Skip to main content

Questions tagged [nash-equilibrium]

A basic solution concept in game theory that requires each player to select their best response to the strategies chosen by others.

Filter by
Sorted by
Tagged with
0 votes
0 answers
33 views

Bidding game with asymmetric information

Players $A,B$ are bidding for the outcome of 200 coinflips $X\sim Bin(200,1/2)$. The winning player gains $X$ minus their bid. Player $B$ has advantage of knowing the outcome of 20 randomly selected ...
enryuxbt's user avatar
0 votes
0 answers
15 views

Game Theory Extensive Game

1st question: What is the SPNE? My answer: A(BW), B(W): (2,1) 2st question: Show the game at its strategic form My answer: B W BB 2,1 1,2 BW 1,1 2,1 WW 3,0 0,3 WB 3,0 0,3 3rd question: Find all ...
Gametheory's user avatar
1 vote
0 answers
32 views

Existence and uniqueness of equilibrium points for concave n-person games

I hope you are doing well. I am reading Rosen's paper. I am having a difficulty in understanding the following statements on page 530 The set $U(x) \subset E^k$ is determined as follows: $$ U(x)=\...
Tran's user avatar
  • 11
1 vote
0 answers
24 views

Topkis lattice theorems for strong Nash equilibria?

Apologies in advance if my question is unclear. A well known result of Topkis is that, in short, the set of Nash equilibria of a supermodular game is non-decreasing. Is there an equivalent result for ...
raving-bandit's user avatar
1 vote
1 answer
66 views

Finding the mixed-strategy Nash equilibrium in this game

Find the pure and mixed-strategy Nash equilibrium in this game: \begin{array}{c|cccc} P_1 \text{/} P_2 & \text{Ll} & \text{Lr} & \text{Rl} & \text{Rr} \\ \hline \text{T} & (3,2) &...
user9487's user avatar
0 votes
0 answers
53 views

Game theory one shot deviation principle

Consider a variant of the alternative offers bargaining game studied in class. Two players are bargaining over the split of a pie of total size/value 1; each player likes as big a share as he can get. ...
Jordon Lee's user avatar
5 votes
1 answer
104 views

About Two Methods of Computing Bayesian Equilibria

Question I want to compute the Bayesian equilibria for the following Bayesian game: With probability $p$, player 1 would be of type 1.1. With probability $1-p$, player 1 would be of type 1.2. Player ...
Beerus's user avatar
  • 505
1 vote
2 answers
79 views

Mixed Strategy Nash Equilibirum, Contributing to a Public Good

I'm a economics undergrad student currently studying the basics of Game Theory. I'm trying to solve the following mixed strategy game: -Two players, Player 1 and Player 2 -Available actions: Each ...
EconIsHard's user avatar
2 votes
0 answers
61 views

Are there Sequential Equilibria that are not Trembling Hand Perfect Equilibria, that don't involve Weakly Dominated strategies?

I'm taking an advanced course (graduate level) in Game Theory. My class has covered several equilibrium concepts, up to Sequential Equilibrium. The professor said that there are already more ...
Nicolas Torres's user avatar
0 votes
1 answer
205 views

On and off equilibrium path game theory

I am super confused about on and off equilibrium path equilibria. Is it safe to say Nash equilibria can be on or off the equilibrium path due to the fact that one player could be irrational and ...
GraceLynn87's user avatar
0 votes
0 answers
30 views

Sequential Bertrand competition Nash equilibrium when marginal costs are zero

How do I find the Nash equilibrium in sequential Bertrand competition between 2 firms if both their marginal costs are zero?
needeconshelp00's user avatar
1 vote
1 answer
99 views

Find the Pure Nash Equilibria in this Two-Player Strategic Game

Players 1 and 2 are involved in a joint project. Each player i independently chooses an effort $c_{i}$ that can be any number in the interval from 0 to 1; that is, $0 \leq c_{1} \leq 1$ and $0 \leq c_{...
user9487's user avatar
0 votes
1 answer
69 views

How to find BNE of the exchange game?

