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
32 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
28 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
42 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 ...
0
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1answer
41 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
37 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 ...
1
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1answer
89 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
72 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
24 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, ...
0
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0answers
29 views

Inforamtion 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
53 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
29 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
88 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
63 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
42 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
48 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
26 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
60 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 ...
0
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0answers
7 views

In search for a simple mental bayesian model

I have read many articles about Bayesian thinking. Most of the time, they fall under 2 categories (or a mix of both). The first category of articles focuses on Bayes’ formula. The second category of ...
5
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1answer
97 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 ...
0
votes
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 ...
0
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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 ...
0
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1answer
44 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
72 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
90 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 $N$-...
-1
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1answer
335 views

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

What is the basic difference between Nash equilibrium and Bayesian equilibrium?
2
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1answer
50 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....
1
vote
1answer
25 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
votes
1answer
100 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
53 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. ...
1
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2answers
150 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
votes
1answer
172 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 \...
0
votes
1answer
61 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
397 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 ...
7
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1answer
98 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 ...
1
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1answer
44 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 ...
3
votes
1answer
201 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
votes
1answer
80 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 ...
1
vote
2answers
107 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
votes
1answer
69 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
votes
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
votes
1answer
138 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
votes
1answer
71 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(...
1
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0answers
77 views

Mixed Strategies in Bayesian Games

I am confused about the following statement from Wikipedia: "A mixed strategy is an assignment of a probability to each pure strategy. This allows for a player to randomly select a pure strategy. ...
1
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0answers
74 views

Prisoner's dilemma as a Bayesian one-shot game

What happens if we assume that there is incomplete information to the prisoner's dilemma game? For example, suppose we have the following matrix with the utilities $T>R>P>S$ and $2R>S+T$ ...
5
votes
1answer
49 views

Bayesian game and the set of types

In a finite Bayesian game, in most textbooks, a type of player $i$ is defined as $\theta_i\in\Theta_i$. Little is said about the "nature" of the set of types. For example, could we have a two-element ...
6
votes
1answer
411 views

Bayesian-Nash equilibrium in a first-price auction

In a famous textbook example of a Bayesian-Nash equilibrium, there is a first-price auction with two independent players. Each player $i$ values the item as $v_i$, which is distributed uniformly in $[...
6
votes
2answers
150 views

Bayesian Mechanism vs Prior-free Mechanism

I have a double auction mechanism in which the valuations of the agents for the items are drawn from a known random distribution. To be precise, the valuations are the probability of each agent ...
4
votes
1answer
58 views

Why system of beliefs, $\mu(x)$, needed in dynamic incomplete information games

We need to make statements about the sequential rationality of players who are in information sets that are not singletons. In these non-trivial information sets, we need to be able to say something ...
3
votes
1answer
681 views

Game theory with rational and irrational players

Are there game theoretic models where one player is rational and the other is irrational (i.e., plays with behavioral limitations)? The motivation for this question is that behavioral economics has ...
1
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2answers
190 views

Compute Nash Equilibrium in median voter game

Consider a spatial model in which two candidates A and B compete for office. The policy space ranges from -1 to 1 and each candidate can take one of three positions, -1, 0, and 1 (so that they have ...