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

learn more… | top users | synonyms

1
vote
0answers
13 views

Nash Equilibrium

Player A chooses a random integer between 1 and 100, with probability pj of choosing j (for j = 1, 2, . . . , 100). Player B guesses the number that player A picked, and receives that amount in ...
0
votes
0answers
16 views

Compute the set of subgame perfect equilibria for this game (mixed strategies help)

In the above game there are 2 proper subgames (not including the whole game itself). I know there's 9 sub-game perfect equilibrium i have to figure out. I've managed to work out 4 of those, the ...
0
votes
1answer
35 views

nash equilibrium and best response dynamics

I have a very basic question : How is nash equilibrium found in real life problem. I mean, in theory it exists and we can prove it but how this knowledge will be applied in real life especially with ...
2
votes
2answers
38 views

While finding an optimal strategy for a mixed nash equilibrium, why do we not consider strategies which are never a best response?

"A strategy cannot be plausibly chosen by a rational player if and only if it is never a best response." I understand the logic behind neglecting the strategies that are strictly dominated. But why ...
2
votes
1answer
37 views

A bin-assignment infinite 2-player zero-sum game

What is known about the following infinite 2-player zero-sum game? There are $k$ bins. Each player has 1 unit of mass and, simultaneously, divides it arbitrarily among the $k$ bins. The player wins ...
0
votes
0answers
31 views

Visualizing Nash Equilibria of a 4 dimensional matrix

Are there any good ways to visualize Nash equilibria of a 4-d matrix? I have created an game theory model which consists of of four players (P1; P2; P3; P4) who can all choose between a set of 27 ...
1
vote
1answer
27 views

How to compute a mixed Nash Equilibrium where only one payoff is given.

Let's say I have this: $$ \begin{matrix} & A & B \\ X & 1 & 2 \\ Y & 2 & 1 \\ \end{matrix} $$ That is the payoff for me if I make ...
0
votes
0answers
29 views

Software or code to solve a congestion game for n players

First of all, I am pretty new to game theory so if I say something wrong, please correct me. I have a congestion game (similar to the bookcase of machine job scheduling problem). The jobs are the ...
0
votes
0answers
23 views

Mixed strategy, find an equilibrium pair

In this example I need to find equilibrium pair X = ($x_1$, $x_2$, $x_3$), Y = ($y_1$, $y_2$, $y_3$) The matrix looks like this $[0, -1, 2]$ $[3, 1, 0]$ $[-2, 2, 1]$ P(X, $B_1$) = 3$...
0
votes
0answers
15 views

Concavity of the equilibrium

Suppose we have have $n$ players taking action $a_i \in [0,1]$ to generate some value $v(a_1,...,a_n)$ together. The utility for player $i$ given by $\lambda_iv(a_1,...,a_n) - u_i(a_i)$ where $u_i$ ...
2
votes
2answers
37 views

The Nash Demand Game

I am having troubles to figure out how to find all pure strategies and two mixed strategies (one in which the shares received by players are always $0$, and one in which $\omega$ is often - but may be ...
2
votes
1answer
44 views

Maximum of minimums

Suppose $v_1,\ldots, v_k \in \mathbb{R}^n$ are vector with all coordinates non-negative. How to explicitly calculate: $$ \max_{x\geqslant 0, ||x||_1=1} \min_{1\leqslant i \leqslant k} <x,v_i>$$ ...
0
votes
1answer
37 views

Finding all mixed Nash equilibria in a $3\times 3$ game

I was looking at the exercise $2$ in this file http://isites.harvard.edu/fs/docs/icb.topic1531493.files/Practice%20Problem%20Solutions%20on%20Nash%20Equilibrium.pdf pages 4 to 7. I do not understand ...
2
votes
1answer
71 views

What's the difference between a Nash, Correlated, and Extreme equilibrium?

As the title states, what's the difference? As I understand it: The Nash Equilbirum (NE) is a solution concept in non-cooperative games where no player has incentive to unilaterally deviate from a ...
1
vote
1answer
37 views

Nash Equilibria of P-Beauty

I'm a little confused with the work I am currently doing in Game Theory. Here is the questions I'm working on: ...
0
votes
0answers
22 views

Mixed Strategy Probability Distribution

Problem Two firms with equal capacity constraints k but different marginal costs $c_i$ compete in a pay-as-bid auction for a fixed demand of (balancing) energy. The information on capacity ...
1
vote
0answers
33 views

Can't solve matrix for Nash Equilibrium?