Each of two players receives a ticket t on which there is a number in [0,1]. The number on a players ticket is the size of a prize that he may receive. The two prizes are identically and independently ...
Hãru2you's user avatar
0 votes
0 answers
68 views

Bertrand Duopoly game

Consider the Bertrand’s Duopoly game with demand D(p) = α − p. Assume that each firm is restricted to choose a price is an integer. Also, assume that each firm has a constant marginal cost c is an ...
SHYAM's user avatar
  • 1
0 votes
1 answer
66 views

Proof of existence and uniqueness

Please help me out with the conditions for existence of a pure strategy Nash equilibrium. The game is one of two players with symmetric strategies. After that, please help me out with the conditions ...
user46371's user avatar
0 votes
0 answers
45 views

Iterative deletion and Nash equilibria in a 3 players game

I was waked with finding all the Pure Nash Equilibrium in this game. After using the "circle the best response" method of finding each players rational choices it seems as though there is no ...
FrankStanton's user avatar
1 vote
1 answer
64 views

About infinite strategy sets and $\epsilon$-equilibrium from Game Theory: Analysis of Confilct by Roger Myerson

I am studying infinite strategy sets using Myerson's Game Theory: Analysis of Conflict. On Page 143, he defines an $\epsilon$-equilibrium as follows: Definition For any nonnegative number $\epsilon$, ...
Beerus's user avatar
  • 505
0 votes
1 answer
85 views

Auction with independent private values - An example from Game Theory: Analysis of Conflict by Roger Myerson

I have difficulties understanding the equilibrium analysis of the following auction game: Suppose that there are $n$ bidders in an auction for a single indivisible object. Each player knows privately ...
Beerus's user avatar
  • 505
0 votes
1 answer
69 views

Using Variance for Nash Equilibrium

For the mixed strategies, the expected utility (or payoff) is used to find the mixed strategy Nash Equilibrium. The main assumption is players try to maximize their expected payoffs. However, I think ...
Tunay Sabri Yüksel's user avatar
0 votes
0 answers
67 views

Mixed Strategy Nash Equilibrium

Consider the game of Battle of Sexes, where $$\begin{matrix} &&Women\\ && Football & Resaurant\\ Men&Football&2,1 & 0,0 \\ &Restaurant&0,0 & 1,2 \end{...
Tunay Sabri Yüksel's user avatar
1 vote
1 answer
80 views

Equilibrium of Perturbed Dollar Auction Game - An Example from Game Theory: Analysis of Conflict by Roger Myerson

I am studying game theory using Myerson's textbook (Chapter 3 - Equilibria of Strategic-Form Games, Section 3.6 - The Decision-Analytic Approach to Games). I have difficulties understanding and ...
Beerus's user avatar
  • 505
0 votes
2 answers
116 views

Nash Equillibrium - Depend On The Opponent's Strategy?

Say I have the following pay-off matrix: For a one-shot game, it is easy to see, that (low, low) is the only Nash Equillibrium in the payoff-matrix. However, say we're playing an infinitely repeated ...
BurgerMan's user avatar
1 vote
1 answer
77 views

Proving the existence of mixed-strategy NE for 2-player zero-sum symmetric game

I am trying to prove the existence of mixed-strategy NE for 2-player zero-sum symmetric game, under the condition that given they have $I$ pure strategies and for the pay-off matrix $A$, $\exists x\in ...
Paul Huang's user avatar
2 votes
1 answer
59 views

How do the assumptions $p'+q_ip''<0$ and $p'-c''<0$ ensure the stability of the Nash equilibrium among private firms in basic mixed oligopoly model?

