# Questions tagged [nash-equilibrium]

For questions regarding the Nash equilibrium solution concept in strategic games.

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### Existence of mixed strategy involving a "best" pure strategy

$\textbf{Set up}$: Let $G$ be a two player zero-sum game, and suppose $A$ is a $n \times m$ payoff matrix for this game, so that player $1$ has (pure) strategy set $\{s_1^1,...,s_n^1 \}$ and player $2$...
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### How related are the magnitude of surreal number combinatorial game values and the propensity to win in spite of potential mistakes?

Surreal numbers are used to represent values of positions in partizan games with perfect information and discrete outcomes (win/lose or win/draw/lose). The primary example is Blue-Red Hackenbush, but ...
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### What are the arguments for/against interpreting the magnitude of the value of Blue-Red Hackenbush as an objective function?

There appears to be a common assumption in Blue-Red Hackenbush that the Blue player should make whichever move will maximize the position value of the game, and the Red player should make whichever ...
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### how do I find a Mixed strategy nash equilibrium for a 5x3 matrix?

(Player A is on the left, Player B is on the top.) I am trying to find a mixed strategy Nash equilibrium for a $5\times 3$ matrix (table below). I've only gone as far as proving that the one strategy ...
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### How to write down a SPNE (Game Theory)

This may be a very simple and silly question, but since I am unfamiliar with Game Theory and am currently working towards a test for which my college lecturer gave very few materials to work on / ...
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### Can the same support hosts multiple isolated Nash equilibria?

As from the title, in a strategic game in normal form, can a given support (e.g. actions [1,3,5] for the first player, [2,4] for the second, [1,3] for the third one..) hosts multiple isolated Nash ...
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### Existence of approximate Nash equilibrium (continuous game)

My question concerns continuous games $((S_i)_{1 \leq i \leq n}, (u_i)_{1 \leq i \leq n})$, where $S_i$ are (continuous) compact strategy sets and $u_i$ denotes the utility function of agent $i$. From ...
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I'm currently studying non-atomic congestion games, and i've come accross the following definition of the price of anarchy: Let $f$ be a Wardrop equilibrium and let $f^*$ be a system optimal flow. ...