# 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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### 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
43 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....
41 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
119 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 ...
21 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 ...
28 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
49 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 , ...
18 views

### PBE solution strategy

I am not comfortable with dynamic games of incomplete info. I am trying to solve the example at https://pubs.aeaweb.org/doi/pdfplus/10.1257/jel.54.2.442 , but can't even come up with a good strategy. ...
1 vote
33 views

### 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
17 views

### 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 ...
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62 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)...
109 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
147 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 ...
67 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 ...
323 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 ...
507 views

### Sequential and Perfect Bayesian Equilibrium: an example?

My question is quite simple. Could someone given an example of how to determine a Sequential Equilibrium given a set of Perfect Bayesian Equilibria? The definition of sequential equilibrium where ...
35 views

### Is playing against state of nature considered Stochastic game or Bayesian game?

Say if there is a team of gamblers betting on stock exchange. We can model the outcome of stock exchange as state of nature, because it is not deterministic. So the objective of team of gamblers is to ...
1 vote
31 views

### What is the difference between Partially Observable and Incomplete information in Game theory

In reference to this paper that discusses Partially Observable Stochastic Game, it also mentions of Bayesian Game which is characterized by incomplete information. Rather then pointing out the ...
65 views

### Correlation device that induces a specific transition probability

Taking a look at this paper of Forges and Vida the authors define a correlation device in page $102$, that is a standard probability space $\left(\Omega,\mathcal{B},\mu\right)$, They assume that the ...
1 vote
37 views

### What if Bergemann and Morris setting used mixed (or bbehavioral) actions instead of pure actions as reccomendations?

Once again, I will refer to the setting of Bergemann and Morris (2016) and write here the payoff formula of player $i$ from the perspective of the information designer. The payoff formula is the ...
25 views

### Pre-play, interim-play, intra-play communication games

I have a question that seems easy but I want some clarification. Suppose that we have a communication Bayesian game. The game starts when the players learn their prior infornation and after this they ...
63 views

### Bergemann and Morris information designer and decision rule concept

Taking a look in the paper of Bergemman and Morris in 2016, they refer to the desicion rule as mapping $$\sigma:\Theta\times T\to\Delta(A)$$ The explanation to understand the notion of it is given as ...
51 views

### Repeated Games of Incomplete information set up and questions

The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration). The preliminaries of the model Formally, a repeated game with incomplete information is given by the ...
1 vote
39 views

### How to define a dynamic programming problem in an incomplete information game?

How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
201 views

### How to analyze this two-player, imcomplete-information, extensive-form game?

Game tree: Note that the information sets for player 1 are represented by red dotted lines, while the information sets for player 2 are represented by blue shaded tapes. Described in words, the game ...
784 views

### Is it a weakly dominant strategy to bid your true value in a third-price auction with two identical goods and N uniform distributed bidders?

I am interest in finding the optimal strategy for a single bidder (the BNE), when I have a third-price auction with N bidders and two identical goods. The bidders have iid valuations: U(0,1) I have ...
1 vote
33 views

### What is the difference between a communication mechanism and a protocol of communication?

What is the difference between a communication mechanism and a protocol of communication in mechanism and information design. Although most papers in the literature make this distinction, it is not ...
1 vote
112 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 ...
1 vote
48 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 ...
1 vote
1k 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 ...
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 ...