Nash Equilibrium

In defining the concept or term known as “equilibrium,” the late Thomas Schelling wrote:

“An equilibrium is a situation in which some motion or activity or adjustment or response has died away, leaving something stationary, at rest, “in balance,” or in which several things that have been interacting, adjusting to each other and to each other’s adjustment, are at last adjusted, in balance, at rest.”

There is also a caveat to the whole concept of equilibrium, which Schelling noted:

“An equilibrium can be exact or approximate. It can be always approached but never quite achieved, the potential equilibrium itself continually changing. And equilibrium can be partial or complete, short run or long run.”

In turn, a state of “equilibrium” can either be good or not-so good depending on who you are and where you come from per se. For instance, an enduring global peace would not be such a great outcome or a favorable permanent state for bankers on Wall Street. And as Schelling wrote:

“The point to make here is that there is nothing particularly attractive about an equilibrium. An equilibrium is simply a result. It is what is there after something has settled down, if something ever does settle down. The idea of equilibrium is an acknowledgement that there are adjustment processes; and unless one is particularly interested in how dust settles, one can simplify analysis by concentrating on what happens after the dust has settled.”

To illustrate the point about how equilibrium can actually be an unfavorable state for certain entities and individuals, Schelling used the following analogy: “The body of a hanged man is in equilibrium when it finally stops swinging, but nobody is going to insist that the man is all right.” Game theory encapsulates the concept of “equilibrium” in what is known as “Nash Equilibrium.” Why equilibrium can either be favorable or unfavorable to certain entities and individuals is because equilibrium is ultimately the result of competition. As Presh Talwalkar wrote: 

“The point of a Nash equilibrium is that it is the result of competition when players take into account what others will do and how they can influence the game. Some Nash equilibria will seem fair while others will not.”

In a technical sense, a “Nash Equilibrium” is “a system of beliefs and a profile of actions for which each player is playing a best response to his beliefs and, moreover, players have correct beliefs.” Also, a “Nash Equlibrium” can equate to “a profile of strategies for which each player is choosing a best response to the strategies of all other players.” Why information becomes critical in determining a favorable outcome out of a “Nash Equilibrium” is because a favorable outcome hinges on whether one’s beliefs about his or her opponents – with beliefs being shaped largely by knowledge and information – are actually correct. 

It follows that “adding information to a player can never be to his detriment, and may well be to his advantage.” In turn, the two basic assumptions of Nash’s theory on equilibrium are that all the players in a “non-cooperative game” are rational in the sense that all players are pursuing a ‘best response’ to what everyone else is doing and that all the players are informed in the sense that all players are getting good information and that their beliefs about all the other players are correct and informed. But as mentioned before, one need not have all the players be rational and informed in order to establish a state of equilibrium. Rather, the outcome of an “equilibrium” will simply be favorable to the players whose actions and beliefs were rational and informed, and will be unfavorable to the players whose actions and beliefs were irrational and uninformed. In turn, the “payoffs” which are associated with the outcome of a competition or “non-cooperative game” largely depend on conditions and circumstances. Thus, the “payoff” for each player can be fluid and subjective rather than fixed and “objective.”