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5 votes

The core and competitive equilibrium

tldr: The core is a very general concept that can be used in a vast amount of models. Applying it to the setting of a general equilibrium, you can show that every competitive equilibrium is in the ...
tdm's user avatar
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4 votes
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Is the Nash product really maximised ex post?

The Nash bargaining solution DOES maximize the Nash product. You have to separate the playing of the game from the bargaining problem. If the players negotiate a binding agreement they will realize ...
VARulle's user avatar
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4 votes
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Can there be a game where there are no opponents?

In a coordination game, players' interests are perfectly aligned, so there is no "opposition" in the ordinary sense of the word. The game has simultaneous moves, which means, at the time of ...
Herr K.'s user avatar
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4 votes

Core in a replicated economy

In the economy provided in the question, competitive equilibrium allocations is equal to the set of efficient allocations. This along with the fact that the competitive equilibrium allocations always ...
Amit's user avatar
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3 votes
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Slight Uncertainty of Continuation in Repeated Prisoner's Dilemma

Imagine you have played the first 19 rounds. Now a chance event decides on whether there will be another, final, round. What's your optimal action in this last round, in case it actually occurs? ...
VARulle's user avatar
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3 votes

Shapley value — any real world applications?

It is used quite a bit in machine learning. I think it's becoming a bit of an industry standard in finance. My former employer used it in credit modeling. I worked there as a software developer. I ...
David's user avatar
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3 votes
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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

The center allocation $z_{i}:=(v(N)/|N|)$ for all $i \in N$ is in the core of the symmetric game $v$, whenever $z(S) = \sum_{i \in S} z_{i} \ge v(S) $ holds for all $S \subseteq N$. Now, if $v(N)/|N| \...
Holger I. Meinhardt's user avatar
2 votes

World as a society of interlinked multiplayer individuals

Chess is EXPTIME-Complete, which makes it significantly harder than NP-Complete problems. Perhaps you are interested in the study of economic networks. Strategic network formation sounds like a good ...
ml0105's user avatar
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2 votes
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What is the most general definition of “the core” in game theory?

We can talk of the core for any arbitrary game. To explain how let me compare it directly to how we define non-cooperative games. In a standard non-cooperative game we define Players, $I$, action sets ...
Regio's user avatar
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1 vote

Convex games: equivalence of definitions

Define the marginal contribution of $i \in N$ to any $C \subseteq N \setminus \{i\}$ by \begin{align} m_i(C) = v(C \cup \{i\}) - v(C). \end{align} We are going to show C.1 $\Rightarrow$ C.2 $\...
clueless's user avatar
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