# 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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### Bidding game with asymmetric information

Players $A,B$ are bidding for the outcome of 200 coinflips $X\sim Bin(200,1/2)$. The winning player gains $X$ minus their bid. Player $B$ has advantage of knowing the outcome of 20 randomly selected ...
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### Game Theory Extensive Game

1st question: What is the SPNE? My answer: A(BW), B(W): (2,1) 2st question: Show the game at its strategic form My answer: B W BB 2,1 1,2 BW 1,1 2,1 WW 3,0 0,3 WB 3,0 0,3 3rd question: Find all ...
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### Equilibrium of Perturbed Dollar Auction Game - An Example from Game Theory: Analysis of Conflict by Roger Myerson

I am studying game theory using Myerson's textbook (Chapter 3 - Equilibria of Strategic-Form Games, Section 3.6 - The Decision-Analytic Approach to Games). I have difficulties understanding and ...
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### Nash Equillibrium - Depend On The Opponent's Strategy?

Say I have the following pay-off matrix: For a one-shot game, it is easy to see, that (low, low) is the only Nash Equillibrium in the payoff-matrix. However, say we're playing an infinitely repeated ...
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### Different payouts of pure strategies in mixed strategies

I have a question with mixed strategies. The question is as follows, if we're in a strategy profile that is a Nash equilibrium and a player is playing a mixed strategy, can the pure strategies that ...
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### Understanding the Nash equilibrium for quadratic utilities

I need help to understand some steps of the article "Who's Who in Networks. Wanted: The Key Player" and I would greatly appreciate if someone can provide me with references or if they can ...
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### Can game theoretic concepts be applied to any groups of strategies collectively partitioning the strategy space?

It is clear that players of a game can almost always create trivial variations on strategies without breaking game theoretic conclusions. For example, a player playing Rock Paper Scissors can play ...
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### Geometric Interpretation of the Potential Function of a Game

One geometric interpretation of (at least one term of) the potential function I've come across is as the Riemann-approximated area under an individual player's cost as a function of the number of ...
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### Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?

In a Mixed Strategy Nash Equilibrium, each player constructs their own probability distribution over the set of their respective possible strategies. In a Correlated Equilibrium or a Coarse Correlated ...
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### Asymmetries in Equilibrium Utility

In this lecture, the professor says that all Nash Equilibria have the same utility in non-atomic selfish routing, whereas this is not guaranteed in atomic selfish routing. It is unclear how general ...
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### Rationalizable strategies/ Nash equilibrium

For the question below, how can we solve it generally for every value of θ? As the θ is not discrete, I am not sure how to apply iterated elimination of dominated strategies in this question. And is ...
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### Slight Uncertainty of Continuation in Repeated Prisoner's Dilemma

In a repeated prisoner's dilemma with some probability δ of continuing after each round, a Subgame Perfect Nash Equilibrium may be found which induces cooperation instead of defection in each round. ...
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### Does introducing mixed strategy Nash Equilibria override the pure strategy Nash Equilibria?

I am a bit confused as to why pure strategy Nash Equilibria are often used in analyzing a game alongside mixed strategy Nash Equilibria. While I understand that pure strategy Nash Equilibria can be ...
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### Existence of Nash Equilibrium

I know there are two proofs of the existence of Nash equilibrium: One by using Kakutani's fixed point theorem in Nash (1950), and the other by using Brouwer's fixed point theorem in Nash (1951). I saw ...
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### Mulitiple equilibria in zero sum games

How could we prove that for all two-player zero-sum games: if 𝑅𝑖, 𝐶𝑗 and 𝑅𝑛, 𝐶𝑚 are Nash equilibria, then so are 𝑅𝑖, 𝐶𝑚 and 𝑅𝑛, 𝐶𝑗; Can we also proof all Nash equilibria have the same ...
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### Every Nash equilibrium is Subgame perfect Nash equilibrium

Every Nash equilibrium is Subgame perfect Nash equilibrium. This statement is wrong. I show this by an counter example. Is this example enough and good to disprove this statements? Please share your ...
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### Sequential version of all-pay auction

Sequential version of the all-pay auction. Two bidders alternate in bidding. A prize of \$5 is auctioned. At each move of the game, the bidding player decides whether to raise the current bid by \$1 ...
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### How to find all mixed strategy Nash equilibrium

So I have been taught how to find a single mixed strategy Nash equilibrium in a 2 player game by ensuring both players are indifferent to which strategy is played. So for example: ...
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### How realistic is the conclusion that players do not change their mixing proportions in response to changes in their own payoffs?

A major lesson from game theory seems to be that in simultaneous move games, a player does not change mixing proportions in response to changes in their own payoffs. Rather, their opponents change ...
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### All-pay auction question

Two players take part in the following auction for a £1000 prize. The two players submit bids simultaneously, and the higher bid wins the prize (if bids are identical each gets £500). Both the winner ...
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### MWG 8.B.7 - Any strictly dominant strategy must be a pure strategy

This question from MWG 8.B.7 Any strictly dominant strategy must be a pure strategy. How can I show this? My explanation is as follows: Suppose we have a strictly dominant strategy, $\sigma_i$ . ...
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### Why is pre-specification of punishment order necessary to manipulate compliance?

According to the book Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, a government can coerce every citizen to register for the military by threatening to punish only the first ...
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