I have two quick question regarding basic oligopoly models: What is meant by we impose the assumptions to $p'+q_ip''<0$ and $p'-c''<0$ to ensure the stability of the Nash equilibrium among ...
Froter's user avatar
  • 31
0 votes
0 answers
101 views

Signaling Game: Beer and Quiche Payoffs and Extensive Form Representation

I am working on a signaling game scenario named "Beer and Quiche" and need some assistance with understanding the payoffs and representing the game in an extensive form. In this game, there ...
lasagna's user avatar
0 votes
0 answers
19 views

Moral Hazard in Teams. Deriving Nash Equilibrium with bonus paying sheme

I have a few mathematical problems with the paper Moral hazard in teams, by Bengt Hölmstrom 1982. Theorem 4 Denote the conditional distribution of $x$, given the action vector $a$, by $F(x, a)$ and ...
contracttheory's user avatar
0 votes
1 answer
76 views

Nash Equilibria in a Game with Three Firms and a Shared Resource

I’m trying to understand the Nash equilibria in a game involving three firms that use water from a shared lake. Each firm can choose to purify the water before returning it to the lake or not purify ...
lasagna's user avatar
1 vote
1 answer
57 views

Understanding the notations in Bayesian game definition

I am having trouble understanding the definition of a Bayesian game based on the following definition from class. I would appreciate it if you could explain the notations and overall meaning for point ...
coderDcoder's user avatar
1 vote
1 answer
95 views

Optimality of the free market and game-theoretic arguments

I recently heard an informal argument that went something like this: Through individual self-interest and freedom of production and consumption, the best interest of society, as a whole, are ...
Richard Hardy's user avatar
1 vote
0 answers
151 views

Nash equilibrium in p-beauty contest game where p=1

Setup: players must chose a number between 0 and 100. The winner of the game is the player whose chosen number is closest to the average of all chosen numbers multiplied by "p". Assume that ...
Arif's user avatar
  • 11
0 votes
2 answers
63 views

How to find the equilibrium amount of $p_{2}$ in terms of $p_{1}$?

There are $100$ tons of crops remaining to supply for the two months. The crop holders consider whether to sell crops now or one month later. Holders face the demand curve of each period as below: $...
Ernst Chen's user avatar
1 vote
1 answer
97 views

Different payouts of pure strategies in mixed strategies

I have a question with mixed strategies. The question is as follows, if we're in a strategy profile that is a Nash equilibrium and a player is playing a mixed strategy, can the pure strategies that ...
Haus's user avatar
  • 125
0 votes
1 answer
86 views

Understanding the Nash equilibrium for quadratic utilities

I need help to understand some steps of the article "Who's Who in Networks. Wanted: The Key Player" and I would greatly appreciate if someone can provide me with references or if they can ...
Haus's user avatar
  • 125
2 votes
1 answer
125 views

Can game theoretic concepts be applied to any groups of strategies collectively partitioning the strategy space?

It is clear that players of a game can almost always create trivial variations on strategies without breaking game theoretic conclusions. For example, a player playing Rock Paper Scissors can play ...
user10478's user avatar
  • 423
2 votes
1 answer
44 views

Geometric Interpretation of the Potential Function of a Game

One geometric interpretation of (at least one term of) the potential function I've come across is as the Riemann-approximated area under an individual player's cost as a function of the number of ...
user10478's user avatar
  • 423
0 votes
1 answer
174 views

Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?

In a Mixed Strategy Nash Equilibrium, each player constructs their own probability distribution over the set of their respective possible strategies. In a Correlated Equilibrium or a Coarse Correlated ...
user10478's user avatar
  • 423
1 vote
1 answer
35 views

Asymmetries in Equilibrium Utility

In this lecture, the professor says that all Nash Equilibria have the same utility in non-atomic selfish routing, whereas this is not guaranteed in atomic selfish routing. It is unclear how general ...
user10478's user avatar
  • 423
0 votes
1 answer
92 views

