Questions tagged [cooperative-game-theory]
The cooperative-game-theory tag has no usage guidance.
22
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Core in a replicated economy
I'm trying to solve the following problem on general equilibrium:
Consider an economy with two individuals with utility functions $u^A(x^A,y^A) = \min \{ x^A, y^A \}$ and $u^B(x^B,y^B) = \min \{ x^B, ...
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Slight Uncertainty of Continuation in Repeated Prisoner's Dilemma
In a repeated prisoner's dilemma with some probability δ of continuing after each round, a Subgame Perfect Nash Equilibrium may be found which induces cooperation instead of defection in each round. ...
- 421
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Can there be a game where there are no opponents?
I am considering a scenerio where all the players a in collaboration with each other in an attempt to maximize some profit. However, each player is not 100% sure of the strategy of other player so ...
- 135
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Providing an example in cooperative - games and coalitions
Here is the paper from chich I previously posted another definition here Definition of a $k-$strong Nash Equilibrium
I am trying to construct an example to understand the idea of the following ...
- 949
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2
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766
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Shapley value — any real world applications?
The Shapley value has been around for seven decades now. It is intuitive, tractable, and has many desirable properties. To my surprise, however, its actual applications in the real world are not ...
- 15.3k
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The core and competitive equilibrium
Can someone please explain why the concept of a core is equivalent to a competitive equilibrium?
I am just writing a term paper for my matching theory class and I'm having a hard time following along ...
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200
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Is the Nash product really maximised ex post?
In my game theory class this term, we studied Nash bargaining. It is only now when starting to prepare for the exam that I have come to realise there is something I fundamentally don't understand, and ...
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Simple hawk-dove type super-game
We have the following super-game:
\begin{array}{cc}
& a_1 & a_2 \\
a_1 & 0,0 & -1,1 \\
a_2 & 1,-1 & -2,-2
\end{array}
I want to show that both the trigger (or grim) ...
- 468
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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 ...
- 1,559
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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 ...
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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 ...
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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.
...
- 1,559
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2
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977
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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
...
- 111
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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 ...
- 161
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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 ...
- 127
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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 ...
- 2,648
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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 ...
- 111
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2
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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 ...
- 553
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641
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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 ...
- 553
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470
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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 ...
- 255
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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, ...
- 825
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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 ...
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