Remember the movie A Beautiful Mind? Directed by Ron Howard, it starred Russell Crowe, who played a brilliant but schizophrenic mathematician, John Forbes Nash, Jr. Though at heart a mathematician, Forbes received the Nobel prize in Economic Sciences in 1994. There is no Nobel prize for mathematics.
Why economics? Because his mathematics of partial differential equations combined with game theory explains so much of why people act the way they do, and industry structures form the way they do.
Core to this is the concept of a particular equilibrium that is now called the Nash Equilibrium.
A group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others. That is, each player plays his or her own optimal strategy with that knowledge that the others are playing their optimal strategy too, and what that strategy is. If no player has an incentive to change, it’s an equilibrium. A game may have one, many, or no equilibriums. According to Mathworld, cited above, “in a Nash equilibrium, no player has an incentive to deviate from the strategy chosen, since no player can choose a better strategy given the choices of the other players.”
Let’s take a famous example, the prisoner’s dilemma. Two criminals cooperated in a crime, and are arrested and placed in solitary confinement. The prosecutor can charge each for a minor offense, but he is thinking strategically. Each is offered the same plea deal:
If both confess the crime, each of them serves two years in prison
If one confesses but the other denies the crime, the confessor will be set free but the other will serve five years in prison
If both deny the crime, each will only serve a six-month sentence
No matter what the other does, it is better to rat on your accomplice. There is one equilibrium for this — where they both squeal. This is true even though both are worse off than if they remained silent.
Now, let’s consider stag hunting. A hunter can hunt a stag or a hare. Stags are much more valuable than hares, so why not hunt stags? Stag hunting, in this game theory exercise, requires cooperation from another hunter to be successful, but hare hunting doesn’t. This game has two equilibriums. Both hunters either hunt stags, or hares, but never mixed. If both are hunting stags, why change? Of course, this is an equilibrium, because both are highly rewarded with the prized stags, and any change causes them both to lose. If both are hunting hares, one hunter changing would deny himself the hare, but he would not get the stag. Each hunter loses if they alone change, so they won’t. That’s the second equilibrium. One hunting stags, and the other hares, is not stable. Sooner or later one will adopt the hunting of the other, and the game then snaps to that equilibrium. Both of the above examples assume there is no communication between the players.
OK, let’s get to electronics. The Beta vs. VHS VCR war was a two-equilibrium game theory model, much like the stag and hare conundrum. VHS could have won. Beta could have won. But there was only room for one winner. Though equally balanced at one time, once the rental stores started leaning towards VHS, the transport vendors did also, and eventually the entire market flipped to a VHS-centric world. The same thing happened later with Blu-Ray and HD-DVD. Either could have won, but only one did. Once the players sense a winner, more investment is made in that direction, and the market flips heavily.
This is why Nash won a Nobel prize in economics. The game theory explains so much of how industries are structured. In my own specialty, electronic test automation, I see Nash game theory playing out in a complex way. In this case, traditional instrument architectures of boxes with serial interfaces have about 85 percent market share, with 15 percent taken by the disrupting modular architectures, such as PXI or AXIe. Using the above example, one would think the traditional architectures would win, because they have the critical mass. The modular standards are, however, gaining.
Here’s why. Besides some advantages, which are crucial for a change, it is the nature of the industry. The industry isn’t homogeneous. Some segments have already shifted to the new architecture. Critical mass exists in those segments, and almost exists in adjacent segments, which are those that require nearly the some set of products. Game theory suggests that vendors pursue those adjacent segments, since a marginal investment brings them great returns. Sure enough, that is how modular instrumentation has advanced — segment by adjacent segment.
Game theory isn’t limited to games and economics. It also explains much of politics in democracies. Public choice theory uses these same game theory and economic constructs to explain the structure of politics itself. James Buchanan, also a winner of the Nobel prize in economics, applied these same concepts to politics, where individuals are all maximizing their gains, whether voters or politicians, and discovered that political structures can also have Nash equilibriums. Like those in industry, these equilibriums are not necessarily optimal for the participants. Did you ever wonder why the US has a “two party system,” though that isn’t legislated anywhere? Another Nash equilibrium!
Thanks to Nash, I can now recognize Nash equilibriums in unusual places, not just my own industry. Have you ever watched competitive cyclists as they break into cooperative groups in a road race, even though they are from competing teams? More Nash equilibriums.
This was my epiphany, when I saw the game theory being played out in so many domains. It explains so much, including many aspects of the innovator’s dilemma.
The movie title was spot on — Nash had a beautiful mind. Any other Nash equilibriums that come to mind?