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.

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Take it or Leave it Offer [closed]

[![I am having a bad time solving second price auctions and lotteries with resale with credit constrains. Does someone know how to answer these?][1]][1] I have to solve some microeconomic bonus ...
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1answer
69 views

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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1answer
27 views

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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1answer
34 views

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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1answer
54 views

Simultaneous vs Sequential Games

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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43 views

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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1answer
124 views

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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1answer
34 views

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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1answer
87 views

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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1answer
137 views

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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1answer
76 views

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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1answer
68 views

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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1answer
122 views

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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1answer
88 views

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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2answers
106 views

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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1answer
45 views

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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81 views

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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1answer
131 views

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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1answer
126 views

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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1answer
45 views

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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1answer
61 views

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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1answer
46 views

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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1answer
48 views

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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1answer
78 views

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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1answer
109 views

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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2answers
80 views

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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1answer
61 views

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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32 views

Inforamtion asymmetry modeling

Is there any cook book, in finance, for models in information asymmetry, so as to make some practice?
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1answer
67 views

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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1answer
37 views

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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1answer
783 views

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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2answers
68 views

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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1answer
110 views

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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1answer
51 views

Risk neutrality in single-agent choice problem under uncertainity

Consider the following static single-agent choice problem under uncertainty. Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{V})$. ...
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1answer
34 views

Bayesian Correlated Equilibrium in a one player case: relation with literature

I am curious about the connection between one-player Bayesian Correlated Equilibrium (hereafter, BCE) introduced by Bergemann and Morris for a generic $n$-player setting with $n\geq 1$ (here) and the ...
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1answer
69 views

Adverse selection problem

The classic literature refers to the problem where information asymmetry exists between an informed and an uninformed counterpart as the adverse selection problem, but how can we verify what kind of ...
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1answer
101 views

Features of the set of Bayes Correlated Equilibrium in a single-agent decision problem with uncertainty

I would like your help to better understand the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty The notion of BCE is provided in this paper for a ...
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1answer
110 views

Perfect Bayesian Equilibrium in a two stage game with incomplete information

I would like to solve a game where firms have private information about their own type, but only know the distribution of the other firm's type. They interact in two stages, where the strategies ...
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1answer
18 views

Existence of optimal strategy in a choice problem with uncertainty and information structure

Consider a decision maker choosing an action, $y$, from the finiteset $\mathcal{Y}$, possibly without having complete information about the state of the world. More precisely, let $V$ be a ...
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1answer
46 views

Robust predictions in single-agent decision problem with uncertainty

I would like your help to better understand the possibility of using the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty to make predictions on optimal ...
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1answer
47 views

Optimal strategy in a single-agent choice problem under uncertainty

Consider the following single-agent choice problem under uncertainty. Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{v})$. First, ...
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1answer
98 views

Confusion about multiple information Sets

I'm confronted with the following situation: First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played....
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1answer
102 views

The notions of Bayes Correlated Equilibrium and Bayesian Nash Equilibrium in a game with one player

I would like your help to use the correct terminology to define a Bayes Correlated Equilibrium (BCE) and a Bayesian Nash Equilibrium (BNE) in a "game" with one player. The notion of BCE in an $N$-...
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1k views

The difference between a Nash equilibrium and Bayesian Nash equilibrium [closed]

What is the basic difference between Nash equilibrium and Bayesian equilibrium?
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1answer
58 views

Clarification on the definition of Bayes Correlated Equilibrium

I would like your help to understand the definition of Bayes Correlated Equilibrium (BCE) in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper....
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1answer
29 views

Implications of the concepts of combination/expansion of an information structure

I would like your help to understand the concept of combination/expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in ...
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1answer
235 views

Why is it called Bayesian Persuasion?

I'm sure most of you are familiar with the paper titled "Bayesian Persuasion" by Kamenica and Gentzkow (2011), (you can find it here). I was wondering what are your thoughts as to why it is called "...
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1answer
81 views

The concept of expansion of an information structure

I would like your help to understand the concept of expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in the paper. ...
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3answers
201 views

The concept of information structure in incomplete information games

I would like your help to understand the concept of information structure in the incomplete information game at p.6-7 of this paper. Let me summarise the game as described in the paper. There are $...
4
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1answer
198 views

Bayes Correlated Equilibrium: obedience

I would like your help to understand the definition of obedience in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper. There are $N\in \...