All Questions
Tagged with nash-equilibrium mathematical-economics
23 questions
5
votes
1
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122
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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 ...
- 505
1
vote
1
answer
82
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 $\epsilon$, ...
- 505
0
votes
1
answer
95
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 ...
- 505
1
vote
1
answer
89
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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 ...
- 505
2
votes
1
answer
49
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 ...
- 455
0
votes
1
answer
100
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 ...
- 11
3
votes
1
answer
134
views
Nash Equilibrium with Constraints on Decision Variables
I am trying to solve a two player game with constraints on decision variables. The general structure looks something like this:
$$\max_{x_1} f(x_1, x_2)$$
$$\max_{x_2} g(x_1, x_2)$$
subject to
$$x_1 + ...
4
votes
0
answers
106
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Perfect Bayesian Equilibium - Application to game with inconsistent beliefs / no common prior
Does the concept of a Perfect Bayesian Equilibrium apply only to incomplete games with a common prior / consistent belief?
In both Bonanno's "Game Theory" and Osborne's "A Course in ...
- 83
4
votes
1
answer
70
views
Equivalence from correlated/communication equilibrium to Nash Equilibrium?
Taking into account the seminal papers of Forges and Imre Bárány, they proove a very strong result that gives an exact connection among the communication and the correlation equilibrium solution ...
- 969
4
votes
1
answer
71
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Correlation device that induces a specific transition probability
Taking a look at this paper of Forges and Vida the authors define a correlation device in page $102$, that is a standard probability space $\left(\Omega,\mathcal{B},\mu\right)$, They assume that the ...
- 969
1
vote
0
answers
40
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What if Bergemann and Morris setting used mixed (or bbehavioral) actions instead of pure actions as reccomendations?
Once again, I will refer to the setting of Bergemann and Morris (2016) and write here the payoff formula of player $i$ from the perspective of the information designer. The payoff formula is the ...
- 969
3
votes
1
answer
73
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Bergemann and Morris information designer and decision rule concept
Taking a look in the paper of Bergemman and Morris in 2016, they refer to the desicion rule as mapping
$$\sigma:\Theta\times T\to\Delta(A)$$
The explanation to understand the notion of it is given as ...
- 969
3
votes
1
answer
108
views
Bayes correlated equilibrium of Bergemann and Morris
The paper of Bergemann and Morris proves a theorem based on some foundations about the information sets and their expansions. I am trying to understand theorem one intuition, more precisely I cite the ...
- 969
3
votes
0
answers
50
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Providing an example in cooperative - games and coalitions
Here is the paper from chich I previously posted another definition here Definition of a $k-$strong Nash Equilibrium
I am trying to construct an example to understand the idea of the following ...
- 969
2
votes
1
answer
106
views
Definition of a $k-$strong Nash Equilibrium
Consider a game $G=(N, (A^i)_{i\in N}, (g^i)_{i\in N})$, $N=\{1,2,\dots,n\}$, $A=\Pi_{i\in N}A_i$ is the set of actions and $g^i:A\to \mathbb{R}$ is the payoff function. The latter can be extended ...
- 969
2
votes
1
answer
465
views
Defining the set of strategies, mixed strategies and the simplex set
Suppose that we have a two players game, where $(S^i)_{i=1}^2$ denotes the set of pure strategies for each one. The set of mixed strategies of player $i$ is denoted by $\Sigma^i=\Delta(S^i)$ while $\...
- 969
6
votes
1
answer
391
views
Prove that for every Nash equilibrium $\sigma^*$, the probability distribution $p_{\sigma^*}$ is a correlated equilibrium
This is a classic theorem in game theory, that is left as an excersice in my textbook. Can anybody proove it? I can not thing of anything excpet from the definition of the correlated equilibrium in ...
- 969
1
vote
0
answers
46
views
Nash in demand functions!
I am searching for some types of games that are played in linear demand functions. Altough I hear that there is a vast literatrure for games that are played in the intercept or the slope of the demand ...
- 969
0
votes
2
answers
174
views
How can I build a fixed point theorem argument in pure strategies?
To begin with, I am recalling the Banach Fixed Point Theorem.
Let $(X,d)$ be a non-empty complete metric space with a contraction mapping $T:X\to X$. Then $T$ admits a unique fixed-point $x^*$ in $X$ ...
- 498
0
votes
1
answer
231
views
How to find mixed optimal strategies in this zero-sum game?
I'm trying to solve this problem from last year final exam in game theory:
Consider the zero-sum game $G=(X, Y, g)$ where $X=Y=[0,1]$, and $$\forall (x,y) \in X \times Y: g(x, y)=\max \{x(1-2 y), y(1-...
- 101
4
votes
0
answers
106
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Existence of symmetric trembling hand perfect equilibria
Consider symmetric and finite game. By Nash (1950), the game must have at least one symmetric equilibrium (proof). Also, it must have at least one trembling hand perfect equilibrium (proof).
...
user17900
2
votes
1
answer
114
views
Proving the existence of Nash Equilibrium using alternate approaches
Most of the standard books/papers/reading materials prove/state the existence of a Nash Equilibrium by appealing to Sperner's Lemma, or to Brouwer's/Kakutani's FPT. However, I've recently come to know ...
- 525
1
vote
0
answers
85
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Deviating from Cournot-Nash
Suppose player $1$ and $2$ are playing a simultaneous move game where with continuous strategies $x_1$ and $x_2$. The Cournot equilibrium is $x_1^*,x_2^*$. The following diagram purports to show that ...
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