Questions tagged [nash-equilibrium]

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

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Finding a Nash equilibrium

I'm doing the exercises at the end of the paper A Brief Introduction to the Basics of Game Theory by Matthew O. Jackson. I would be grateful if somebody could provide me with solutions to it. I'm not ...
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Stability of Nash equilibria in best response dynamics

If we define a Nash equilibrium as a fixed point of the best-response mapping, i.e. a strategy $x$ s.t. $$x\in BR(x),$$ where BR denotes the (set-valued) best-response mapping, then $$\dot x \in BR(x)-...
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Nash equilibrium: mixed strategy

I'm struggling with basic Nash equilibrium question. There is a game I have to find Nash equilibria. I know that (a,w) and (c,y) are pure strategy Nash equilibria. However, I'm confused when looking ...
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Meaning of pure Nash equilibrium in the context of Lagrangian game

I'm reading a paper on solving an optimization problem for a non-convex function. This paper is suggesting a method using a game theoretic approach: Optimizing the Lagrangian can be interpreted as ...
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1-to-N or N simultaneous Zero sum games

Consider a zero-sum game between a row player $R$ and a column player $C$. Finding the NE is quite straightforward. Now consider the row player is going to play the same game with $N$ different column ...
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The set of Nash equilibrium is convex?

In our class professor said [0,0 1,0 0,1 2,2] this game has 2 NE. (0,0) and (2,2). Then he said "well this serves as an example that set of NE is not ...
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Microeconomics Nash Equilibrium

Describe the process that you used to find the equilibria. Use this game to explain why it is important to describe an equilibrium by using the strategies employed by the players, not merely by the ...
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Discount factor to refrain a player from deviating

So I had asked a question yesterday about the rational choices a company can make to produce a product. The link to that problem is Possible output of a firm using game theory. This was the a part. In ...
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Possible output of a firm using game theory

Let there be two firms A and B. Let the price(P) output(X) graph be a linear one $P =a-bX=5-(1)X,c=2$ The parameter a is MAX price. b is the slope of the curve profit vs output(line) c is the price ...
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Why is Nash equilibrium such an important solution concept?

I'm taking an introductory course in game theory and we've recently reached the chapter that discusses Nash equilibrium. The concept itself is clear to me; what's not entirely clear, however, is the ...
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pure strategy equilibria and mixed strategy equilibria

Three players simultaneously pick a point on the interval $[0,1]$. The player closest to the average of the three points wins $1$ dollar. If there is a tie, then the dollar is split equally among ...
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how to solve the Bayesian Nash equilibrium when there is payoff unknown

in this situation, I don’t know how to solve this. Is it correct that the answer of (a) is ε E [0,1]? I cannot even solve the problem a.
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Game theory: what if I find a negative probability when I look for a mixed strategy Nash equilibrium [duplicate]

I read in my notes that "every strategic game in which each player has finitely many actions has a mixed strategy Nash equilibrium". Now let's look for such equilibrium for this payoff matrix (...
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The welfare impact of having multiple NE & subgame perfect equilibria

Suppose we have a two-stage simultaneous game with X subgame perfect equilibria. We then modify that game in a way that there now are X+B subgame perfect equilibria (more than before), but the payoffs ...
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39 views

Mixed strategy Nash equilibrium - what dose a negative probability mean? [closed]

Consider the game table below for a zero-sum game with two players, a row player (who wants to maximize the payoff), and a column player (who wants to minimize the payoff). I am looking for a mixed ...
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Interpretation of Multiple Mixed Nash Equilibria

The following game has the following payoffs. 3 x 3 Payoff matrix for Player A: 0 0 -4 -1 -5 -1 -3 5 4 3 x 3 Payoff matrix for Player B: 4 -2 -1 0 2 3 -5 -4 -5 According ...
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Nash Equilibrium for Game that requires an “action” and a “guess” alternating between two players

