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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31 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
55 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
67 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
61 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
58 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
34 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
77 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
102 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
77 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
39 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
38 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
44 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
44 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
74 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
105 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
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2answers
78 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
34 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
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
58 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
34 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
139 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
64 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
56 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
50 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
29 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
65 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
98 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
16 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
44 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
45 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, ...
3
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1answer
74 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....
3
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1answer
93 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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1answer
569 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
54 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
26 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 ...
3
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1answer
110 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 "...
3
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1answer
60 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
172 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
184 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 \...
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1answer
74 views

How to approach such question of two periods and asymmetric information game?

There are two players 1 and 2, playing a two-period public good contribution game. The benefits from the public good per-period to each player is $b_1$ and $b_2$ respectively, which are common ...
2
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1answer
520 views

Bayesian Nash Equilibria in Battle of Sexes

Consider the static Bayesian game as described below. $\ t_1$ and $\ 𝑡_2$ are the types of the row and column player respectively, which are both uniformly distributed on the interval $[0,1]$. The ...
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1answer
101 views

Robust asymmetric information?

Bergeman and Morris (2014) explain how the concept of Bayesian Correlated equilibrium contains all the robust predictions in games of incomplete information. In particular, their question is what are ...
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1answer
45 views

Probability of the event knowing that I received no informations

First I want to thank you if you pay attention to my post. I apologize if it seems elementary to you, note that I searched a lot an answer before posting. I have a particular informational framework ...
4
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1answer
259 views

Definition of Bayesian Nash equilibrium

I have a basic doubt on the definition of Bayesian Nash equilibrium. Consider the following game: 1) $N$ players. 2) Each player $i$ has a type, assigned by nature and denoted by $\epsilon_i$. ...
0
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1answer
115 views

Spence's Job Market Signaling Game

I have a little doubt in the Job Market Signalling Game. I am referring to A Primer in Game Theory: Gibbons, Chapter 4, Signaling Games The attached paragraph refers to a Separating Equilibrium case ...
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2answers
117 views

Bayesian Nash Equilibria: Strong and Weak Types

I need a little help with the question. I understand that since both players have two types each, there will be 4 different payoff matrices to be considered, $(S,S)$,$(S,W)$,$(W,S)$,$(W,W)$, each type ...
4
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1answer
87 views

Are there multiple equilibria in the second price auction?

Suppose that $n\geq 2$ bidders compete in a second price auction. Each bidder $i$ knows their own valuation $v_i$, but only knows the distribution generating the valuations of the other players. ...
4
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2answers
304 views

Questions of the type “What do you think other people would think?”

For a study in the adoption of new technology, a student and I are developing a questionnaire that will poll domain experts on their opinions of what their colleagues would think about benefits/...
4
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1answer
152 views

Computing pure strategy Nash equilibria in finite games

I am trying to compute the (pure strategy) Nash equilibria of some discrete auctions. More precisely, let us define the strategy of each player as a function mapping from every valuation that they ...
4
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1answer
74 views

Social Welfare and Pareto Optimality in a Bayesian Game

In a normal form game with two players, we call a joint strategy $s=(s_1,s_2)$ a Pareto optimal outcome if for no joint strategy $s'$, for all players $i\in\{1,2\}$, we have $$u_i(s')\geq u_i(s)\qquad(...