Tagged Questions
0
votes
0answers
38 views
Nash equilibria in 3-player game
Consider 3-player game.
Players $x,y,z$, each player has two strategies. $x$: $x_1$ and $x_2$, $y$: $y_1$ and $y_2$, $z:z_1$ and $z_2$.
The outcome of the game are represented by the triple ...
2
votes
3answers
73 views
nash equilibirum help! seems tricky
Any advice for finding all nash equilibrium for this symmetric game? (B,B) looks like one but I feel like there are more. I tried looking for strictly dominant strategies, but only A weakly dominates ...
2
votes
1answer
42 views
Is there an example of zero-sum game that has a Nash equilibrium which is not subgame perfect?
As a refinement of Nash equilibrium, it is known that not all Nash equilibria are subgame perfect. But it seems to me in zero-sum games of perfect information, Nash equilibrium coincides with subgame ...
0
votes
0answers
25 views
Algorithm to verify that a weak Nash equilibrium is an ESS, or a strict Nash equilibrium
Is there any algorithm that might assist me in checking whether a weak Nash equilibrium in a signalling game is also an Evolutionarily Stable Strategy, or a strict Nash?
0
votes
0answers
50 views
Game theory: Efficient and stable mechanisms
I am having some trouble understanding the notion of efficient and stable mechanisms in game theory. Could someone explain both concepts informally?
1
vote
1answer
29 views
Question on the construction of mapping from space of strategy profile into itself in Nash(1951)
To appeal to Brouwer fixed point theorem, Nash(1951) constructed a continuous mapping $\operatorname{T}$ from strategy profile space into inself:
For player $i$, the probability of a pure strategy ...
3
votes
0answers
64 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 ...
7
votes
1answer
98 views
Finding the payoff matrix of a game
A two player zero-sum game can be represented by a $m\times n$ payoff matrix $M$ having $m$ rows and $n$ columns with values in $[0,1]$. The value $M(x,y)$ represent the payoff given to player $1$ ...
1
vote
2answers
114 views
Cournot-Nash Equilibrium in Duopoly
This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way of solving the following question:
There are 2 firms in an industry, ...
0
votes
1answer
38 views
Theorem that stable equilibria in iterated games are equivalent to coalition-based static equilibria
Consider an $n$-player nonzero sum finite game $G$. I have a vague recollection of a wonderful paper proving an equivalence between (1) steady state Nash equilibria of $G$ played countably many times ...
-4
votes
1answer
232 views
Nash equilibria and best response functions
a) Let $G=(A,u)$ be a strategic game such that, for each $i \in N$
$A_i$ is a nonempty, convex, compact subset of $R^{m_i}$
$u_i$ is continuous
For each $a_{-i}$, $u_i(a_{-i}, . )$ is quasi-concave ...
0
votes
1answer
127 views
Prove set of Nash equilibria is closed?
Is this even possible with just the formal definition of a Nash equilibrium, that is, without any additional conditions, such as the utility function is continuous?
Thanks.
4
votes
2answers
108 views
What is the Nash Equilibrium of the Monty Hall Problem?
The Monty Hall problem or paradox is famous and well-studied. But what confused me about the description was an unstated assumption.
Suppose you're on a game show, and you're given the choice of ...
2
votes
0answers
73 views
Comparing Nash equilibrium and Pareto optimal actions
Suppose that $(x_{i}, x_{j})$ identify actions for two players $(i,j)$. If we define Pareto optimal actions by
$$h(x_i) +h(x_j)- \eta[p(x_i)+p(x_j)]=2\gamma$$
and Nash equilibrium actions by
...
3
votes
1answer
125 views
Finding mixed Nash equilibria in continuous games
I'm taking my first (graduate-level) game theory class. I understand how to find Nash equilibria in simple games, such as those given in finite tables, and can see (usually) how to find the mixed ...
2
votes
2answers
188 views
Are all Nash equilibrium pure strategies also Nash equilibrium mixed strategies.
while going over wiki page on Battle of the Sexes game I found something funny.
This game has two pure strategy Nash equilibria, one where both go to
the opera and another where both go to the ...
3
votes
0answers
243 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 ...
2
votes
0answers
255 views
Analytically solving (calculating Nash equilibrium for) 3-player extensive form games
Let's say we extend the popular half-street Kuhn poker variant to 3 players. The rules would be as follows:
...
0
votes
0answers
45 views
Can the Nash bargaining solution be applied in repeated game?
I am trying to develop a model involving two agents who interact strategically to set an optimal time for a joint work. These agents will have to meet repeatedly. I want to derive the optimal time for ...
2
votes
2answers
178 views
Does chess have more Nash equilibria than you can find through backwards induction?
All equilibria found with backwards induction on a tree of a perfect information game are Nash equilibria, but in general the reverse is not true:
...
1
vote
1answer
67 views
vickery auction question(second-price auction)
The question is as follow,
Alice and Bob would both like to own the same manuscript. The manuscript is worth 5 million to Alice and worth 3 million to Bob. The present owner of the manuscript ...
1
vote
1answer
39 views
Correlated Equilibrium - Transforming a non-linear objective function into a linear one
I am trying to transform a non-linear objective function into a linear one, in order to create a LP. How might I go about to do this (I have never taken a course in linear programming).
I have that I ...
0
votes
1answer
77 views
subgame perfect nash equilibrium for war of attrition
the question is as follow:
suppose that two players are playing war of attrition,
that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
1
vote
2answers
761 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 ...