Hi I'm trying to write an CFR (Counterfactual Regret Minimization) script to calculate the Nash Equilibrium for a popular hand game in Taiwan where you can play with another person. The rules is as ...
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Sensitivity of pure strategy Nash Equilibrium

It is well known that the Nash Equilibrium means that players will not better off by deviating from the equilibrium. If some irrational player deviates, its cost may increase. I am wondering does ...
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How do I solve this game by mixed strategy Nash equilibrium

L C R T (7,2) (2,7) (3,6) B (2,7) (7,2) (4,5) I can not find any strategy dominated by mixed strategy. So it is impossible to ...
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67 views

Proving the existence of a Symmetric Bayesian equilibrium

I am currently faced with the following question: Consider the public goods game. Suppose that there are $I > 2$ players and that the public goods is supplied (with benefit of 1 for all players) ...
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Nash equilibrium concept and fixed poind theorems

I am searching about the intuition of the fixed point theorems that are used in some game theoretic problems to find the Nash equilibrium. In some cases, I also see some other games that they do not ...
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1answer
35 views

How can I prove this about Nash equilibrium

Show that in each Nash equilibrium of the game, each player receives the same (and maximum) payo↵ from any two strategies that are played with positive probabilities (under, of course, the assumption ...
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What are predetermined variables in the context of dynamic systems with expectations feedback?

The techniques to solve the determinacy of a dynamic system (= DSGE model in economics), does this branch of maths have a name? E.g. for non-rational expectations, this technique is named by Evans, G....
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Change (discontinuity) in Nash Equilibrium with change in parameter

I am solving for duopoly competition between two firms who decide a product characteristic and price. I find that I get two different types of equilibria based on a parameter 'a' - with a ...
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Connection between two minimax theorems

According to Wikipedia, Parthasarathy's theorem is a generalization of Von Neumann's minimax theorem, but I don't see how how this connection is made. Can someone clarify this please?
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Find the SPNE of the following game

The game works as follows: assume that there are two players, 1 and 2. 1 decides to lie or tell the truth. If 1 tells the truth, 2 needs to decide to take her medications or not. Later, in case 2 did ...
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137 views

Subgame Perfect Nash equilibrium (Mixed strategy)

The following extensive form game is given: Find a Subgame Perfect Nash equilibrium of the game featuring one player using a mixed strategy. I know that in order to find a SPNE (Subgame Perfect Nash ...
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Help with a definition of a two-person game in a referenced paper

In the paper "Finding Mixed Nash Equilibria of Generative Adversarial Networks" the authors write in equation (1) on page 2: Consider the classical formulation of a two-player game with finitely ...
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For a mixed extension of a finite game, why is every perfect equilibrium undominated?

In every reference text I can find on the subject of perfect equilibria in mixed extensions of finite games, I see some version of the following statement: "It is clear that every perfect equilibria ...
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Nash equilibrium and score

I'm investigating a 3-player Nash game, and I need a sanity check. Is it true that the outcome of a 3 player nash game need not be determined, even when the strategies are pure? The game is cubicup, ...
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63 views

Game Theory - Nash Equilibrium (Example)

Consider the following game (two players, two actions): (1) Find values of $A$, $B$, $C$, and $D$ such that this game has no pure strategy Nash equilibrium. If we set A=1, C=-1, B=-1, D=1, than this ...
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Equilibria of first-price auctions with discrete valuation

Assume we have a first-price auction with discrete and independent private values and identical distributions of all bidders. It is known that there exists a Bayes-Nash equilibrium where bidders bid ...
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Formulating platooning with game theory

Imagine a platoon, such as the "peloton" in a cycling competition or cars on a highway, where the players benefit from travelling close to each other due to wind drag reduction. If each speed would be ...
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Minimax theorem in a changed game

I have a question regarding the minimax theorem https://en.wikipedia.org/wiki/Minimax_theorem Does anyone know whether the theorem holds also for negative x and y? i.e. $x_i <0, y_j <0$ ...
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2-player Nash equilibrium