So, I have the following 9 by 9 probability matrix. I want to solve it for a nash equilibrium. https://docs.google.com/spreadsheets/d/16Y1FqxRIAHsHpgEz1ckxDt2sEOInOG3zz_wU8kBHvB4/edit?usp=sharing For ...
1
vote
1answer
35 views

Iterated Best Response to find Pure Nash Equilibria

The context of this question is Game Theory. I've been trying to apply a simplified (?) version of the Iterated Best Response (IBR) technique to find Pure Nash Equilibria (PNE) in games generated by ...
0
votes
0answers
18 views

How to find convergence with a learning rule that depends on the outcome of a game?

my first post here and really excited about the community. In a game theory set in which agents choose from a finite set of actions with a probability distribution, how can I look for convergence ...
0
votes
0answers
19 views

Finding All Nash Equilibrium

$N \geq 2$ firms simultaneously, and independently, decide to enter a market. The pay-off for each firm entering the market is, $$\pi(n) = \begin{cases} \pi_{M} - I & \text{if } n = 1 \\ -I &...
0
votes
1answer
21 views

How to solve mixed strategy Nash equilibrium.

Lets say I have following problem: Zero sum game. Payoff matrix for player one: -1 4 4 2 6 -2 I start by writing equations for each strategy. ...
1
vote
1answer
137 views

How to interpret negative probability for a strategy in mixed nash equilibrium?

I am trying to get the mixed strategy in Nash equilibrium for the following matrix. $$\begin{pmatrix} 0 & 3 & 4 & 5 & 6 \\ 3 & 0 & 5 & 6 & 7 \\ 4 & 5 & 0 &...
5
votes
1answer
71 views

How can I find the Nash-equilibrium of the following zero sum game?

I want to find the Nash-equilibrium of the following zero sum game. $$A=\begin{bmatrix}0&2&-1\\-2&0&3\\1&-3&0\end{bmatrix}$$ I used the Minimax Theorem. $$min_{x \in X} max_{...
2
votes
1answer
104 views

Game theory: Finding Nash equilibrium in $3\times 3\times 3$ matrices

I tried to find how to solve $3\times 3\times 3$ matrix to find Nash equilibrium but I could not find anything on the web. Maybe I am searching with wrong keywords... I understand how to solve Nash ...
1
vote
0answers
18 views

Difference between Sequential and Weak Sequential Equilbria

This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. ...
2
votes
0answers
109 views

Game theory, Book by Tirole and Fudenberg, Never a weak best response,unclear example

In this book, I have the following problem: on page 446, there is a sentence: Note that $(0.9,0.9)$ is not removed by NWBR, as D is not dominated after C is deleted. I do not understand this "as". ...
0
votes
1answer
62 views

Mixed Nash equilibria in $n$-player games

I'm reading up on Game Theory. So far, I feel like I have a pretty good understanding on two-player games and their properties. Consider a two person game where the payoff matrices are $A_{m\times ...
0
votes
0answers
17 views

Subgame perfect nash equilibrium in a non-Prisoner Dilemma Game

working on this for hours but I can't find any solution yet ... I got a 3x3 matrix of a non-Prisoner dilemma game It looks like that:      C2      D2  ...
1
vote
0answers
213 views

Game theory book by Tirole,Fudenberg, zero up to first order of $\epsilon$,equilibrium

In this book on Game Theory, on page 186,I do not understand the very end of the page: [T]he incentive to deviate$-$the left hand side of equation 5.18$-$ is $0$ in first order of $\epsilon$, so that ...
0
votes
0answers
18 views

Having more than one Nash-Equilibirum

For my term paper, I'm trying to explain a symmetric game in the music industry. The two players two different singers rehearsing for a duet. $$ \begin{matrix} & {\bf Song 1} & {\bf Song2} &...
1
vote
0answers
26 views

Differential equation, Cournot competition, Game theory

I would like to solve differential equation derived from differentiating $u_i(q_1,q_2)=q_ip(q_1+q_2)-c_i(q_i)$ by $q_1$ and $q_2$, resp. and putting them equal to zero,and taking $q_2$ to be $r_2(q_1)$...
0
votes
0answers
28 views

Best voting strategy

Let us assume there are two parties in a country with population $p$. There are $c$ constituencies. Each party knows exactly who are their supporters and can choose where each supporter votes. Note ...
0
votes
1answer
50 views

Is this Nash-Equilibrium valid?

