Questions tagged [bayesian-game]
For questions about Bayesian games. These are strategic interactions when one or more players have incomplete information about other players. General topics of games with asymmetric information may use this tag.
152 questions
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What is the difference between Partially Observable and Incomplete information in Game theory
In reference to this paper that discusses Partially Observable Stochastic Game, it also mentions of Bayesian Game which is characterized by incomplete information. Rather then pointing out the ...
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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 ...
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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 ...
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Pre-play, interim-play, intra-play communication games
I have a question that seems easy but I want some clarification. Suppose that we have a communication Bayesian game. The game starts when the players learn their prior infornation and after this they ...
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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 ...
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Repeated Games of Incomplete information set up and questions
The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration).
The preliminaries of the model
Formally, a repeated game with incomplete information is given by the ...
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How to define a dynamic programming problem in an incomplete information game?
How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
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How to analyze this two-player, imcomplete-information, extensive-form game?
Game tree:
Note that the information sets for player 1 are represented by red dotted lines, while the information sets for player 2 are represented by blue shaded tapes.
Described in words, the game ...
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Is it a weakly dominant strategy to bid your true value in a third-price auction with two identical goods and N uniform distributed bidders?
I am interest in finding the optimal strategy for a single bidder (the BNE), when I have a third-price auction with N bidders and two identical goods. The bidders have iid valuations: U(0,1)
I have ...
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What is the difference between a communication mechanism and a protocol of communication?
What is the difference between a communication mechanism and a protocol of communication in mechanism and information design. Although most papers in the literature make this distinction, it is not ...
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Expected payoff calculation difficulty in the Bayesian environment of Bergemman and Morris
Suppose that we have two states of the world equally likely to occur, and say $\psi$ is the common prior of the state $\theta\in\Theta=\{G,B\}$. The types of the players are given by the following ...
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Bayesian update in the beliefs about the signals
Suppose that we have tow states of the world $\omega_1$ and $\omega_2$, where $p(\omega_1)=p(\omega_1)=1/2$ and there are three different signals, $s_H,s_M,s_L$ that are equally likely to occur in ...
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When should my beliefs be a martingale?
Suppose that I am wondering about whether an event will happen (e.g. whether it will rain tomorrow in a particular location). Suppose that my beliefs about whether the event will happen can be ...
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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 ...
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Mechanisms of communication in game theory
In the spirit of the previous question that I have done, here considering the paper here I am trying to make the matching definition $2.2$ here.
I will give two definitions and I would like to clarify ...
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Difficulty in understanding the notation related from probability theory with game theory
The question that I have is a little technical and it has to do with the notation and the combination between some mathamatical properties in the probability theory of information economics.
Say $\...
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Alternative way to calculate the symmetric BNE of the game
My problem.
Consider the following auction for a single object. There are $n \geq 2$
bidders. They submit their bids simultaneously. The object is allocated to the player
who submits the largest bid. ...
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Job Market Signaling
My Solution is this
Separating equilibrium
High type worker chooses $e_H = e^* >0$
Low type worker chooses $e_L =0$
Firms believes that if education is $e^* >0$ then the worker is high type and ...
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Rule for Number of Strategies in Bayesian Games
Is there a general rule for finding the number of strategies (denote as $S$) for each player in a Bayesian game? I think it's related to the number of types (denote as $T$) and the number of actions (...
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310
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Bayesian Nash Equilibrium in a Duopoly Cournot Competition
I am having a hard time to solve a Bayesian Nash equilibrium game in a duopoly cournot competition setting. So, I have two firms with given production quantities, let's say $q_1$ and $q_2$ (i.e., not ...
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Find a separating perfect Bayesian equilibrium
Exercise Question 2, Chapter 28, Strategy: An Introduction to Game Theory 3rd Edition by Joel Watson
In part (a) of the question, we have to check if any separating perfect Bayesian equilibrium ...
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Strong sequential equilibria and the existence of others
I am working on the following game
and I have to find all strong sequential equilibria here.
I determined that here any belief derived from a fully mixed strategy gives a distribution (1/2, 1/2) over ...
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Simultaneous vs Sequential Games [closed]
Is there a way to characterize the distinction between simultaneous vs sequential games? I'm trying to describe a situation where players can only take actions without knowledge of other players' ...
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How to find an optimal strategy in an auction?
I have asked this question in mathematics forum as well but since I have not recieved an appropriate answer yet, I ask it here as well.
Consider an auction of sculptures by four artists: A, B, C and D....
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What does 'continuation' as in continuation games, strategies, plays, etc. exactly mean?
I am in my first course in grad level game theory. While I was reading through Fudenberg and Tirole's Game Theory, I constantly come into contact with the word 'continuation' to describe some games ...
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142
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Find a Perfect Bayesian Equilibrium with a game that includes Nature
I want to determine all pure-strategy Perfect Bayesian Equilibria for this task, but I cannot get very far. Side note: First number is payoff for A, second number payoff for player B.