Consider a simple two player game with players 1 and 2, such that the actions of each player is given by $a_1$ and $a_2$ respectively, both are reals. Let the payoffs for the two players be given by ...
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1answer
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Game is repeated twice and SPNE

I am currently learning about SPNE in repeated game, and I came across this problem with the following payoff table (denote columns as A,B,C and rows as D E F.) $$\begin{array}{|c|c|c|} \hline (-9, -...
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Upper-hemicontinuous of infinitely repeated rubinstein game

Given an infinitely repeated Rubinstein Bargaining Game (for those who are not familiar with this game, here is its description). Prove that it is upper-hemicontinuous. My attempt: I can find the ...
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n-firm Cournot model in an infinitely repeated game

Given $n$ firms ($n\geq 3$). Assume $x_i\in R^{+}$. The market price is $1-\sum_{i=1}^{n} x_i$ if $1-\sum_{i=1}^{n} x_i\geq 0$, and $0$ otherwise. Each firm has a constant marginal cost of $c<1$. ...
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Big zero sum game matrix

I've been trying to solve a nash equilibrium for a game. The game is zero sum and symmetric. Unfortunately, it is also quite large. The payoff matrix is (n! , n!) in size. To simplify, I used n=4 (the ...
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Guess the Average Game; Nash Equilibria and n-Person Games

Game: Guess the Average (a) Consider the following n-person game. Each person writes down an integer in the range 1 to 100. A reward is given to the person whose number is closest to the mean. (In ...
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Finding Payoff Matrix and Nash Equilibria

There are two drivers, one who will travel from A to C, the other from B to D. Each road is labeled (x;y), where x is the cost to any driver who travels the road alone, and y is the cost to each ...
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Are all strategies that survive IESDS part of Nash equilibria?

I know that Iterated Elimination of Strictly Dominated Strategies (IESDS) never eliminates a strategy which is part of a Nash equilibrium. Is the reverse also true? And is there a proof somewhere? I ...
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What is the expected payoff in the following matching pennies game

So we have the following matching penny game $\begin{bmatrix} \ & L & R \\ T & (1,-1) & (-1,1)\\ B & (-1,1) & (1,-1) \end{bmatrix}$ Let $p_1$ denote the row player, $p_2$ ...
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First-price sealed-bid auction with information advantage

Consider two bidders $A$ and $B$ bidding for a box of 10 coins. The auction is performed in a first-price sealed-bid manner. The winner gets $k$ dollars if there are $k$ heads in the box. The ...
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Best Pokemon Type

There are 18 different types in pokemon with different strengths and weaknesses like rock-paper-scissors. For example, Fire beats Grass, Grass beats Water, and Water beats Grass. My goal is to ...
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Minmaxizer maxminimizer definition

I have trouble understanding the definition of these two terms after reading these two sites. http://www.science.unitn.it/~bagagiol/esercizi_game_theory.pdf A notation mistake in MinMaximizer? It ...
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Evolutionarily stable strategy and Harm thy neighbor

I'm studying ESS, and I have found the harm my neighbor example on wikipedia: https://en.wikipedia.org/wiki/Evolutionarily_stable_strategy in Examples of differences between Nash equilibria and ...
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Proving existence of a Nash equilibrium without fixed-point theorems

Is there a way to prove the existence of a Nash equilibrium in finite games without using Kakutani or Brouwer's fixed-point theorems?
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Nash Equilibria in second-price sealed-bid auctions

I'm trying to understand how nash equilibria can be found in auctions. I understand that a dominant strategy is one where players bid so their bid should equal their valuation. I want to ...
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Is my game exploitable?

It is a game with the following rules. It is loosely based off a game called goofspiel but I want to see if the rules can apply to a continuous variant. There are 2 players $A$ and $B$. Each defines ...

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