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.
138
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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 ...
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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....
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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 ...
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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 ...
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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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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 ...
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49
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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 , ...
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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. ...
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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 ...
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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 ...
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Question regarding a Bayesian game and the number of proper subgames
I have to find all Nash and subgame perfect Nash equilibria of the following Bayesian game:
By writing the whole game in normal form I've been able to find the Nash equilibria which are $(L,L')$ and $...
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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 ...
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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/...
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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 ...
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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 ...
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Perfect Bayesian Nash Equilibrium
Suppose a seller has a product which can be of quality H (high) or quality (L). There is a buyer who values H at (vH) and L at (vL), but can not distinguish between H and L without consuming it. ...
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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 ...
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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 ...
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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 ...
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146
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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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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 ...
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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 ...
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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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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 ...
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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 ...
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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.
...
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83
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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 ...
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111
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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}...
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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)...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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112
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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 ...
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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 ...
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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 ...
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91
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Bayes correlated equilibrium of Bergemann and Morris
The paper of Bergemann and Morris proves a theorem based on some foundations about the information sets and their expansions. I am trying to understand theorem one intuition, more precisely I cite the ...
- 949
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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 ...
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