Game Theory and Markets: Schelling Points and The Nash Equilibrium

Author: Duane M. Tilden, P.Eng.        Date: June 10, 2018

Prologue:  It’s been a few weeks since my last blog post as I have been quite involved in other matters. As part of my work involves research and learning I would like to organize some of my discoveries and thoughts and relate them further by curation and publication on my blog.

Some things that I have been aware of it seems to me, intuitively, are rules which have been previously codified by others. Two now under examination are named after their discoverer’s respectively; Schelling Points and The Nash Equilibrium.  These ideas have profound implications in various forms of trade, microeconomics, macroeconomics, and cryptoeconomics.

Schelling or “Focal” Points

In the study of crowds or markets as an example we will find that there will be a tendency of people to gravitate towards the familiar in the absence of information. Such information is useful in the study of how people tend to behave. This information can also used to make optimal choices between two or more people in games of strategy whether between strangers where the others’ choice is unknown, or between friends or groups who may be more predictable in behaviour.

Image result for grand central station new yorkImage 1:  Grand Central Terminal turned 100 years old in 2013. Photo: Buck Ennis

In my own study of markets and their behaviour it is noticeable that one can postulate certain cycles based on common patterns where conflicts for disposable income can affect the movement of capital in and out of the market. I find that this is very similar to what has been found by Thomas Schelling and is also known as “focal points”.

Image result for thomas schellingImage 2: Thomas Schelling received his Ph.D. from Harvard in 1946 and joined the Harvard faculty in 1958. Photo by Martha Stewart

Thomas Schelling, the Nobel-winning game theorist … found in an informal survey that many of his students tended toward the same answer when posed this question about New York City: they would wait under the clock in Grand Central Station at 12 noon, hoping their partners had the same idea.

He introduced this concept in his 1960 book The Strategy of Conflict as a “focal point” – a solution to a coordination problem that somehow stands out as the natural answer even if the participants don’t have a chance to arrange it beforehand. Schelling argued that people’s apparent ability to coordinate without communicating was key to understanding how real-life strategic games are solved.

As game theory has developed in the decades since, Schelling’s ideas about focal points have been rarely studied, partly because the existence of focal points was perceived more as a mysterious, sociological phenomenon rather than an economic one amenable to analysis.

Schelling argued that people’s apparent ability to coordinate without communicating was key to understanding how real-life strategic games are solved.

Schelling himself said trying to determine the focal point of a game analytically is like trying to use a computer to understand whether a joke will be funny – it depends on cultural context and the relationship of the people trying to coordinate. Even the classic Schelling focal point of Grand Central might not apply if you asked different groups of New Yorkers who lived in different parts of the city or never took the trains that pass through the station.

The Nash Equilibrium

The Nash Equilibrium is a basic solution set which can be identified in every day life through some observation. One of the better examples it the driver matrix on a two-way street, where the optimal solution is for both drivers to drive on the left hand or right hand side of the road. If not, then a collision will likely result as both cars will be moving in opposing directions head-on.

Generally speaking one can view this equilibrium as an expectation that in various scenario’s where a choice is required, the person will behave in their own best interests. Understanding this concept is essential to how incentives work in an economy and how such incentives can be used to modify a person’s behavior, whether in a game, company, group, or a market.

Nash Equilibrium is a term used in game theory to describe an equilibrium where each player’s strategy is optimal given the strategies of all other players. A Nash Equilibrium exists when there is no unilateral profitable deviation from any of the players involved. In other words, no player in the game would take a different action as long as every other player remains the same. Nash Equilibria are self-enforcing; when players are at a Nash Equilibrium they have no desire to move because they will be worse off.




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