# Questions tagged [nash-equilibrium]

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

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### Why does Scarf's algorithm only need to examine a small fraction of points in the simplex?

Scarf's algorithm for finding the Brouwer fixed-point searches for the fixed-point in an non-repeating fashion examining a finite number of points. It finds the fixed point however by examining a very ...
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### Favorite 3-player zero-sum-game?

I am looking for a $3$-player game that meets the following requirements: It should be a zero-sum-game It should be simple in the sense that the payoff table is not too large (ideally memorisable by ...
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### Finding a Nash Equilibrium of a Two-Players Game based on Best Response Functions - Taking a partial derivative from a piecewise, weird, function!

I need to find a nash equilibrium of a two-player game based on their best response function. The problem I have is that the functions I'm dealing with are somehow weird and hard to work with! So, let ...
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### Mixed Nash Equilibria

Does it hold for all bi-matrix games that all mixed Nash equilibria have the same expected pay-off ? Or is it necessary that the game is zero-sum ? Finally how can I see and how is it used that the ...
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### Cournot Nash Equilibrium

The market demand for a good is described by the inverse demand function $P(Q) = 120 - Q$ where $Q$ is total quantity demanded and $P(Q)$ the market price. Two firms $i =1,2$ have identical cost ...
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### In game theory, are there easy ways to rule out the existence of either (i) all pure Nash, (ii) all completely mixed Nash?

For example, in a rock paper scissors game, there are no pure Nash equilibrium and only a completely mixed Nash equilibrium. in prisoner's dilemma, there is no mixed Nash equilibriumand only a pure ...
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### Can we find Nash Equilibrium payoffs in degenerate games

In a 2 person, constant sum game, all NE strategies have identical payoff, the 'value' of the game. Typically this is calculated by first calculating one NE strategy. In many algorithms for ...
1answer
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### Nash Equilibrium - El Farol Bar Problem

Statement of the problem, from Wikipedia: Every Thursday night, a fixed population want to go have fun at the El Farol Bar, unless it's too crowded. If less than 60% of the population go to the bar, ...
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### When is Counterfactual Regret Minimization appropriate?

I must be missing something fundamental here. In a 'stacked normal form 2 person zero-sum game' we can solve for the NE strategies and payoffs recursively. If we have access to the full tree we can ...
1answer
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### Question about proper subgames in game theory.

Consider the following game presented as a tree. As we can see there are $3$ players and the question is to find all N.E and all S.P.N.E. But I have a doubt about one thing. As we can see, if the ...
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### Difference between simultaneous and ordered N.E. in the problem.

Consider the following game. There are two players and one of them could be in two states: $A$ with probability $p$ and $B$ with probability $1 - p$. Both players actions are $1, 2,$ and to not ...
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### Mix of first price and second price auction problem.

Suppose we have two participants. They play the game with utilities: $u_1 = v_1 - b_2$ if $b_2 \le b_1$ and zero otherwise. For the second participant $u_2 = v_2 - b_2$ if $b_2 \ge b_1$ and zero ...
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### What techniques are there for solving extensive form games where we discover the tree on-line

To my knowledge all counterfactual regret algorithms require that we have the tree completed, even if it's only an abstraction of the tree. In other computational strategy settings, there are ...
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### Mixed Statregy Nash Equilibrium - probability higher than one?

I have found the Nash equilibrium of the following game but I have doubts that the result makes sense The game is: ...
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### Equilibrium from regret matching

I'm reading an article that states that this regret matching algorithm: • For each player, initialize all cumulative regrets to 0. • For some number of iterations: – Compute a regret-matching ...