# 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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### 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 "...
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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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### Nash equilibrium - mistake in proof of paper?

I have a question regarding the proof of Proposition 1 in Besley and Ghatak (2007) in Appendix A of their paper. It is a quite highly cited paper but I believe there is a mistake in the proof of their ...
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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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### Rosen's Diagonal Strict Concavity condition

Consider a game with $n$ players, with strategy space $S \subset \mathbb{R}$, where $S$ is bounded set, and player's $i$ payoff function $\pi_i:S^n \rightarrow \mathbb{R}$. Rosen's condition (J. B. ...
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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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### 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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### Can a game with a unique pure strategy Nash equilibrium also have a mixed strategy equilibria?

Consider an arbitrary 2x2 simultaneous game with complete information. Say that the model has only one pure-strategy Nash equilibrium. For example (first pay-off refers to Player 1): ...
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### Game theory software

I was wondering what software/libraries everyone uses to simulate games? For instance finding the Nash Equilibrium. I see that Gambit is a popular one, but I was wondering if there are any other good ...
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### Existence of Symmetric Pure Strategy Equilibrium

I have 2 symmetric players $A$ and $B$. Each of them has 2 decision variables $x_i\in[0, \beta]$ and $y_i\in[0,1]$, where $i\in\{A,B\}$. Their payoff functions are symmetric, i.e., if you swap the ...
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### Interpretation of Solution Concepts

I was wondering whether there is a neat overview over different interpretations of game theoretic solution concepts such as Nash equilibrium, Sequential Equilibrium and the like. Textbooks I found ...
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### Definition of Bayesian Nash equilibrium

I have a basic doubt on the definition of Bayesian Nash equilibrium. Consider the following game: 1) $N$ players. 2) Each player $i$ has a type, assigned by nature and denoted by $\epsilon_i$. ...
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### Existence of nash equilibria in finite games

I was going through the proof of existence of a Nash Equilibria in finite normal form games (Proof via Brouwerās theorem) and got a question regarding the requirement of finiteness for the number of ...
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### Why is the symmetric grim trigger not a Nash?

Consider the stage game: Let $\delta\in(0,1)$ be the discount factor. Let $G$ be the symmetric grim trigger strategy profile. The payoffs are then E_{A}(G) = E_{B}(G) = \sum_{i=0}^{\infty}3\delta^{...
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### In a game with alternating moves and complete information, the Nash equilibrium cannot be a non-trivial mixed equilibrium?

Where I can find a simple proof for this fact? For example, a trivial bimatrix game with alternating move has the following payoff matrix: \begin{array}{|c|c|c|} \hline & 1 & 2 \\ \hline U &...
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