All Questions
Tagged with bayesian-game game-theory
131 questions
0
votes
2
answers
62
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finding BNE: when the player with no private information has strictly dominating strategies
I'm solving this question, where I'm supposed to find all the BNE for the following game. There are two players, 1 and 2, where 1 has type a and b, and 2 has just one type (so no private information). ...
2
votes
1
answer
136
views
Bayesian form games, situations in real life for which having more information is not necessarily better
I was given these two bimatrices, for two different versions of a Bayesian-form game.
In the first version of the game, a player named The Nature chooses between $A$ or $B$ with probability $1/2$ each....
1
vote
1
answer
140
views
Incomplete information bidding game with cutoff strategies
I have tried solving a question from Watson's book "Strategy" and my answer doesn't match with the solutions provided online. I am unable to figure out why. Please help.
The question:
...
- 119
2
votes
1
answer
112
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Proving Truthful bidding is weakly dominant strategy and not just very weakly dominant strategy in second price sealed bid auction
In most books on auction theory, it is left as exercise to prove that the truthful strategy $s_{i} = v_i$ is a weakly dominant strategy and not a very weakly dominant strategy. To eliminate confusion, ...
- 85
3
votes
0
answers
69
views
How could define the certainty equivalent in a Bayesian Persuasion model?
For once again I will start describing the Kamenica and Gentzkow Bayesian persuasion model.
Suppose that $\Theta$ is a finite set of states and $\theta$ is the element of the state set. To simplify ...
- 440
0
votes
0
answers
37
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 ...
0
votes
0
answers
20
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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 ...
5
votes
1
answer
122
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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 ...
- 505
4
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0
answers
56
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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
63
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 ...
- 440
0
votes
1
answer
116
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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 ...
- 1
1
vote
0
answers
59
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 ...
- 440
2
votes
0
answers
84
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 $N$ (...
- 440
1
vote
2
answers
132
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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 \...
- 440
2
votes
1
answer
75
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 ...
- 440
0
votes
1
answer
95
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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 ...
- 505
1
vote
0
answers
90
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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 ...
- 440
1
vote
1
answer
96
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....
- 113
2
votes
0
answers
55
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 ...
- 21
1
vote
1
answer
454
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
2
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0
answers
31
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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 ...
- 440
0
votes
0
answers
98
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 ...
- 440
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 , ...
1
vote
0
answers
56
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 ...
- 141
1
vote
0
answers
22
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 ...
- 440
1
vote
1
answer
207
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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 ...
- 440
3
votes
0
answers
73
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/...
- 440
1
vote
0
answers
241
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 ...
- 888
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 ...
- 440
5
votes
2
answers
133
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 ...
- 378
3
votes
0
answers
45
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 ...
- 888
1
vote
0
answers
159
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 ...
- 192
0
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0
answers
189
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 ...
- 51
2
votes
0
answers
97
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 ...
- 43
1
vote
0
answers
81
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 ...
- 43
0
votes
1
answer
49
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 ...
- 969
2
votes
1
answer
78
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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.
...
- 46
4
votes
0
answers
106
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 ...
- 83
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}...
- 378
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)...
- 969
3
votes
0
answers
175
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 ...
- 83
1
vote
1
answer
197
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 ...
- 83
4
votes
1
answer
70
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 ...
- 969
4
votes
1
answer
809
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 ...
- 969
2
votes
1
answer
1k
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 ...
1
vote
0
answers
41
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 ...
- 135
4
votes
1
answer
71
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 ...
- 969
1
vote
0
answers
40
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 ...
- 969
2
votes
0
answers
30
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 ...
- 969
3
votes
1
answer
73
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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 ...
- 969