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

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1answer
465 views

I can't find the Nash equilibrium of this 3x2 game.

Sorry for my English, I am French but i couldn't find help on the French website (so I am here). I have a question about this two-player game: $$ \begin{array}{c|cc} & y_1 & y_2 \\ \hline ...
2
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2answers
868 views

Splitting the dollar Nash equilibrium

I'm working on a game theory problem I can't seem to figure out. Players 1 and 2 are bargaining over how to split $\$10$. Each player names an amount $s_i$, between 0 and 10 for herself. These ...
0
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0answers
13 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 ...
-1
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1answer
202 views

Calculating the value of a bi-matrix game.

So I know this question is very simple, however in my text and from what I can find online, the solution tends to simply be given (such as in this example) Example: Let the following bimatrix game ...
3
votes
1answer
1k views

Mixed Strategy Nash Equilibrium of Rock Paper Scissors with 3 players?

It seems like most game theory tutorials focus on 2-player games and often algorithms for finding Nash equilibria break down with 3+ players. So here is a simple question: Is ...
0
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1answer
17 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. ...
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2answers
575 views

Nash equilibrium in first price auction

I'm trying to understand Exercise 18.2 from Martin J. Osborne and Ariel Rubinstein A Course in Game Theory about finding pure Nash equilibria in a first-price auction. There are n players, named ...
1
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1answer
77 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 ...
4
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1answer
59 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} ...
2
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1answer
72 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 ...
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0answers
16 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
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0answers
89 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". ...
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1answer
41 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 ...
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0answers
12 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
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0answers
110 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 ...
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0answers
16 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
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0answers
20 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 ...
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0answers
26 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
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1answer
47 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 ...
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2answers
7k views

cournot competition with N-firms

The question is as follow: Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
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0answers
29 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
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0answers
22 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 ...
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1answer
42 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
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0answers
29 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 ...
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0answers
25 views

Finding mixed strategies question

Suppose I have a payoff matrix where each of the two players has three pure strategies. For player two, one of his staegies is weakly dominated. If I am seeking the mixed Nash equilibrium, do I ...
0
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1answer
22 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
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1answer
55 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 ...
10
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3answers
33k views

How to compute ALL Nash equilibria in an example of a 3x3 matrix

I am trying to understand how to compute all Nash equilibria in a 2 player game, but I fail when there are more than 2 possible options to play. Could somebody explain to me how to calculate a matrix ...
0
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0answers
24 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
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1answer
30 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
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1answer
64 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?
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1answer
25 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
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0answers
85 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
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1answer
151 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" ...
2
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1answer
90 views

How can I find the Nash equilibrium for this game?

Sorry for my English, I am French but i couldn't find help on the French website (so I am here). I have a question about this two-player game: $$ \begin{array}{c|cc} & y_1 & y_2 \\ \hline ...
7
votes
4answers
867 views

Can Nash Equilibrium be more than two?

In the Prisoner's Dilemma example, we know that there is only one Nash Equilibrium. That is both of them confess. Is it possible that there are two Nash equilibrium in one example? Can you roughly ...
5
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1answer
157 views

Unexpected hanging paradox maxmin strategies

I have a question about strategies of the players of Unexpected hanging paradox (I am very sorry for a long topic, topic exist already for a while, during this time I try to develop idea how to solve ...
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0answers
37 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 ...
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2answers
10k views

Pure vs mixed strategy Nash Equilibria

Just learning about Nash Equilibria. The pure strategy one is explained as an outcome where both/all players feel like they couldn't have done better given what the others were doing. Mixed strategy ...
2
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2answers
90 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 ...
0
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1answer
57 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
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2answers
60 views

Mixed Strategy Nash Equilibrium in this game?

L (q) R (1-q) l (p) [(2, 1), (0, 1)] r (1-p) [(-1, 0), (1,7)] I'm having a lot of trouble understanding what the mixed strategy nash equilibrium is ...
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1answer
71 views

Nash equilibrium in mixed strategies with p = 0

I am currently writing a program to calculate nash equilibria in mixed strategies. My algorithm simply tries a lot of different probabilites and then decides which one is the best. However I came ...
1
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1answer
4k views

Mixed-strategy Nash equilibria

I didn't find in books, so I'm asking - Mixed-strategy Nash equilibria is always only one or doesn't exist for the one certain game? And I know that there can be several(and can not be at all) pure ...
0
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1answer
43 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, ...
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2answers
593 views

Third and average price auction

Third price auction: the winner is the highest bidder but this time instead of paying the second highest bid, he would pay the third highest bid. -assume there are at least 3 bidders. - Average price ...
3
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1answer
71 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 ...
0
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0answers
9 views

Why Nash product is strictly quasiconcave?

The book "Bargaining theory with applications" mentioned that Nash product is continuous and strictly quasi-concave. But why Nash product is strictly quasi-concave? I haven't found any illustration ...
0
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0answers
88 views

Undestranding Basic Game Theory

Lately I'm studying game theory for an exam. I'm having troubles in understanding some theorems since notes I'm studying on are very brief and concise about sense of definition. In this question I'll ...
0
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0answers
12 views

Can the joint decision of car purchasing in a household be formulated as Nash bargaining problem?

Suppose that in a household, husband and wife jointly decide whether to buy a car or not. If they decide to buy, husband and wife contribute their share for the cost of purchasing according to their ...