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 ...
- 10.3k
4
votes
Accepted
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 ...
- 6,540
4
votes
Accepted
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 ...
- 15.3k
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 ...
- 8,206
3
votes
Accepted
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? ...
- 6,540
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 ...
- 131
3
votes
Shapley value — any real world applications?
Allegedly, Barclays uses (or once used) Shapley allocation. Quoting Mauro Cesa:
The basic objective of every bank is to find an optimal business strategy that maximises return on capital (ROC). To ...
3
votes
Accepted
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| \...
3
votes
Accepted
Computing the core in a transferrable utility game
It depends on the set of feasible allocations for the coalitions $S$. Suppose for all $S$ a best allocation exists (the sum of the individual utilities of the members of $S$ is maximal). Then as in ...
- 28.7k
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 ...
- 1,236
2
votes
Computing the core in a transferrable utility game
Computing equilibria is an active area of research. Big name complexity theorists like Lance Fortnow are working in this area. When you have continuity, computing core allocations becomes much easier ...
- 1,236
2
votes
Accepted
Writing the core as the intersection of pareto efficient outcomes of all coalitions
Most of what you write is correct, but the definitions of the $F_i$ sets is imprecise. The problem is that in the core $A$ and $B$ may get goods that do not match their initial endowments. In this ...
- 28.7k
2
votes
Accepted
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 ...
- 4,188
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 $\...
- 1,559
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