Rationalizable strategies/ Nash equilibrium

For the question below, how can we solve it generally for every value of θ? As the θ is not discrete, I am not sure how to apply iterated elimination of dominated strategies in this question. And is ...
KK econ's user avatar
  • 11
1 vote
1 answer
55 views

Slight Uncertainty of Continuation in Repeated Prisoner's Dilemma

In a repeated prisoner's dilemma with some probability δ of continuing after each round, a Subgame Perfect Nash Equilibrium may be found which induces cooperation instead of defection in each round. ...
user10478's user avatar
  • 423
2 votes
1 answer
222 views

Does introducing mixed strategy Nash Equilibria override the pure strategy Nash Equilibria?

I am a bit confused as to why pure strategy Nash Equilibria are often used in analyzing a game alongside mixed strategy Nash Equilibria. While I understand that pure strategy Nash Equilibria can be ...
user10478's user avatar
  • 423
3 votes
1 answer
232 views

Existence of Nash Equilibrium

I know there are two proofs of the existence of Nash equilibrium: One by using Kakutani's fixed point theorem in Nash (1950), and the other by using Brouwer's fixed point theorem in Nash (1951). I saw ...
Teacup's user avatar
  • 31
0 votes
0 answers
43 views

Mulitiple equilibria in zero sum games

How could we prove that for all two-player zero-sum games: if 𝑅𝑖, 𝐶𝑗 and 𝑅𝑛, 𝐶𝑚 are Nash equilibria, then so are 𝑅𝑖, 𝐶𝑚 and 𝑅𝑛, 𝐶𝑗; Can we also proof all Nash equilibria have the same ...
jayil's user avatar
  • 21
0 votes
0 answers
65 views

Every Nash equilibrium is Subgame perfect Nash equilibrium

Every Nash equilibrium is Subgame perfect Nash equilibrium. This statement is wrong. I show this by an counter example. Is this example enough and good to disprove this statements? Please share your ...
studentp's user avatar
  • 172
1 vote
0 answers
53 views

Sequential version of all-pay auction

Sequential version of the all-pay auction. Two bidders alternate in bidding. A prize of \$5 is auctioned. At each move of the game, the bidding player decides whether to raise the current bid by \$1 ...
Mark F's user avatar
  • 11
1 vote
1 answer
3k views

How to find all mixed strategy Nash equilibrium

So I have been taught how to find a single mixed strategy Nash equilibrium in a 2 player game by ensuring both players are indifferent to which strategy is played. So for example: ...
pk00's user avatar
  • 13
0 votes
1 answer
60 views

How realistic is the conclusion that players do not change their mixing proportions in response to changes in their own payoffs?

A major lesson from game theory seems to be that in simultaneous move games, a player does not change mixing proportions in response to changes in their own payoffs. Rather, their opponents change ...
user10478's user avatar
  • 423
1 vote
0 answers
177 views

All-pay auction question

Two players take part in the following auction for a £1000 prize. The two players submit bids simultaneously, and the higher bid wins the prize (if bids are identical each gets £500). Both the winner ...
studentp's user avatar
  • 172
1 vote
1 answer
537 views

MWG 8.B.7 - Any strictly dominant strategy must be a pure strategy

This question from MWG 8.B.7 Any strictly dominant strategy must be a pure strategy. How can I show this? My explanation is as follows: Suppose we have a strictly dominant strategy, $\sigma_i$ . ...
studentp's user avatar
  • 172
11 votes
3 answers
1k views

Why is pre-specification of punishment order necessary to manipulate compliance?

According to the book Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, a government can coerce every citizen to register for the military by threatening to punish only the first ...
user10478's user avatar
  • 423
0 votes
0 answers
130 views

Find SPNE in the two stage game

Consider a firm in a two period world. The firm operates as a monopolist in the first period. In the second period, another firm will enter and the two firms will act as Cournot duopolists (i.e., in ...
studentp's user avatar
  • 172

1
2 3 4 5 6