorial Prize in Economic Sciences for 2005 for his work in the study of game theory. 

On Jan. 29, the College of Computing and the School of Economics planned to host hundreds of people in the Scheller College of Business to hear Professor Aumann speak. Due to inclement weather, the large lecture was cancelled and instead exchanged for an intimate talk between Aumann and members of the on-campus Jewish organization Chabad. 

Nobel Laureate Aumann never once tired his audience with the complicated mathematical equations, theorems or proofs behind his work in game theory, speaking of the concept and its applications in a simple manner. He explained how this science of strategic interaction could be seen in everyday life and in things as simple as a game of chess or baseball. 

“There are a number of entities. They could be people, they could be corporations, they could be parties in a parliament. And each entity is striving for a goal, and the entities are interactive,” he explained. “Each one takes action, and those actions not only impinge on him but also on the other person… Each has to figure out what he should do to advance his goal, and he realizes that the other one is advancing his goals, and that the other one’s goal is not the same as his own goal.”

How does a person achieve his goal when their objectives differ from those of the person he is interacting with? Aumann stressed the importance of knowing that any action taken affects not only the actor but the other player as well. Therefore, understanding the other player and this other player’s goals are vital to winning the game. 

In some scenarios, the goals of the two entities are completely opposite and opposing: an advantage gained by one player automatically signifies a disadvantage incurred by the other player. Scenarios like these have been termed “zero-sum games,” and although they are the foundations of games like chess or baseball, Aumann explained that zero-sum games are rare in life. 

“In real life, it is quite unusual for interacting entities to strive for the opposite goal of the other side,” he explained. 

“In war, the sides are striving towards different goals. But even in war, the goals are not opposite. War is not a zero-sum game. Even though each side wants to win the war, it is advantageous to both sides to have as little as destruction as possible.”

Even if the goals between two different entities are not as different as originally thought, how does one still end up victorious over the other? Aumann stressed the importance of incentives: if player A wishes to win, she must understand the power of incentives so that she can get player B to do what is advantageous for her.

Aumann shared a memory of his past in order to illustrate the power of incentives. He described the bickering that used to occur between him and his brother as they fought over the larger piece of candy. His mom, who he cites as an “early game theorist,” devised a clever way to stop their bickering. Instead of splitting the candy bar into two pieces herself, she had one son split the candybar and the other son choose the piece of candy he wanted. 

This way, there existed an incentive for the person who was splitting the candy bar to divide it equally. That this new method of sharing candy had the ability to stop sibling bickering and solve an argument, something some would have formerly deemed as an impossible task, reveals the importance of incentives. 

Aumann extended his discussion on incentives by explaining its effects on arbitration, the settling of disputes between two parties by an impartial third party. Despite the idealism that is often held for compromising, Aumann explores how compromising can give the conflicting parties the wrong incentives. 

“The incentives [compromising] creates is to exaggerate your demands, because you know the end is going to be a compromise,” Aumann explained. 

“So from a dispute that could have been reasonably small, it becomes a huge difference, because both sides are exaggerating their demands and have an incentive to misrepresent the evidence.”

Although it at first seems counterintuitive, Aumann explained how both sides can benefit from an agreement in which a compromise is not allowed. In fact, Aumann argued that the sides are drawn closer together as they begin to view the dispute more reasonably. 

“When compromise is not allowed, then the incentive of the sides change completely. Because now the sides want to be as reasonable as possible, because they want the arbitrator to pick their sides. So they come closer together,” Aumann explained. 

Aumann explored the power of game theory, a theory that is able to bring different entities with different goals together. 

The Nobel Laureate presented game theory not as an abstract mathematical construct, but as something that applies to our everyday lives. 

Game theory could be something that has the power to not only benefit those similar to oneself, but also the power to benefit those who are different from oneself. It is important to realize that an opponent’s goals are not so different from one’s own.