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.

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Can't solve this matrix for Nash Equilibrium?

So, I have the following 9 by 9 probability matrix. I want to solve it for a nash equilibrium. https://docs.google.com/spreadsheets/d/16Y1FqxRIAHsHpgEz1ckxDt2sEOInOG3zz_wU8kBHvB4/edit?usp=sharing For ...
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Show that an equilibrium in strictly dominant strategies is a unique Nash equilibrium

I am new to game theory and I came across this line, " A strategy profile (s1, . . . , sn) in which every si is dominant for agent i (strictly, weakly, or very weakly) is a Nash equilibrium." But why ...
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Arguing uniqueness of Bayes-Nash equilibrium in an auction setting

In an auction setting with interdependent values, let $\theta_i$ denote the type of player $i$ and $m_i$ that player's message (a bid, essentially). I have calculated the best response function as: $$...
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189 views

Choosing the nondominant strategy in a duopoly

Would a company ever choose a nondominant strategy in a duopoly? Let's take this specific example (2007 AP MicroEcon B #2). Two airlines, Airtouch and Windward, are scheduling flights for either ...
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Equilibria for multi-round 'Markov' games?

I'm interested in zero-sum symmetric games which have the following form. Each player has a counter which starts at 0. Each turn, a player may choose from a fixed set of actions. A player's counter is ...
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Comparing Nash equilibria

Suppose two players play the following game: \begin{array}{cc} & L & R \\ U & 1,1 & 0,0 \\ D & 0,0 & 4,4 \end{array} Is there any way to compare the top-left Nash ...
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Difference between Sequential and Weak Sequential (Weak Perfect Bayesian) Equilibria?

This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. ...
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perfect bayesian nash equilibrium is simply nash equilibrium

Is it true that for two player zero sum game, Perfect Bayesian Nash equilibrium is simply Nash Equilibrium? I am learning game theory and our lecturer does not explicitly cover it.
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Is there a term for a game whose pareto optimal solutions and nash equilibria are disjoint?

Is there a term for a game whose pareto optimal solutions and nash equilibria are disjoint? (e.g. prisoner's dilemma)
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Identifying Nash equilibria in extensive form game

Is there a systematic way of identifying all (pure strategy) Nash equilibria (not just the subgame perfect ones) in an extensive form game? In the following Entrant v Resident example, there are three ...
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Monopolistic and Bertrand (Nash) Competition

Can we view the monopolistic competition equilibrium (a la Dixit-Stigliz) as the limit case of a Bertrand competition with an infinite number of firms providing differentiated products, where the ...
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Finding Nash's Equilibrium in mixed strategies [closed]

How to find the mixed strategy equilibrium in the following game: ...
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How infinite Nash equilibria are possible in a game?

I was studying games when one of the players seems to be indifferent between two or more pure strategies because he gets the same payoff with each strategy. We say that there are infinite Nash ...
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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, ...
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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 ...
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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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276 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 ...
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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 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 "...