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

learn more… | top users | synonyms

0
votes
0answers
13 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
23 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
40 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
23 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
72 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
27 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
votes
1answer
70 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 ...
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 ...
7
votes
4answers
396 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
votes
1answer
149 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 ...
1
vote
0answers
23 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 ...
0
votes
2answers
4k 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
votes
2answers
38 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
votes
1answer
33 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
2answers
44 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 ...
0
votes
1answer
52 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
vote
1answer
3k 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
votes
1answer
32 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, ...
1
vote
2answers
263 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 ...
2
votes
1answer
50 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
votes
0answers
6 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
votes
0answers
86 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
votes
0answers
9 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 ...
6
votes
1answer
988 views

Find the Nash equilibria for a joint project modeled as a strategic game

I am currently working out of the Introduction to Game theory book by Martin J Osborne and I am looking to solve this given question: Two people are engaged in a joint project. If each person ...
0
votes
0answers
27 views

Signaling game : response to zero-probability message

We have this signaling game : sender type $t$ is uniformly distributed among $[0, 1]$. She takes action A if $t < \phi$, B if $t > \phi$ if receiver takes action A' when seeing A and B' when ...
0
votes
1answer
45 views

Dynamic game of incomplete information

Consider a 2-player game: You and a robber. The robber tells You to give him all your money, otherwise he will kill You. However, the robber could be a 'Good' person (i.e. he would not kill You ...
1
vote
1answer
39 views

Nash equlibrium game theory

Given the following game: Find nash equilibrium (NE) Find subgame perfect nash equilibrium. Main problem i have is with converting this to normal form of the game (because this is i think ...
-1
votes
1answer
56 views

Mixed strategy nash equilbrium

In a mixed strategy Nash equilibrium it is always the case that: a) for each player, each pure strategy that is played with negative probability yields the same expected payoff as the equilibrium ...
0
votes
0answers
12 views

Lemke Howson Algorithm Tableau

I am working on an implementation of Lemke Howson Algorithm and I am reading this paper below. http://cnl.gmu.edu/TAVRI/research/LemkeHowson.pdf Can someone please explain why on page 7 they say ...
2
votes
1answer
85 views

Subgame perfect Nash equilibrium & perfect Bayesian Nash equilibrium - Game theory

For a week or so I have been struggling with the topics around the concept of subgame perfect Nash equilibrium (SPNE) and the perfect Bayesian Nash equilibrium (BNE). Namely: Is it possible to apply ...
6
votes
3answers
23k 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 ...
1
vote
1answer
20 views

Algorithms for computing Nash equilibria

Excuse me, since I am modeling a situation into a nonzero-sum n-player non-cooperative game. I wonder if there is any algorithm for computing its Nash equilibria?
2
votes
2answers
197 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
votes
0answers
35 views

Finding the expected revenue of a first price auction

I'm currently trying to solve for the expected revenue of a first price auction involving n players who draw their values v independently from F with support $[\underline{v}, \bar{v} ]$ and positive ...
0
votes
1answer
122 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 ...
0
votes
2answers
49 views

Nash Equilibria in simultaneous game with four players

Four parliamentary parties are working on a necessary but highly unpopular law. Each party decides whether to put forward the law on its own behalf. If $n$ parties will put forward the law on its own ...
2
votes
1answer
59 views

How do I show that this game played on a Markov chain has a unique Nash equilibrium?

There are $k$ stages in this game, and each stage is worth one unit of utility to a player (of which there are $n$). Each player $i$ finishes stages at a rate $\lambda_i$ (in a continuous time Markov ...
0
votes
2answers
50 views

Static game with complete and incomplete information

I am currently trying to learn game theory on my own. I have a question regarding the solution methods for static games with complete information vs that of incomplete information. The textbook ...
0
votes
1answer
122 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
vote
1answer
54 views

Mixed strategy Nash equlibria (defending territory)

Hi I am trying to figure out the MSNE of this game. I am confused wether there are 2 MSNE or 3. Player 2 would put (1/2) on xx and yy and then player 1 would either put (1/4)on all or (1/2) on xxx ...
1
vote
1answer
70 views

Best response dynamics in Bertrand duopoly game

Question: Consider Bertrand's duopoly game in which the set of possible prices is discrete. Does the sequences of prices under best response dynamics converge to a Nash equilibrium when both prices ...
0
votes
0answers
22 views

Not every correlated equilibrium is equivalent to a Nash equilibrium?

This is a statement made under Theorem 3.4.13 on page 84 in the book by Yoav Shoham and Kevin Leyton-Brown, Multiagent Systems. Could someone explain this to a lay-man and also elaborate on why they ...
12
votes
1answer
366 views

Equilibrium existence proof

Problem: Let $J$ be an integer and let $I$ be an integer multiple of $J$. Let ${\cal I}= \lbrace 1,2,\ldots, I\rbrace$ and ${\cal J}= \lbrace 1,2,\ldots, J\rbrace$. The set $X_{I,J}$ of all ...
2
votes
1answer
265 views

Lemke-Howson pivoting in degenerate bimatrix games

I'm working on an implementation of the Lemke-Howson algorithm for finding Mixed Nash Equilibria of bimatrix games, and I'm running into a roadblock when the algorithm is fed a degenerate game. For ...
0
votes
1answer
25 views

Sub-game perfection when an agent is indifferent

If looking at one of the sub-games the player is indifferent between two actions. How does the backward induction work to recognize sub-game perfection? I.e., suppose player 3 has two action $A_3 = ...
1
vote
0answers
22 views

House allocation with existing tenants

In a house allocation with existing tenants model using the TTC mechanism, consider the incentive of an agent to misreport his/her preferences. Can it ever be that misreporting the true preferences by ...
1
vote
1answer
39 views

Mixed Nash equilibrium in two players game three stategies

I have this problem about finding the mixed Nash equilibrium. The payoff matrix is the following A(p) B(q) C(1-p-q) A 4 0 0 B 0 4 0 C ...
0
votes
0answers
34 views

Nash equilibrium in marriage market stable matching

Consider a marriage market where matchings are formed using the DA women-proposing algorithm. However, there is an additional constraint that only matches among agents that have previously gone out on ...
0
votes
1answer
108 views

Find the Nash equilibria in pure strategies in the following games.

Payoffs on the left correspond to Player 1 and payoffs on the right correspond to Player 2—for instance, in (U, L), player 1 gets a payoff of 3 and player 2 gets a payoff of 4. Explain in detail why ...
0
votes
1answer
367 views

Dominant-Strategy Equilibrium vs Nash Equilibrium

What's the difference between dominant-strategy solution and Nash Equilibrium? I could not tell the difference judging from the definitions. It would be appreciated if these concepts can be ...