Cooperative Game - Relation With Non-cooperative Theory

Relation With Non-cooperative Theory

Let G be a strategic (non-cooperative) game. Then, assuming that coalitions have the ability to enforce coordinated behaviour, there are several cooperative games associated with G. These games are often referred to as representations of G.

  • The α-effective game associates with each coalition the sum of gains its members can 'guarantee' by joining forces. By 'guaranteeing', it is meant that the value is the max-min, e.g. the maximal value of the minimum taken over the opposition's strategies.
  • The β-effective game associates with each coalition the sum of gains its members can 'strategically guarantee' by joining forces. By 'strategically guaranteeing', it is meant that the value is the min-max, e.g. the minimal value of the maximum taken over the opposition's strategies.

Read more about this topic:  Cooperative Game

Famous quotes containing the words relation with, relation and/or theory:

    To criticize is to appreciate, to appropriate, to take intellectual possession, to establish in fine a relation with the criticized thing and to make it one’s own.
    Henry James (1843–1916)

    We shall never resolve the enigma of the relation between the negative foundations of greatness and that greatness itself.
    Jean Baudrillard (b. 1929)

    ... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.
    Naomi Weisstein (b. 1939)