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.
152 questions
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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). ...
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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....
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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:
...
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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 ...
CommunityBot
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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, ...
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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 ...
CommunityBot
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Blackwell's ordering and the algebraic structure of Blackwell's experiments in a book
I was reading an article in econometrica about Bayesain persuasion. The mathematics behind the proofs, all these techical definitions and lemma's in the appendicies made me wonder if there exeists any ...
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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 ...
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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 ...
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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 ...
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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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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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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?
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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 ...
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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 ...
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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 \...
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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 $N$ (...
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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 ...
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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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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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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 ...
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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 ...
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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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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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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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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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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 ...
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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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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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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 ...
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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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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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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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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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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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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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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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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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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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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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