Sentence examples for core of a game from inspiring English sources

This leads to the definition of the core of a game.

The core of a game is nonempty if and only if the game is balanced.

The core of a game is the set of aspiration vectors such that.

It is easy to see that whenever the core of a game is non-empty, the nucleolus lies in it [4].

For the cost saving allocation problem, the core of a game presents a set of imputations as follows: {text{core}}(0) = left{ {overrightarrow {y} in Yleft| {,e(S,overrightarrow {y} ) le 0,,forall S subset P} right.} right} = left{ {overrightarrow {y} in Yleft| {,v(S) - sumlimits_{p in P} {y_{p} } le 0,,,foralll S subset P} right.} right} (31).

We can study the non-emptiness of the core without explicitly solving the core equation, using the following lemma: Lemma 1[13]: A necessary and sufficient condition for the core of a TU game to be non-empty is the TU game to be balanced.

Incidentally, Maschler et al. [7] (cf., Edmonds [8]) noticed that the dimension of the core of a convex game was determined by the decomposability of the game, which is a measure of how much "additivity" (as opposed to the kind of superadditivity imposed by convexity) there is in the value function of the game.

In an interview with IndieGames.com, Cavanagh said that he was interested in using this idea as a core concept of a game, something he felt other games which include a gravity-flipping mechanism had never done before.

Since a linear program is solved at extreme points, the results of Edmonds (stated in the language of polymatroids) and Shapley (stated in the language of convex games) imply that any linear function defined on the core of a convex game (or the dominant face of a polymatroid) must be extremized at a marginal vector.

The coaches who didn't choose them are blind to the values that are at the core of a team game.

In particular, the extreme points of the core of a convex game are precisely the marginal vectors.