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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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19 views

What kind of figures are insightful in game theory?

I am finishing my thesis on a signalling model in which I characterize the perfect bayesian equilibria of the game. However, I find that my final expressions are too mathematical and that the ...
1 vote
1 answer
49 views

bayesian nash equilibrium cournot game

Consider the Cournot game with two companies, whose function (Q) P is in the form of a relation: P (Q) = 60 − Q if Q ≤ 60 0 if Q ≥ 60 where q2 + q1 = Q is the sum of outputs in the market. The cost of ...
5 votes
1 answer
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About Two Methods of Computing Bayesian Equilibria

Question I want to compute the Bayesian equilibria for the following Bayesian game: With probability $p$, player 1 would be of type 1.1. With probability $1-p$, player 1 would be of type 1.2. Player ...
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14 views

Papers on signalling + validation?

Looking to see if there's any game theory literature in which 2+ players play a game of incomplete information. One set of (informed) players gives Spence-like signals to the uninformed player(s). The ...
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1 answer
62 views

How to find BNE of the exchange game?

Each of two players receives a ticket t on which there is a number in [0,1]. The number on a players ticket is the size of a prize that he may receive. The two prizes are identically and independently ...
4 votes
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49 views

Game where you don't know (but can learn) your own type?

Is there a literature out there for games where you don't know your own type, but know it's from a distribution, and can e.g., invest resources to learn your own type prior to moving on with the game? ...
1 vote
1 answer
54 views

Judge prosecutor example of Kameinica and Gentzkow

Based on Kamenica and Gentzkow example about the prosecutor and the judge. The utilities of the sender and the receiver are $v(\alpha,\omega)=\alpha$ and $u(\alpha,\omega)=-(\alpha-\omega)^2$. The ...
1 vote
1 answer
173 views

Can anyone help with these calculations?

This is from the this paper in section $3$ about the two period example. Suppose that we have the following two period, $t=1,2$, sender(S) - receiver(R) model. For an action path $a=(a_1,a_2)$ and a ...
1 vote
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48 views

Why did Bergemann and Morris chose a different setting with respect to Kamenica and Gentzkow only to reach to the same results?

Why did Bergemann and Morris choose a different setting with respect to Kamenica and Gentzkow only to reach to the same results? However none of both approaches seem to present the problem in a ...
1 vote
2 answers
123 views

Unwrapping Kamenica and Gentzkow model

Let's start with the basics. Suppose that $\Theta$ is a finite set of states and $\theta$ is the element of the state set. To simplify the model, we assume that $\Theta = \{\theta_1 = G, \theta_2 = B \...
2 votes
0 answers
67 views

How Kyle's $\lambda$ emerges in the demand functions of the informed and uninformed traders?

From Albert S. Kyle's 1989 model. Suppose that the are trhee types of traders in the market, informed traders (I), uninformed traders (U) and noise traders. The population of $I$ traders is $N$ (...
2 votes
1 answer
70 views

Beyond quadratic loss preferences?

I have a complex question. Is there any other way to model the preference misalignments of the sendres (in senders-receivers games) towards the desire of some specific state apart from the quadratic ...
1 vote
2 answers
62 views

In games of Bayesian Persuasion, under what conditions is Receiver better off than under uninformative signals?

I've been working through a few Bayesian Persuasion (BP) models à la Kamenica and Gentzkow (2011), and a feature that seems to arise often is that commitment to a persuasion mechanism is Pareto ...
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173 views

The concept of 'truthfulness' and 'indirect' in mechanism design

I'm a beginner in mechanism design. I learned that 'a (direct) mechanism is truthful if an agent truthfully reveals his/her type.' Then, how can we define a truthful indirect mechanism? I'm not sure ...
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1 answer
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Auction with independent private values - An example from Game Theory: Analysis of Conflict by Roger Myerson

I have difficulties understanding the equilibrium analysis of the following auction game: Suppose that there are $n$ bidders in an auction for a single indivisible object. Each player knows privately ...
1 vote
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61 views

What is the relation between Blackwell's order and Stochastic Dominance order?

