Game Theory: Superadditivity & Imputation Explained

[bigjoe5263]

Hi,

In a n-person game theory.. I have encountered these terms, superadditivity and imputation, however i do not understand much their definition. Anyone have a simple explanation to this terms?

Somebody here knows where can I find a dictionary of mathematical expressions/equations in game theory?

thanks in advance.

 

[EnumaElish]

Can you explain the context? Does it involve cooperative games (e.g. Shapley)?

http://www.britannica.com/ebc/article-22625

For example, a cooperative game may be called superadditive if the value (payoff) of a coalition that consists of two players is greater than the sum of the individual values (payoffs) for each of the two players: V(a + b) > V(a) + V(b). See also http://en.wikipedia.org/wiki/Superadditive

In the same context, an imputation is a payoff vector associated with a possible outcome. In a cooperative game, an outcome is a coalition; more than one imputations may correspond to a coalition. The Britannica article has some examples.

A good starting point for game theory is http://en.wikipedia.org/wiki/Game_theory

 

[bigjoe5263]

yes it involves cooperative games, the shapely value and the core of an n-person game theory...

Just one question on the prisoners dilemma non constant sum game and non-cooperative...the equilibrium is both of them confess but it confuses me because i think when one of them change the strategy the other one will benefit...??

 

[EnumaElish]

That's why you should be careful whether you are operating under "cooperative" assumptions or "non-cooperative" (competitive) assumptions.

Prisoner's Dilemma (P.D.) is a classic example in non-coop. theory. Each prisoner is assumed to care about his/her utility (payoff) only; they are not allowed to interact; there are no side payments; and there are no "future payoffs." Each prisoner will first ask: "if the other prisoner confesses, am I better off confessing or not confessing?" He will find out that he is better off confessing. Then the same prisoner will ask: "if the other one does not confess, am I better off confessing or not confessing?" Again he will find out that he is better off confessing. He will conclude that he is better off confessing regardless of what the other one does.