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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66 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
48 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
27 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
45 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
20 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
48 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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0answers
6 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
95 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
15 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
41 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
42 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
70 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
88 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
168 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
49 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
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
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1answer
82 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
49 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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2answers
149 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
163 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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0answers
39 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 ...
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1answer
328 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
89 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
43 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
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1answer
169 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 $\epsilon_i$. ...
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1answer
60 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
68 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
53 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. ...
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2answers
299 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
112 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
66 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(...
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0answers
58 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. ...
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0answers
68 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
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1answer
46 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
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1answer
392 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
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2answers
148 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
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1answer
54 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
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1answer
613 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 ...
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2answers
180 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 ...
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0answers
200 views

Bayes Nash Equilibrium in a game with continuous actions

I am attempting to think through a particular type of game with continuous strategies, with Bayes Nash equilibrium as the solution concept. I first describe the game below, followed by questions. ...
7
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1answer
93 views

Uniform bounds on rate of merging for Bayesian learners

Update. Cross posted at Cross Validated. In a well-known paper, Blackwell & Dubins (1962) show that the posterior probabilities of two Bayesian agents, whose priors agree on events of measure $0$,...
5
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1answer
341 views

Checking incentive compatibility of a mechanism

I was thrilled at seeing an interesting bidding system in an academic institutions. This bidding is for registration of courses. Each student is allocated some points based on her grade point(GPA). So,...
5
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1answer
498 views

Divinity for Dummies

I understood the general idea of divinity: that it helps to rule out "unreasonable" equilibria. However, can someone explain it in more details with simple examples so that a senior undergrad student ...
6
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1answer
206 views

Arguing uniqueness of Bayes-Nash equilibrium in an auction setting

In an auction setting with interdependent values, let $\theta_i$ denote the type of player $i$ and $m_i$ that player's message (a bid, essentially). I have calculated the best response function as: $$...
5
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2answers
368 views

Bayes-Nash equilibrium and correctness of beliefs

Define a Bayesian game as follows: $$G = \left\langle I, \left(A_i,T_i,(p_{t_i})_{t_i \in T_i}, u_i \right)_{i \in I} \right\rangle$$ $I$ is the set of players $A_i$ is the action set for player $i$,...
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1answer
967 views

What is the difference between Stochastic game and Bayesian game ?

I was studying definitions of Stochastic and Bayesian game and it appears that Stochastic game is a generalized form of Bayesian game. Could anybody please explain the fundamental differences between ...
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0answers
364 views

Which economic game theory model is most similar to poker?

Propeties the model should have: Well motivated: the game is actually is a plausible model of a real world situation. Maybe with some parameters learnt from data. Complete: it is a complete game ...
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0answers
95 views

Can repeated bidding in an auction make each player's type common knowledge?

In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information: we assume that all values are common ...
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2answers
3k views

Bayesian Nash Equilibrium - Mixed Strategies

What's the correct way to solve BNE in mixed strategies? I've found two conflicting methods used. Two players. Player 1 knows which game is being played, player 2 knows the game is chosen with ...
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0answers
276 views

A Perfect Bayesian Bargaining problem

Thought I'd post interesting questions that come my way to try and boost activity! A seller and a buyer negotiate over trade of a single indivisible good. The good is either of low quality (in which ...