In game theory, specifically cooperative game theory, a game is described as inessential if the players receive no more or less in total by working together than by working alone. Thus the players will be indifferent to the formation of coalitions- to do so brings no greater reward, but incurs no penalty either.

This idea can be captured formally as follows:

A game in coalitional form (X,v) is inessential (or additive) if Σi v({i}) = v(X), where i runs from 1 to n.

If this condition does not hold, then the game is described as essential.

Any two player zero-sum game is inessential, but this does not generalise to larger numbers of players, nor to general sum games: the simple majority game is a zero-sum counterexample with three participants; whilst the prisoner's dilemma is an essential two player game.


Part of A survey of game theory- see project homenode for details and links to the print version.

In`es*sen"tial (?), a. [Pref. in- not + essential: cf. F. inessentiel.]

1.

Having no essence or being.

H. Brooke.

The womb of inessential Naught. Shelley.

2.

Not essential; unessential.

 

© Webster 1913.

Log in or registerto write something here or to contact authors.