In Kamenica and Gentzkow (2017) as well as in Bergemann and Morris (2016) the notion of Blackwell comparioson of experiments is used to compare different information structures. I am trying to find ...
1 vote
1 answer
51 views

Understanding the notations in Bayesian game definition

I am having trouble understanding the definition of a Bayesian game based on the following definition from class. I would appreciate it if you could explain the notations and overall meaning for point ...
1 vote
1 answer
67 views

Definition of information structure in an incomplete information game

I try to understand the model in this paper, pages 48-49. (Bergemann, D., & Morris, S. (2019). Information design: A unified perspective. Journal of Economic Literature, 57(1), 44–95. https://doi....
2 votes
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47 views

question about lemma 1 of Crawford & Sobel (1982)

In Crawford & Sobel (1982), they proved in lemma 1 that for the basic model of a cheap talk game, every equilibrium induces finitely many actions. Here is a special case of their model where the ...
1 vote
1 answer
319 views

First price sealed-bid auction with discrete bids

I really couldn't solve this problem. Can someone help me with this? Consider the sealed-bid auction for a single item, where there are only two allowable bids. There are two risk-neutral bidders who ...
2 votes
0 answers
27 views

Two questions in Bergemann and Morris (2016) - BCE and Comparison of Information Structures in games

Based on Begemann and Morris (2016) we have the following definition about a standard game of incomplete information A standard game $\Gamma = <G,S>$ of incomplete information consists of a set ...
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72 views

What is the difference between the utility with the ex-post or the ex-ante utility function?

What is the difference of the ex-post utility function of the utility function. For example in Bergemann and Morris (2019) the utility function is defined as an ex-post utility function. Check in page ...
1 vote
1 answer
53 views

Equations 12 and 13 in Scharfstein and Stein (AER, 1990)

I am working my way through Scharfstein and Stein's seminal paper on herding. Herd Behavior and Investment Author(s): David S. Scharfstein and Jeremy C. Stein Source: The American Economic Review , ...
5 votes
3 answers
681 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 $i$,...
1 vote
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In a standard labor market signaling game, which weak Perfect-Bayesian equilibria (PBE) are actually sequential equilibria?

In a standard labor market signaling game with two types, the only "sensible" equilibria are the least-cost separating equilibria; as such these are the equilibria that survive a standard ...
1 vote
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What is the difference among information acquisition, information providing and information design?

Taking a look at the literature of information economics I see three different terminologies about information that seem to have some intersection, though my understanding is not so good. These terms ...
3 votes
2 answers
521 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 ...
3 votes
0 answers
59 views

How to model the payoff (or utility function) of the information provider?

After a thorough look in the literature of information design like Bergemann and Morris and Kamenica and Gentzkow I am still not so sure how the utility gain or payoff of the information provider/...
5 votes
2 answers
127 views

Information structure for complete information

Model A decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. $\mathcal{Y}$ is a finite set. The state of the world is a random ...
10 votes
1 answer
1k views

Perfect Bayesian Equilibrium

I've been given a question which I'm struggling with: Take the standard Prisoner's Dilemma game and consider it is played twice. (Players observe the outcome of the first game before playing the ...
1 vote
0 answers
181 views

Signalling with continuous actions and continuous types

Consider the following signalling game. Individuals choose an action $a \in \mathbb{R}$ to maximise \begin{equation} U(a, \theta) = \theta a - \frac{a^2}{2} + \mathbb{E}[\theta|a] \end{equation} where ...
2 votes
0 answers
28 views

Modelling common incentives and strategic manipulation

There are many situations in the markets when small or larger portions of traders collude and make a strategy manipulation through communication, even they have heterogeneous endowments and ...
3 votes
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39 views

Solution concept in Benabou/Tirole (2006)

In a well known paper, Benabou/Tirole (2006) examine `pro-social' behaviour in an environment in which others draw inferences about one's motives given the map from motives to behaviour in the ...
1 vote
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153 views

Please check for payoffs which I calculated in the incomplete and imperfect game

Taxpayers may either have a high income or low income, and they may be either opportunistic or honest. The tax collector cannot observe any of these characteristics, but after receiving a report from ...
1 vote
1 answer
104 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 ...
8 votes
1 answer
2k 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 ...
1 vote
0 answers
77 views

I present a communication game - Could you please make comments on my assumptions, notation and properties that I may have not considered yet?

