Questions tagged [cooperative-game-theory]

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6
votes
2answers
156 views

Modified core for cooperative games

In the core of cooperative games, the total cost of forming a coalition is shared by all members in a coalition (efficiency). However for my problem I only require that all members are individually ...
6
votes
1answer
634 views

How does the core relate to strong equilibrium?

An allocation is in the core if there's no coalition that blocks it. A strong equilibrium (Aumann, 1959) is a Nash equilibrium in which no coalition, taking the actions of its complements as given, ...
5
votes
1answer
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 ...
5
votes
1answer
80 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 ...
5
votes
0answers
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 ...
4
votes
1answer
48 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. ...
3
votes
1answer
529 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 ...
1
vote
2answers
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 ...
1
vote
1answer
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 ...
1
vote
2answers
724 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 ...
1
vote
0answers
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 ...
0
votes
0answers
73 views

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 ...
0
votes
0answers
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 ...