With the recent death of Nobel-winning economist and mathematician John Nash, whose life story was told in the Academy Award-winning movie A Beautiful Mind, people are suddenly starting to talk about game theory again. Game theory is a significant component of fields such as behavioral science and is also coming up in the context of discussions ranging from the Greek economic situation to voting behavior. So what is it?
It’s not actually about games, though the initial work in game theory actually was about how people behaved while playing poker. Instead, it’s described by Kenneth Chang in the New York Times as “the study of how to come up with a winning strategy in the game of life—especially when you do not know what your competitors are doing and the choices do not always look promising.”
In particular, Nash—who was co-awarded the 1994 Nobel prize in economics for his work—is known for developing the Nash equilibrium, which Chang describes as “a stable state in which no player can gain advantage through a unilateral change of strategy assuming the others do not change what they are doing.”
In other words, if your strategy wouldn’t change even if you did know what your competitors’ strategy was, you’ve reached a Nash equilibrium. “A key insight of game theory is that how you balance the different options in an ‘optimal’ (meaning equilibrium) strategy isn’t just a matter of how good each option seems in a vacuum,” writes Benjamin Morris in FiveThirtyEight, going on to describe its application in sporting events. “It matters how your opponent will adapt to your strategy overall.”
At the same time, it’s important that your actions not be too predictable, so that your competitors don’t always know what you’re going to do.
“Rarely is it wise to stick to a single strategy,” writes Tom Siegfried in Science News. “In any but the simplest situations, Nash equilibrium is achieved only when players pursue a ‘mixed strategy. In other words, a behavior is chosen from a probability distribution—a mix—of different specific strategies.”
Nash’s work considered situations other than one person wins and one person loses. It also covers situations where everyone wins—or everyone loses. In particular, it covered non-cooperative situations, which doesn’t necessarily mean that cooperation between the parties can’t happen, but that there isn’t a mechanism, such as a legally binding contract, to ensure that the parties commit to their agreements.
Nash’s work also considers possibilities such that people wouldn’t act rationally, and that people wouldn’t necessarily make the best decisions possible.
“Game theory provides a common mathematical language for analyzing research across the entire spectrum of the social sciences,” writes Siegfried. “Game theory provides a method for quantifying human behavior, even though humans don’t always behave in the way a naïve application of game theory would suggest.”
While applications of the Nash Equilibrium are usually thought of in terms of politics, it comes up in business as well. Pricing of goods and supplies, the wages companies pay, competitive bidding—all of these are areas in which game theory and the Nash Equilibrium play a part.
For example, notes the Independent, when the U.S. government in 1994 sold off large portions of the electromagnetic spectrum to commercial users, it used Nash’s equilibrium theory to design a multiple-round procedure to maximize both the revenues to the government and the utility of the purchased wavelengths to the respective buyers. “The result was highly successful, bringing more than $10bn to the government while guaranteeing an efficient allocation of resources.”
In comparison, a similar auction in New Zealand without such a careful design meant the government not only received just 15 percent of its expected earnings, but the wavelengths were not efficiently distributed.
In fact, Nash equilibria are relevant to many types of government policy decisions, writes John Cassidy in the New Yorker. “Whenever a government agency is considering a new rule—a set of capital requirements for banks, say, or an environmental regulation—one of the first questions it needs to ask is whether obeying the rules leads to a Nash equilibrium,” he writes. “If it doesn’t, the new policy measure is likely to prove a failure, because those affected will seek a way around it.”
Similarly, business acquisitions—such as the fight between Facebook and Google to acquire the messaging app WhatsApp—can also be thought of in a game theory context. Each of the companies were looking at the acquisition not just for their own needs, but also in terms of what the acquisition could mean to the competitor.
Ultimately, writes Eyal Winter in the Independent, game theory is the theory of putting yourself in the other person’s shoes. “To manage a conflict or to resolve it you have to understand the motives of all the parties involved,” he writes. “You have to be able to assess the benefits that each party might gain and the costs that they will have to incur as a result of any possible action that they might choose to undertake.”
That includes not just financial gains and costs, but also emotions, moral sentiments, and ideologies, Winter continues, adding that Nash once wrote him to say that “finding ways to measure these types of costs and benefits poses a great challenge to us game theorists.”
Figure that out, and maybe you can win a Nobel Prize, too.
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