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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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Uniqueness of equilibria in first-price auction with discrete valuations

Assume we have a first-price auction with discrete and independent private values and identical distributions of all bidders. It is known that there exists a Bayes-Nash equilibrium where bidders bid ...
AlexanderJI's user avatar
3 votes
0 answers
60 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/...
Oliver Queen's user avatar
3 votes
0 answers
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 ...
afreelunch's user avatar
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}...
Star's user avatar
  • 446
3 votes
0 answers
142 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 ...
oswinso's user avatar
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3 votes
0 answers
89 views

Perfect Bayesian Equilibrium for banks

I'm reading this paper on credit lending cycles and trying to understand how it works for the case of one bank. This is the set-up of the model: There are two players, a bank and the market. There ...
Meera Unni's user avatar
2 votes
3 answers
364 views

The concept of information structure in incomplete information games

I would like your help to understand the concept of information structure in the incomplete information game at p.6-7 of this paper. Let me summarise the game as described in the paper. There are $...
Star's user avatar
  • 446
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)...
Hunger Learn's user avatar
2 votes
1 answer
132 views

I cannot understand Sobel & Crawford 1982 (cheap talk)

I am a master student, currently reading this paper for fun during the break. I got lost during the part $U^S(\bar y, \bar m, b) = \max_{y \in Y} U^S(y,\bar m, b)$ on page 5. I dont understand why ...
Aspiring Economist's user avatar
2 votes
2 answers
105 views

Information and search

Consider a game where a decision maker (DM) has to choose action $l\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The choice set $\mathcal{Y}$ has cardinality $L$....
Star's user avatar
  • 446
2 votes
1 answer
4k views

Finding Bayesian Nash Equilibrium

I'm recently new to Game Theory and I've recently started teaching myself about Bayesian Nash Equilibirum. I've stumbled across a problem set that I can't seem to wrap my head around concerning ...
Lundu Chibwa's user avatar
2 votes
1 answer
323 views

Alternative way to calculate the symmetric BNE of the game

My problem. Consider the following auction for a single object. There are $n \geq 2$ bidders. They submit their bids simultaneously. The object is allocated to the player who submits the largest bid. ...
DanIsabel's user avatar
2 votes
2 answers
743 views

Pure-Strategy Bayesian Nash equilibrium with general common prior

I'm doing a problem set on the subject of Bayesian Nash equilibrium. I'm asked to find the pure-strategy BNE of the following. I've calculated to matrix shown below. My first concern is if I've ...
Justin Malik's user avatar
2 votes
1 answer
1k views

Bayesian Nash Equilibria in Battle of Sexes

Consider the static Bayesian game as described below. $\ t_1$ and $\ 𝑡_2$ are the types of the row and column player respectively, which are both uniformly distributed on the interval $[0,1]$. The ...
Student's user avatar
  • 352
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. ...
Fulcanelli's user avatar
2 votes
1 answer
912 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 ...
Econometric Novice's user avatar
2 votes
1 answer
471 views

Find a separating perfect Bayesian equilibrium

Exercise Question 2, Chapter 28, Strategy: An Introduction to Game Theory 3rd Edition by Joel Watson In part (a) of the question, we have to check if any separating perfect Bayesian equilibrium ...
ryan1's user avatar
  • 123
2 votes
1 answer
96 views

Clarification on the definition of Bayes Correlated Equilibrium

I would like your help to understand the definition of Bayes Correlated Equilibrium (BCE) in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper....
Star's user avatar
  • 446
2 votes
1 answer
42 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 ...
user0193's user avatar
  • 135
2 votes
1 answer
71 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 ...
Oliver Queen's user avatar
2 votes
1 answer
489 views

Pooling equilibrium in akerlof's lemon market with certification cost

Consider a market for 300 used cars where 1/3 of all cars are good quality cars and the rest are bad quality cars. All these cars are owned by (potential) sellers to begin with and each seller owns ...
Deepanshu Yadav's user avatar
2 votes
1 answer
58 views

Implications of the concepts of combination/expansion of an information structure

