Anyone even vaguely acquainted with Game theory is familiar with the difference between cooperative and uncooperative strategies. While we have clear qualitative delineations between cooperation and non-compliant strategies, what differentiates players from nonparticipants in a game? Any administrator, judge, referee, or rule promulgator could arguably be a player in a game. Typically, these authoritative actors do not operate neutrally and have their incentives structure for their strategies for enforcing or creating rules. The actions of these high-status players have a profound impact on the potential outcomes of the game.
If an administrator can be a player, lower-status players choose to deploy uncooperative strategies against both the administrator and unprivileged players and the administrator. Any uncooperative strategy used against both regular player(s) and an administrator is an example of a Double-Defection Strategy. A mundane example would be in a household where a parent selects a favorite child. The unfavorable child could choose a behavioral strategy that defects concurrently from the parent-sanctioned rules and peacefully co-existing with their sibling. Therefore, creating conditions under which the child’s behavioral strategy defects from the administrator and the ordinary player.
One of Thomas Schelling’s best-known contributions to Game Theory was the concept of a focal point. Otherwise known as “Schelling point”. What is a focal point? We oftentimes hear the term being thrown around colloquially in various settings. Ranging from office board meetings to pundits on network news stations. The common definition of the term slightly differs from its connotation in Game Theory. The common definition of a focal point connotes a point of convergence. A central point from which all other connections radiate. This definition isn’t antithetical to how the term is used in Game Theory. Since most of these assumptions are implicit in the game-theoretical definition. A focal point from Dr. Schelling’s perspective operated as a conceptual bridge in the absence of clear communication. A focal point bridges the gap between information asymmetries when correspondence is lacking.
A focal point is particularly important in what is known as a coordination game. Simply put, coordination games are situations where the players benefit from assuming the same course of action. It can be assumed that in such scenarios nash-equilibrium is faithfully upheld by all participants. Because all players are conforming to the behavior of their opponents. Schelling’s conception of focal point may be applicable even in scenarios outside of the context of coordination games. A focal point could also be seen as a cultural-contingent point of reference, that can serve as a beacon of hope in contextual circumstances fraught with ambiguity. There are certain locations, times, dates, and people that serve as focal points to individuals of various cultural groups. The recognition of these focal points functions on a continuum ranging from locally acknowledge focal points to internationally renowned points of reference. A local bar may be a focal point to residents but in contrast the Panama canal a world-renown point of reference. While Schelling points may be an ingrained feature of coordination games we do see them peppered throughout our daily lives.
In Schelling’s seminal book The Strategy of Conflict (1960) the Nobel laureate details one of the most widely cited examples of a focal point in game theory.
You are to meet somebody in New York City. You have not been instructed where to meet; you have no prior understanding with the person on where to meet, and you cannot communicate with each other. You are simply told that you will have to guess where to meet and that he is being told the same thing and that you will just have to try to make your guesses coincide. (Schelling, 1960, p. 56).
The only tool at your disposal would be to use a common point of reference in the lack of proper information be a common point of reference. In London, England it may be a shrewd strategy to meet at the Big Ben clocktower. However, opting to meet at “Big Ben” in NYC would be wholly inappropriate. A better potential meeting place would be the Empire State Building. In the absence of any cultural context, this task becomes nearly impossible. Without any cultural consensus, it becomes difficult to ascertain what is a crucial landmark. Not only consensus required but also the ability to rank the salience and notoriety of the location is necessary. Your favorite coffee shop in Greenwich Village maybe your favorite location in all of the city, but odds are you wouldn’t find the other “player” at this location in the absence of clear communication. These broad approximations are far from perfect science. One “player” waiting at Central Park and the other waiting at the Empire State Building are rational strategies. Both players missed the mark.
The conventional definition of a focal point isn’t completely different than how the term is used in Game Theory. From a game-theoretical standpoint, does have a “centering effect”. It serves more to operate as a tool to navigate the perils of imperfect information, rather than a noun describing the spatial origin of the reference point or a clumsy synonym for a talking point. When properly estimated by coordinating actors it does effectively operate as a point of convergence. It is just a matter of fine-tuning the location.