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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3
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1answer
31 views

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 ...
2
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0answers
37 views

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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0answers
10 views

Information acquisition problem and desing of information

I am searching some details about the information acquisition problem. I want to understand what this is about and where can I find the beginning of this literature. I think this problem is some kind ...
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0answers
23 views

Questions about the definition of a protocol

The following definition is from this paper about protocols of communications (definition $2.4$ in the paper). You can check the paper for more details and previous of my questions. $\textit{...
1
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1answer
901 views

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 ...
5
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1answer
64 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 ...
3
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1answer
67 views

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 ...
5
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1answer
133 views

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 $\...
2
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1answer
83 views

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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0answers
59 views

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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2answers
45 views

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 (...
5
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1answer
78 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 ...
2
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1answer
49 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
41 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 ...
1
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1answer
67 views

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' ...
5
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0answers
51 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....
5
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1answer
161 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 ...
0
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1answer
37 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 ...
1
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1answer
95 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 ...
1
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1answer
191 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 ...
3
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1answer
93 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 ...
2
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1answer
77 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 ...
2
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1answer
149 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 ...
1
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1answer
98 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 ...
2
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2answers
128 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 ...
3
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1answer
55 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 $\mathcal{V}$. ...
3
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0answers
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 ...
3
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1answer
149 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 ...
1
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1answer
145 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}\\ ...
3
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1answer
47 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{...
3
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1answer
73 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 ...
0
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1answer
47 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 ...
2
votes
1answer
62 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{...
0
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1answer
79 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
113 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{...
2
votes
2answers
85 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 $L$....
0
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1answer
68 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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0answers
47 views

Information asymmetry modeling

Is there any cook book, in finance, for models in information asymmetry, so as to make some practice?
1
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1answer
74 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 ...
0
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1answer
38 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 ...
2
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1answer
1k 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 ...
3
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2answers
78 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 $\mathcal{V}$. ...
1
vote
1answer
136 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 ...
1
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1answer
54 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 $P_V\in \Delta(\mathcal{V})$. ...
0
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1answer
38 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 ...
3
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1answer
73 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 ...
5
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1answer
106 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 ...
3
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1answer
112 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 ...
0
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1answer
19 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 ...
0
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1answer
47 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 ...