0
votes
1answer
529 views
cournot equilibrium and stackelberg equilibrium question
Question is as follow:
there are 2 firms that want to enter the apple juice market in country A. There are no existing firms in the market or potential entrants.
They need to decide on yearly ...
2
votes
1answer
95 views
mixed strategy nash equilibrium question!
Suppose the game consists of only $2$ players, player $1$ and player $2$, and each of them has only $2$ strategies to choose between. This gives a $2$ by $2$ payoff matrix.
Player $2$ has no ...
1
vote
1answer
122 views
Question on mixed nash equilibrium!
The question is as follows:
Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows:
...
2
votes
2answers
63 views
Is equilibrium selection in zero sum game trivial?
Does a zero sum game always has a unique payoff, whatever the nash equilibrium selected is ? even with mixed strategies ?
If so, what is the proof ?
0
votes
2answers
398 views
Subgame Perfect Nash Equilibrium
My homework question is summarized below:
There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...
4
votes
1answer
244 views
Iterated prisoners dilemma with discount rate and infinite game averages
Suppose we have two players who are perfectly rational (with their perfect rationality common knowledge) playing a game. On round one both players play in a prisoners dilemma type game. With payoffs ...
0
votes
1answer
211 views
Finding Nash Equilibria with Calculus
The problem is summarized as:
There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
1
vote
1answer
284 views
Unable to find Nash equilibria in mixed strategies
Here is the strategic form game:
Player 2
Left Middle Right
Top 2,2 0,0 1,3
Player 1 Middle 1,3 3,0 1,0
...
0
votes
0answers
52 views
what exactly does symmetric game and symmetric equilibrium mean?
I am confused about the ideas of a symmetric game and symmetric equilibrium of a game under the following conditions.
1) pure strategy Nash equilibrium
2) Nash bargaining game where players set a ...
0
votes
1answer
802 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
154 views
Find the Nash Equilibrium for a Cournot Game
Consider a Cournot game with $2$ firms. Firm $i$ has constanct marginal cost $C_i$, where $C_1 \lt C_2$. Inverse demand is linear: $p(q)=A-q$ (where $A \gt 2C_2 - C_1$). Find the Nash Equilibrium.
0
votes
2answers
122 views
Am I correct in thinking this game has neither Nash Equilibria nor dominant strategies?
I've taken this example from some lecture slides. The slides state there is no Nash equilibrium. I suspect there is also no dominant strategy for either player. Is this true?
Two players $i$ and $j$ ...
1
vote
1answer
72 views
Nash equilibria of mixed strategies
I am given the following game to find nash equilibria in pure and mixed strategies:
$\begin{pmatrix}& & Litte John &\\ & & c & w \\Big John & c & (5,3) & (4,4) \\ ...
4
votes
2answers
1k views
Cournot Nash Equilibrium Between Two Firms
Suppose we have two firms with specialized, but similar products. Suppose market demand for the two products is:
$$p_1(q_1,q_2)=a-bq_1-dq_2$$
$$p_2(q_1,q_2)=a-bq_2-dq_1$$
where $d \in (-b,b)$. Suppose ...
0
votes
1answer
289 views
Finding Nash equilibria using Support Enumeration
Chapter 3 of the Book "Algorithmic Game Theory" introduces an algorithm (page 8 of that PDF) to find mixed Nash equilibria for a bimatrix game $(A, B)$, which I struggle to understand.
($M$ and $N$ ...
1
vote
1answer
117 views
Mixed strategy nash equilibria in from 2xN bimatrix form
I'm looking for a way of finding (manually!) mixed strategy Nash equilibria in a 2xN game. Calling player 1 the player with two strategies and player 2 the one with N strategies, I've constructed ...
0
votes
1answer
135 views
Apply game theory/Nash equilibrium in computer security scenario
I want to apply the game theory to a scenario in security . where two ppl the optimal outcome of a game is one where no player has an incentive to deviate from his or her chosen strategy after ...
4
votes
1answer
220 views
Meaning of a partial derivative here?
I am given a 'tariff' function for two countries, $i=1, 2$. Both players can select a tariff between 0 and 100. If player $i$ selects $x_i$ and player $j$ selects $x_j$, country $i$ gets a payoff of ...
5
votes
1answer
250 views
Finding Nash equilibrium aka finding where lines intersect
I am tagging this as multivariable calculus because it potentially involves taking partial derivatives.
I am working on some mathematical treatment for Cournot duopoly models (not homework, just ...
5
votes
1answer
172 views
Algebraically finding a Nash equilibrium
Here's the problem that relates to a whole class of problems to which I am trying to figure out a general solution.
Given two players 1 and 2 who can select a number from the interval $[0, 1]$, ...
9
votes
3answers
219 views
Is there experimental evidence that people ever play mixed Nash equilibrium in real games?
Have any studies been done that demonstrate people (not game theorists) actually using mixed Nash equilibrium as their strategy in a game?
4
votes
2answers
224 views
Newspaper competition
A newspaper launches a competition. It said that readers should submit one number between 1 and 1000. A £2000 prize would be awarded to the person that got the closest to 2/3 of the mean of all the ...
1
vote
1answer
865 views
Symmetric nash equilibrium
I was reading this paper on position auctions for web ads. Basically, there are N slots each with an expected number of clicks (in a particular time period) $x$. Each agent makes a bid $B_i$ of how ...
