Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [nash-equilibrium]

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

-1
votes
0answers
18 views

Nash equilibrium for Subgame Perfect Equilibrium? [on hold]

Is there a Nash equilibrium for a game that is not Subgame Perfect Equilibrium?
0
votes
0answers
16 views

Computational complexity of nash equilibrium in continuous games

What is the complexity of computing a Nash equilibrium (or as a decision version, does a pure strategy Nash equilibrium exist?) for continuous games with the following structure? Each player solves a ...
0
votes
0answers
14 views

Problem with Bayes-Nash equilibrium and correlated equilibrium

I'm trying to find the solutions for these two exercises: the first one involves this Hawk-Dove bimatrix I posted here: https://i.stack.imgur.com/SANvV.png In this game both players prefer the same ...
0
votes
0answers
19 views

Game Theory - Finding a Nash Equilibrium in Public Good Consumption.

Two players, 1 and 2, simultaneously choose their consumption of a public good. Given the consumption choices, g1 and g2, player 1 derives a marginal benefit of MB1 = 10 - (g1 + g2), while player 2's ...
3
votes
0answers
76 views

Can you find a winning strategy for this iterated prisoner's dilemma?

This platform allows to create a bot that plays the iterated prisoner's dilemma with other bots. There are some significant differences with the traditional setup: You can choose the bots you want ...
0
votes
0answers
18 views

What is the precise mathematical definition of what becomes a $n$ players game?

Question 1. What is the precise mathematical definition of what becomes a n players game in the context of game theory in which the Nash equilibrium theorem holds? An answer that is the indication of ...
1
vote
0answers
48 views

Mixed strategy Nash equilibria in $3×3$ games

I am confused as to how one would go about finding the Nash equilibria of a game like this. I know that it requires eliminating some of these strategies by showing that they are strictly dominated by ...
0
votes
0answers
14 views

What is the game in which both players are uninformed and have two types?

I understand the screening game and signaling game. What if both players are uninformed and have two types? What type of game is this and how do I find PBE?
0
votes
0answers
19 views

Three players mixed strategy nash equilibrium problem

The table above represents payoff for three players game accordingly. The probability for z1 is z and z2 is (1-z), r1 is r and r2 is (1-r) meanwhile for p1 is p and p2 is (1-p). Firstly, I would like ...
1
vote
1answer
28 views

Mixed Strategy Without an Option = Option is Dominated?

If a matrix game has a Nash equilibrium strategy in which certain options are not used (i.e. chosen with 0% probability), does that mean that those options are strictly dominated? If so, is it also ...
0
votes
0answers
30 views

Proof of the Existence of Bayesian Nash Equilibria

I found the following two Theorems when studying games with incomplete information. "Consider a finite incomplete information (Bayesian) game. Then a mixed strategy Bayesian Nash equilibrium exists." ...
0
votes
1answer
31 views

The Trust Game: what is the Nash equilibrium?

Here is how the experiment goes: Half of the participants were given the role of a first mover, and half that of the second mover. In each round, it was common knowledge that a first mover would be ...
2
votes
0answers
38 views

Best strategy in the game of Shoot-charge-dodge

The rules of the game are the following: There are 2 players, each of them have a gun and plays at the same time in every turn, in a turn they must perform one of three actions, shoot, charge or ...
0
votes
0answers
10 views

Mixed strategy equilibria

How do you find the mixed strategy equilibria from this game. Thank you. As ps strictly dominates qr, and once qr is eliminated, U* strictly dominates DA and DB, so this not suggest that there are no ...
2
votes
1answer
42 views

Lowest Unique Ordinal Game

The "lowest unique integer game" is widely-known: Some number of players each pick an integer from the range $[1, n]$ and the winner is the player who chose the lowest unique integer (if such a player ...
1
vote
1answer
32 views

Nash equilibrium that is not subgame perfect in an infinitely repeated game?

All of the literature on infinitely repeated games with perfect information uses the term subgame-perfect equilibrium. However, I cannot find any such game with a Nash equilibrium that is not subgame-...
0
votes
1answer
17 views

Mixed strategy equilibrium for subgame

A game has 3 players and the last player to move is player 3. In determining the subgame perfect equilibrium there is a subgame where player 3 has two choices and for each choice the payoff for that ...
0
votes
1answer
19 views

How to construct a 2-player normal form game with exactly n Nash equilibria?

