Questions tagged [nash-equilibrium]
A basic solution concept in game theory that requires each player to select their best response to the strategies chosen by others.
260 questions
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 &...
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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 A_{i,...
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Has the Nash Equilibrium led 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 its creation, the Nash Equilibrium has been applied to "...
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