I consider the following communication game. Suppose that we have $I$ players and each one of them learns a private signal $s_i=(s_{i,1},s_{i,2},...,s_{i,k})$, where $k$ is finite and also, every ...
2 votes
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80 views

Is the mixed strategy $\sigma_i^*:S_i\times\Theta\to\Delta(A_i)$ chosen by player $i$ linear?

Suppose that we have a Bayesian game, where the number of players is $I$ and we refer to the generic player with $i$ $\Theta$ stands for the state of the world, where $\theta\in\Theta$ is the typical ...
1 vote
1 answer
576 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 ...
0 votes
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30 views

Bayes Nash equilibrium distribution

I would like to define a decision rule that is induced by a BNE distribution in a game with a continuum of agents. For that, I have a decision rule $\varphi:\Theta \rightarrow\Delta(\Delta(A))$ that ...
0 votes
1 answer
48 views

How does this reporting correspondence is redefined?

Let $\mathcal{R}_i$ be a non-empty, finite set and define the reporting correspondence $R_i:S→2^{\mathcal{R}_i}-\{\emptyset\}$ to be a mapping from player i’s type space to the collection of subsets ...
2 votes
1 answer
74 views

Bayes Correlated equilibrium without information expansion

The questions are with reference to Bergemann and Morris (2013, 2016). I'm trying to give an alternative interpretation to BCE from the analyst/information designer perspective provided in the paper. ...
4 votes
0 answers
98 views

Perfect Bayesian Equilibium - Application to game with inconsistent beliefs / no common prior

Does the concept of a Perfect Bayesian Equilibrium apply only to incomplete games with a common prior / consistent belief? In both Bonanno's "Game Theory" and Osborne's "A Course in ...
3 votes
0 answers
115 views

Are these two definitions of Bayesian Nash Equilibrium equivalent?

Consider a standard game $\Gamma$ with incomplete information. There are $n$ players indexed by $i=1,...,n$. $S_i\equiv \{s_{i1},...,s_{iJ}\}$ is the set of actions of player $i$. $S\equiv \times_{i=1}...
2 votes
1 answer
64 views

Is the following claim written with the right way?

I have a simple question though confusio for me. In game theory we usully write thet a strategy is a mapping from the set of types $T$ to the simplex set of actions (refering to mixed mixed strategies)...
3 votes
0 answers
139 views

Extension of Harsanyi Transform for Two-sided Incomplete Information Games to Beliefs with Zero Probability

In the textbook I'm reading "Game Theory - Giacomo Bonanno", one requirement to applying the Harsanyi transform to convert a two-sided incomplete information game to an imperfect information ...
1 vote
1 answer
173 views

Why does the belief over information sets with probability zero matter in Perfect Bayesian Equilibrium?

I'm struggling to understand why the notion of "belief revision" is an important concept. In particular, why does the belief over information sets with probability zero matter? When ...
4 votes
1 answer
69 views

Equivalence from correlated/communication equilibrium to Nash Equilibrium?

Taking into account the seminal papers of Forges and Imre Bárány, they proove a very strong result that gives an exact connection among the communication and the correlation equilibrium solution ...
4 votes
1 answer
595 views

What is the intuition behind Blackwell's Equivalence Theorem on Information Structures?

Let us suppose that we have a Bayesian game where the information structure is defined to be as $P^X=\{(X,\mathcal{X},P_\theta)\}_{\theta\in\Theta}$ where a signal generated by the information ...
8 votes
1 answer
160 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 $0$,...