# Questions tagged [cooperative-game-theory]

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### If the players are symmetric and the core is nonempty, then $x_i = v(N)/n$ for all $i$ is a Core element

Consider a TU game $\langle N,v \rangle$ with $N = \{1,2,\ldots,n\}$ being the set of players and $v : 2^N \to \mathbb R$, $v(\emptyset) = 0$ the characteristic function. The Core of $v$ is defined by ...
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### Airport problem

Assume that there are $m$ different types of aircrafts. For each type $l$, we know the number of movements, $n_{l}$, and the overall runway costs, $c_{l}$, associated with type $l$ aircrafts. Since we ...
89 views

### What is the most general definition of “the core” in game theory?

I’ve seen definitions of “the core” that rely on some specific assumptions, such as that the game is one of a transfer of resources, or that there is “transferability of utility” (presumably intending ...
49 views

### Convex games: equivalence of definitions

Let $N \subset \mathbb N$ denote the set of players and $v : 2^N \to \mathbb R$ , $v(\emptyset) = 0$, the characteristic function. We call $(N,v)$ a cooperative transferable utility (TU) game. ...
728 views

### How to calculate Shapley Value with uncertainty?

So I'm trying to estimate a Shapley value in a game with uncertain payoffs. Specifically, imagine a game where the payoff function as as follows ...
26 views

### Why do co-ops dominate in certain markets rather than more-conventional enterprises?

Why do co-ops dominate in certain markets rather than more-conventional enterprises? For example, the US dairy processing market seems to be dominated co-ops like Land'O Lakes and Dairy Farmers of ...
50 views

### World as a society of interlinked multiplayer individuals

If you were to take a game-theoretic model of a world in which each individual tried to optimize their utility function / goals then how would you go about designing a computer simulation of the ...
16 views

### Are there examples of businesses that profit from helping consumers coordinate better?

In economics, its often assumed that individuals are unable to coordinate. Moreover, its often assumed that one of the roles for the government is to help consumers coordinate. However, its also ...
50 views

### Coalitional games and Shapley value used for assessing explanatory variable contribution

I have a problem that at the first sight seems not as coalitional game, but rather could be described as logistic regression with all dichotomous variables: 1 response variable Y (I would call it ...
79 views

### Computing the core in a transferrable utility game

An allocation $x^{*}$ is said to have the core property in a game of $N$ players if there is no coalition $S \subseteq N$ that can improve upon $x^{*}$. The core of a game is the set of allocations ...
532 views

### Writing the core as the intersection of pareto efficient outcomes of all coalitions

I have been reviewing general equilibrium models and was trying to find an efficient method for computing the core of a cooperative game. I was taught this topic in a very poor way so I believe I ...
379 views

### How do you determine the strict core in a matching game?

So I have a game in which home owners prefer certain other's homes. The owners are A, B, C, and D with a, b, c, and d referring to their respective homes. They each prefer homes according to the ...