For the last ...
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Exchange Houses game - Bayesian Game
Can anyone help me understand how to solve this type of asymmetric information Bayesian game?
So the game is a different version of the Tadelis 'trading house games'. It involves 2 players
that each ...
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Mixed Strategy Bayesian Nash Equilibrium
There was an exercise question regarding two players with two types each in a game theory class.
The two players were assigned to do a team project together.
The utility from doing the team project is ...
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622
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Mixed Strategies in Bayes Nash Equilibrium (Bayesian Battle of the Sexes). Shouldn't it depend on $p$?
I have a question about calculating mixed strategies in a Bayes Nash Equilibrium in a simple 2-player bimatrix game. To demonstrate the issue, consider ``Bayesian Battle of the Sexes.'' Suppose P1 ...
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I cannot understand Sobel & Crawford 1982 (cheap talk)
I am a master student, currently reading this paper for fun during the break. I got lost during the part $U^S(\bar y, \bar m, b) = \max_{y \in Y} U^S(y,\bar m, b)$ on page 5. I dont understand why ...
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Pooling equilibrium in akerlof's lemon market with certification cost
Consider a market for 300 used cars where 1/3 of all cars are good quality cars and the rest are bad quality cars. All these cars are owned by (potential) sellers to begin with and each seller owns ...
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Find a perfect Bayesian equilibrium
Each of two sellers, $1$ and $2$ owns one indivisible object that a buyer
would like to buy. The two objects are identical. The buyer´s valuation depends on
the number of objects he gets. The ...
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Pure-Strategy Bayesian Nash equilibrium with general common prior
I'm doing a problem set on the subject of Bayesian Nash equilibrium. I'm asked to find the pure-strategy BNE of the following. I've calculated to matrix shown below. My first concern is if I've ...
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Blackwell order of information structures
Consider a model where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world.
The state of the world has support $\mathcal{V}$.
...
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Perfect Bayesian Equilibrium for banks
I'm reading this paper on credit lending cycles and trying to understand how it works for the case of one bank. This is the set-up of the model:
There are two players, a bank and the market. There ...
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How to prove the WPBE is SE in signaling game?
The definition of a signaling game:
A signaling game is an extensive game with the following structure:
(i) A move of chance first determines a state of the world/type $t ∈ T$, which is drawn from T ...
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First Price Auction (Expected Payoff)
I'm trying to solve followed first-price auction problem.
Bidder's pdf is
$$
f(v_i)= \begin{cases}
\dfrac{1}{8}v_i, & \text{if} & 0\leq v_i\leq4\\
0, & \text{if} & \text{otherwise}\\
...
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Example of information structure in a one-player Bayes Correlated Equilibrium
Model
Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world.
The state of the world has support $\mathcal{...
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Uniqueness of equilibria in first-price auction with discrete valuations
Assume we have a first-price auction with discrete and independent private values and identical distributions of all bidders. It is known that there exists a Bayes-Nash equilibrium where bidders bid ...
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Write search model as a signal density inducing posterior belief
Consider a decision maker (DM) who as to choose an action from the finite set $\mathcal{Y}$ with cardinality $L. $
The payoff the he gets depends on the action chosen and the state of the world. The ...
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Bayes Correlated Equilibrium with complete information
Model
Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world.
The state of the world has support $\mathcal{...
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Some basic questions on infromation asymmetry
How does asymmetric information and bid-ask spread are connected? For instance, economic theory tells us that, the more the problem of information asymmetry, the higher the spread is. What is the ...
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Set of Bayes Correlated Equilibria when complete information is not available
Model
Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world.
The state of the world has support $\mathcal{...
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Information and search
Consider a game where a decision maker (DM) has to choose action $l\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$.
The choice set $\mathcal{Y}$ has cardinality $L$....
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Refinements in signaling games with three sender types
What are the pros and cons of the Intuitive Criterion and the Criterion of Divinity in signaling games with three types?
I find that separating equilibria often survive the intuitive criterion, ...
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Algorithm to find Bayesian Nash Equilibria [closed]
I am working on a Bayesian game with a finite number of players and discrete types, but the complexity of the equations is not allowing me to find the BNEs by hand.
I read a paper describing ...
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REE with asymmetric information and Bayesian Nash equilibrium?
What is the difference between a Rational Expectations Equilibrium (REE) with asymmetric information and Bayesian Nash Equilibrium (BNE)? Since agents in both cases play some game or have a strategic ...
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Finding Bayesian Nash Equilibrium
I'm recently new to Game Theory and I've recently started teaching myself about Bayesian Nash Equilibirum. I've stumbled across a problem set that I can't seem to wrap my head around concerning ...
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Exact definition of one-player Bayesian Correlated Equilibrium
Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The state of the world has support $\mathcal{V}$. ...
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First-price symmetric auction with discrete value
I've been trying to work the following problem out but I can't quite seem to understand it, or the whole concept of first-place auctions. I don't understand how we get to the equilibrium.
The problem ...
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