The game is as follows: $$\begin{array}{c|c|c|} &A&B\\ \hline A&2;3&2;3\\ \hline B&-1;2&1;2\\ \hline C&-1;3&4;2\\ \hline \end{array}$$ I've written a program that ...
1
vote
0answers
58 views

Unique Nash Equilibrium

If a game has a unique Nash Equilibrium, then does it have a unique Mixed Nash Equilibrium as well, where this MNE is the unique NE? The game I have in mind is the following (but I am more curious ...
0
votes
0answers
48 views

Game theory, Duopoly problem

. Suppose two firms compete in micro-chip industry. Each period firm 1 produces q1 chips and firm two produces q2 chips and the firms face a demand curve of P = 1000−20Q, where Q = q1 +q2. Both firms ...
1
vote
1answer
106 views

Cournot Duopoly Question [closed]

(Repeated Games). Suppose two firms compete in micro-chip industry. Each period firm 1 produces q1 chips and firm two produces q2 chips and the firms face a demand curve of P = 1000−20Q, where Q = q1 +...
0
votes
0answers
34 views

Perfect Bayesian Equilibria of the following game

Consider the following game between a monopolist firm and a consumer. Consumer's income is $1$, and he needs to allocate it between period 1 and period 2 consumption to maximize his utility $u(c_1,c_2)...
0
votes
1answer
67 views

Nash equilibrium for n players game

There is a question that I am trying to solve but I am not sure about my approach and is hoping I could get some help. Here is the question: There are $n$ companies sharing a water reservoir, let's ...
0
votes
1answer
27 views

Gaining intuition as to why maximal lotteries use randomness to break general ties

The maximal lottery is a voting system based on choosing an optimal candidate game-theoretically. If a winner isn't clear (there is no condorcet winner), then it will return probabilities as to which ...
0
votes
0answers
27 views

numerical solution for nash equillibrium

I have the following setup. $\pi_1=f_1(q,r)$ and $\pi_2=f_2(q,r)$ are the real valued payoff/profit functions of the two players. Player 1 gets to pick $q$ and player 2 gets to pick $r$. I also know ...
0
votes
1answer
38 views

Nash equilibrium for two players game.

Consider a game for two players, say "Player A" and "Player B". The two sets of strategies are denoted by $A$ and $B$, available to the players. Consider a symmetric situation where the players have ...
0
votes
1answer
88 views

Find a Nash equilibrium solver

The solvers I know so far are designed only to allow payoffs as given numbers. But is there a solver allowing users to type payoffs as variables?
-2
votes
1answer
27 views

What is the optimum strategy? Game Theory.

If you invest Rs 1000, you would get a paid back of Rs 4000 at the end of the day, provided atleast 90% of the students invested. If the number of students investing falls below 90%, all those ...
0
votes
0answers
99 views

Finding Nash equilibrium in game with random event at event tree?

I have posted a question about finding the NE of sequential game with imperfect information. It is lucky that the game can solve could be dealt with could be dealt with by a simpler argument. Here is ...
0
votes
1answer
275 views

IESDS and Nash Equilibrium - same solution [closed]

Applying the Iterated Elimination of Strictly Dominated Strategies (IESDS) to a game resulted with the same solution of the Nash Equilibrium. What does this imply? Actually that specific "quadrant" ...
1
vote
0answers
46 views

Example of infinite game without any Nash equiblibria

I have to find an example of a game that does not admit (mixed strategy) Nash equilibria. Consider a game in normal form. Let $N=\{1,2\}$ be set of players and $S_i=\mathbb{R}$ a set of possible ...
2
votes
2answers
156 views

A game with no pure or mixed strategy equilibrium?

I'm trying to find any and all pure or mixed strategy Nash equilibria for the game $$\begin{array}{|c|c|c|c|}\hline & L & C & R \\ \hline T & (6,2) & (0,6) & (4,4) \\ \hline ...
-1
votes
1answer
80 views

Can a game with a pure strategy Nash equilibrium also have mixed strategy equilibria? [closed]

I have questions: If zero-sum game has pure strategy Nash equilibrium (saddle point), can it have also mixed strategy equilibria? What if game is not zero-sum?
0
votes
1answer
52 views

Is 2nd-price with a discount auction truth-telling?

I know that 2nd-price auction is truth-telling, but 3rd-price auction is not. What If I run the regular 2nd-price auction, in the end, the winner is charged at the 2nd bidding price with a discount, ...
4
votes
1answer
93 views

Can mixed strategies outperform pure strategies?

Let $G$ denote a game with a finite number $n$ of players in which each player $i$ can choose a mixed strategy $\sigma_i$ over a finite set of pure strategies $\Sigma$. Pure strategies can be seen as ...