# 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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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: $$... 1answer 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 ... 0answers 68 views ### 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 ... 2answers 161 views ### 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 ... 1answer 8k views ### 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. ... 1answer 1k views ### 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. 1answer 131 views ### 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) 2answers 2k views ### 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 ... 1answer 139 views ### 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 ... 1answer 186 views ### Finding Nash's Equilibrium in mixed strategies [closed] How to find the mixed strategy equilibrium in the following game: ... 2answers 2k views ### 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 ... 1answer 645 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, ... 1answer 97 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 ... 0answers 38 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 ... 0answers 61 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)$$where R(p) = p ... 2answers 3k views ### What is the definition of a “Stackelberg leader-leader equilibrium”? I have encountered the equilibrium concept of "Stackelberg leader-leader equilibrium" while reading Product Line Rivalry (AER, Brander and Eaton (1984). They say "we define a Stackelberg strategy as ... 1answer 239 views ### Is there always a pure Nash equilibrium in a resource selection game? Denote [r]\triangleq\{1,2,\ldots,r\}. Consider a game with n players, [n], each has m strategies, [m]. Each player i has an associated payoff function, which considers only his selected ... 2answers 594 views ### Pareto optimality and Externalities Let's consider 5 farmers, each of them has 2 cows to put into the field. So every farmers can put 0,1 or 2 cows. I denote the three stategies by q_i, i=0,1,2. Now, the payoffs ( i.e. the amout of ... 1answer 276 views ### Submodularity property in congestion games? Let G be a n-players and m-elements congestion game. For an equilibrium e, denote by$$SUP(e)\triangleq<sup_1(e),sup_2(e),\ldots, sup_n(e)>$$Where sup_i(e) contains the support of ... 1answer 317 views ### Is a Nash equilibrium anything more than what it is? (Sorry for the fuzzy title, could not think of something more informative. Feel free to suggest improvements) This question is somewhat of a generalization of "Osborne, Nash equilibria and the ... 1answer 118 views ### Are symmetric equilibria continuous with respect to the payoff matrix? Assume a two player symmetric game where the payoff for the row player is given by:$$ A = \left( \begin{array}{cc} a_{1,1} & a_{1,2} &\cdots & a_{1,n}\\ a_{2,1} & a_{2,2} &\cdots &...
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,...