Just like the title, how to construct a 2-player normal form game with exactly n Nash equilibria? Construct a NxN game with N pure NEs or we could also construct a 2x2 game with as many NEs as we ...
0
votes
1answer
30 views

Solution of a LP, give the probabilities of a mixed strategy of a zero sum game [closed]

Given a zero sum game like this one : \begin{array}{c|rrrr} & A & B \\\hline X & 4 & 3 \\ Y & 2 & 5 \\ \end{array} and the given LP : minimize $ x+y $ s.t. : $x \geq 0, y \...
1
vote
2answers
43 views

Corresponding LP problems to zero sum games

Given a zero sum game like this one : \begin{array}{c|rrrr} & A & B \\\hline X & 10 & 3 \\ Y & 5 & 9 \\ \end{array} how do you find an equivalent linear program ? I think ...
1
vote
0answers
25 views

What is an equilibrium called when a perturbation only moves it slightly?

In game theory, a equilibrium is: Stable, if a perturbation form any of the players returns the equilibrium back to it's original state Unstable, if a perturbation moves the equilibrium away from ...
1
vote
1answer
34 views

How to solve an irreducible problem (without dominated lines) for mixed strategy game matrix

I followed this lecture : https://www3.nd.edu/~apilking/Math10120/Lectures/Topic%2029.pdf It gives a way to reduce a n x m matrix to a 2x2 matrix where we know how to solve a problem of mixed game ...
1
vote
1answer
34 views

Finding Nash Equilibria directly from the extensive form/game tree

How can you find the Nash equilibrium of a game directly from the extensive form game/game tree of a game. You can find Nash equilibria from the strategic form (normal form table), but finding it ...
3
votes
0answers
77 views

Nash equilibrium in Cournot competition

QUESTION: Assume there are two types of products, labelled $l$ and $n$. Firms compete in the market by choosing which product to sell and then choosing the quantities. Let $Q_n$ and $Q_l$ denote the ...
0
votes
1answer
45 views

What is the Nash Equilibrium for the following game?

Neither of these strategies are dominated by other. So, we have to use mixed strategies to find the nash equilibrium with the help of removing dominated strategies. But, I can't not continue to solve ...
0
votes
0answers
14 views

Pure Strategy Equilibrium in Second Price Action

Bayesian Nash Equilibrium is to always bid the true value. Is this the only equilibrium? Are there any other pure strategy bayesian nash equilibria for second price auction?
1
vote
1answer
111 views

Is the game of rock,paper scissors considered solved according to game theory?

Rock, paper, scissors definitely has an optimal strategy of just choose randomly for each toss. And two players using that strategy are in Nash equilibrium. What I'm wondering is if that's the same ...
1
vote
1answer
28 views

Game theory and the Reverse mathematics theme

After having studied carefully Simpson's book SOSOA (Subsystems of second order arithmetic) I've naturally arrived at the question about the connection of Game theory with Reverse mathematics. Is ...
1
vote
0answers
20 views

Nash equilibria and bifurcation point

I have a non-cooperative game involving a number of players. I computed the Nash equilibria which depend on a parameter $\alpha$. For $\alpha<\alpha_0$ there exist two Nash equilibria, e.g. $P$ and ...
0
votes
0answers
45 views

Finding mixed strategy Nash Equilibrium in First Price Sealed Bid Auction with Complete Information

Let we think about $\textbf{First Price Sealed Bid Auction}$ in which bidder who offers highest bid wins the object. There are only two bidders in this auction for the simplicity, $I_1$ and $I_2$. ...
1
vote
2answers
72 views

Inference from Nash Equilibrium Violates Total Probability

This is connected to a question I asked at Cross-Validated. Given a game: k x y x: 1*,2|1*,1* j y: 1*,1*|2,3 The best choices are ...
0
votes
1answer
34 views

Understand mixed strategy N.E

Problem: I'm calculating the mixed strategy N.E for the game $$ \vec g= \begin{bmatrix}(3,3)&(0,1)\\(1,0)&(2,2)\end{bmatrix} $$ for two players (player X plays in rows, player Y plays in ...
0
votes
0answers
33 views

Mixed Strategy Nash Equilibrium Verification

There are 2 players. Player 1 has an infinite set of pure strategies: $[0,2]$ and player 2 has 2 strategies: $L$ and $R$. The payoff to player 1 are $u_1(x,L)=x^2$ and $u_1(x,R)=-x$. The payoff to ...
0
votes
0answers
40 views

What do we know about the set of all games having Nash equilibrium?

