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6
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1answer
72 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, ...
1
vote
1answer
55 views

If a game admits a unique Nash equilibirum, does common knowledge of rationality implies Nash equilibirum?

In a highly controversial paper by Robert Aumann(see here), it is stated as a theorem: In PI games, common knowledge of rationality implies backward induction. If we stick to the strong and ...
1
vote
0answers
9 views

Is the symmetric equiblirium in congesstion games always inferior in terms of social-welfare?

Let $G$ be a finite, symmetric, congestion game. According to Nash theorem, a (mixed) symmetric equilibrium surely exists. Congestion games also known to admit pure-strategies Nash equilibrium as they ...
2
votes
0answers
32 views

Symmetric Nash Equilibrium in Stahl (1996)

Let $F(p)$ denote the distribution of prices in a market, $\pi(p, F)$ are profits choosing $p$ given distribution $F$. $E\pi(p,F)$ is defined to be $$ E \pi(p, F) = R(p) \psi(p, F)$$ where $R(p) = p ...
11
votes
2answers
156 views

What is the definition of a “Stackelberg leader-leader equilibrium”?

I have encountered the equilibrium concept of "Stackelberg leader-leader equilibrium" while reading Product Line Rivalry (AER, Brander and Eaton (1984). They say "we define a Stackelberg strategy as ...
7
votes
1answer
72 views

Is there always a pure Nash equilibrium in a resource selection game?

Denote $[r]\triangleq\{1,2,\ldots,r\}$. Consider a game with $n$ players, $[n]$, each has $m$ strategies, $[m]$. Each player $i$ has an associated payoff function, which considers only his selected ...
1
vote
2answers
47 views

Pareto optimality and Externalities

Let's consider 5 farmers, each of them has 2 cows to put into the field. So every farmers can put 0,1 or 2 cows. I denote the three stategies by $q_i$, i=0,1,2. Now, the payoffs ( i.e. the amout of ...
7
votes
0answers
73 views

Submodularity property in congestion games?

Let $G$ be a $n$-players and $m$-elements congestion game. For an equilibrium $e$, denote by $$SUP(e)\triangleq<sup_1(e),sup_2(e),\ldots, sup_n(e)>$$ Where $sup_i(e)$ contains the support of ...
2
votes
1answer
110 views

Is a Nash equilibrium anything more than what it is?

(Sorry for the fuzzy title, could not think of something more informative. Feel free to suggest improvements) This question is somewhat of a generalization of "Osborne, Nash equilibria and the ...
6
votes
1answer
69 views

Are symmetric equilibria continuous with respect to the payoff matrix?

Assume a two player symmetric game where the payoff for the row player is given by: $$ A = \left( \begin{array}{cc} a_{1,1} & a_{1,2} &\cdots & a_{1,n}\\ a_{2,1} & a_{2,2} &\cdots ...
5
votes
1answer
83 views

Are symmetric equilibria monotone?

Assume a two player symmetric game is given by $n\times n$ payoff matrix $A$ for the row player (and $A^t$ for the column player). Let $B$ be a matrix such that $\forall i,j\in [n]:B_{i, j}\geq ...
11
votes
3answers
294 views

Has the Nash Equilibrium lead to any significant economic discoveries?

The Nash Equilibrium provided a new look at certain economic problems and won the Nobel Memorial Prize in Economic Sciences in 1994. Since it's creation, the Nash Equilibrium has been applied to ...