Let us denote $G$ set of all games (of some particular type), and then consider $N = \{ g \in G | \mbox{game $g$ admits (mixed) Nash equilibrium} \}$. I want to ask you for some good source ...
0
votes
0answers
45 views

Convex combination and zero sum game

Hello, I have some questions regarding zero sum games and linear programming. As you all can see, in Diagram 1, there is no pure Nash Equilibrium unless if we use mixed strategy for both players. I ...
2
votes
1answer
123 views

3x3 pay off matrix with no dominated strategy with nash eq

Create a $3x3$ pay off matrix that does not have any dominated strategy and has exactly two Nash equilibrium. No mixed-strategy is allowed. I have tried and made this $\begin{bmatrix} A &B ...
0
votes
1answer
41 views

Nash Equilibrium Grandfather Problem

A grandfather is writing his will and must decide how much money he will leave to his three children: Sean, Tom, and Brad. The grandfather comes up with the following plan. Each of his children is ...
0
votes
0answers
123 views

What is the Nash Equilibrium of the Dollar Auction?

The dollar auction is a type of auction in which players bid money for a dollar. Whoever bids the most pays what they bid and gets the dollar. Whoever bids the second most pays what they bid and get ...
1
vote
0answers
66 views

Checking whether a Mixed Strategy Nash Equilibrium is Evolutionary Stable

Taking the classic Hawk-Dove game I know that there are 3 mixed strategy Nash Equilibria, (H,D), (D,H), and the mixed strategy ((7/12, 5/12), (7/12,5/12)), where those are probabilities of playing H ...
0
votes
0answers
25 views

Nash-equilibrium in mixed strategies with arbitrary payoff function

So I came across this question in an old exam from the lecture I'm currently studying for regarding nash-equilibria in mixed strategies, which for the life of me I cannot seem to be able to find an ...
0
votes
0answers
28 views

How are all kinds of equilibra in game theory connected to each other? (Please correct my summary)

I am a TA in a basic class on game theory in the economics department. I am ashamed to admit, but I do not entirely understand how all the different kinds of equilibria connected to each other. The ...
0
votes
1answer
27 views

Can Pareto Optimality be compared to Nash Equilibrium?

Given a state $s$, and a value function $v^i$ that determines the expected payoff for the i-th agent in that state, can the two definitions below, one of Nash equilibrium and another of Pareto ...
3
votes
1answer
79 views

What is the format of a mixed strategy nash equilibrium?

Take this game where player 1 has choices T and B, while player 2 has choices L and R. We need to find the Mixed Strategy Nash Equilibria. As a side note, it seems like (B,L), and (T,R) are Pure ...
1
vote
0answers
31 views

Find the threshold strategy of a game with incomplete information

I have a question on how to find the equilibrium outcomes of the following game as a function of $(\epsilon_1, \epsilon_2)$. The game There are 2 players. Let $Y_i$ denote the action of player $i$...
0
votes
1answer
380 views

Nash equilibrium in second price sealed-bid auction

I'm trying to understand the basics of game theory and the topic of auctions has arisen. I understand the basic concepts of auctions but I'm struggling with second price sealed-bid auctions. I ...
2
votes
1answer
69 views

Proving that the Wardrop/Nash equilibirum flow on a graph is “stable”?

Let $[0, 1] \subset \mathbb{R}$ be denoted $\mathbb{R}_{[0, 1]}$. Let $[0, \infty) \subset \mathbb{R}$ be denoted $\mathbb{R}_{\geq 0}$. Let $G$ be a finite, connected graph. Associate with each edge ...
1
vote
1answer
95 views

How to find Nash equilibrium in pure and mixed strategies? Problem.

A two player game. Players choose a number from a segment $[0;1]$. A payoff function of the first player $f_1(x,y)=|x-y|,$ where $x$ and $y$ - the numbers chosen by the first and the second players ...
0
votes
0answers
53 views

game theory-Are second priced bids always a nash equilibrium?

I'm trying to understand the basics of game theory and the topic of auctions have come up. What I want to know is second priced bids always a nash equilibrium? Suppose we have this question. We ...
0
votes
0answers
37 views

How to check if mixed strategy leads to Nash equilibirum?

I have a simple payoff matrix defined here: matrix My question is: If both players play all 4 strategies with 1/4 probability, does that lead to Nash equilibrium? I can't quite figure this out. I ...
1
vote
0answers
23 views

Nash Equilibrium Static or Dynamic? Poker player help!

My buddy and I are professional poker players, we began quite a solid debate tonight and I’d be curious as to what the forum has to say. Is the Nash equilibrium (GTO in Poker terms) a dynamically ...