I would like your help to understand the concept of combination/expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in ...
Star's user avatar
  • 446
2 votes
1 answer
383 views

Mixed Strategies in Bayesian Games

I am confused about the following statement from Wikipedia: "A mixed strategy is an assignment of a probability to each pure strategy. This allows for a player to randomly select a pure strategy. ...
johnny09's user avatar
  • 613
2 votes
0 answers
68 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 $N$ (...
Oliver Queen's user avatar
2 votes
0 answers
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 ...
xyz's user avatar
  • 21
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 ...
Oliver Queen's user avatar
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 ...
Oliver Queen's user avatar
2 votes
0 answers
81 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 ...
studen21's user avatar
2 votes
0 answers
27 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 ...
Hunger Learn's user avatar
2 votes
0 answers
58 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 ...
Hunger Learn's user avatar
2 votes
0 answers
267 views

Bayes Nash Equilibrium in a game with continuous actions

I am attempting to think through a particular type of game with continuous strategies, with Bayes Nash equilibrium as the solution concept. I first describe the game below, followed by questions. ...
saturno's user avatar
  • 88
2 votes
0 answers
354 views

A Perfect Bayesian Bargaining problem

Thought I'd post interesting questions that come my way to try and boost activity! A seller and a buyer negotiate over trade of a single indivisible good. The good is either of low quality (in which ...
Brian's user avatar
  • 431
2 votes
0 answers
67 views

How this ex ante game induce a uniform distribution for interim stage?

In an article (see here) from the blog leisure of theory class, it is shown, in an interim stage for a Baysian game, we could run into a technical problem that the induced belief space for a player ...
Metta World Peace's user avatar
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 ...
smug-face's user avatar
1 vote
1 answer
176 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 ...
oswinso's user avatar
  • 83
1 vote
1 answer
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 ...
afreelunch's user avatar
1 vote
2 answers
99 views

Rule for Number of Strategies in Bayesian Games

Is there a general rule for finding the number of strategies (denote as $S$) for each player in a Bayesian game? I think it's related to the number of types (denote as $T$) and the number of actions (...
Wivaviw's user avatar
  • 23
1 vote
1 answer
158 views

Strong sequential equilibria and the existence of others

I am working on the following game and I have to find all strong sequential equilibria here. I determined that here any belief derived from a fully mixed strategy gives a distribution (1/2, 1/2) over ...
Rodger Haggings's user avatar
1 vote
1 answer
70 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 ...
morteza bigdeli's user avatar
1 vote
1 answer
543 views

Exchange Houses game - Bayesian Game

Can anyone help me understand how to solve this type of asymmetric information Bayesian game? So the game is a different version of the Tadelis 'trading house games'. It involves 2 players that each ...
peninette's user avatar
1 vote
1 answer
194 views

Find a perfect Bayesian equilibrium

Each of two sellers, $1$ and $2$ owns one indivisible object that a buyer would like to buy. The two objects are identical. The buyer´s valuation depends on the number of objects he gets. The ...
crosscut22's user avatar
1 vote
2 answers
124 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 \...
Oliver Queen's user avatar
1 vote
1 answer
54 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 ...
coderDcoder's user avatar
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....
autodidacti's user avatar
1 vote
1 answer
342 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 ...
Hssktr's user avatar
  • 21
1 vote
1 answer
118 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 ...
Hunger Learn's user avatar
1 vote
1 answer
1k views

Simultaneous vs Sequential Games [closed]

Is there a way to characterize the distinction between simultaneous vs sequential games? I'm trying to describe a situation where players can only take actions without knowledge of other players' ...
carlogambino's user avatar
1 vote
1 answer
125 views

Set of Bayes Correlated Equilibria when complete information is not available

Model Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. The state of the world has support $\mathcal{...
Star's user avatar
  • 446
1 vote
1 answer
171 views

Algorithm to find Bayesian Nash Equilibria [closed]

I am working on a Bayesian game with a finite number of players and discrete types, but the complexity of the equations is not allowing me to find the BNEs by hand. I read a paper describing ...
Ishan Kashyap Hazarika's user avatar
1 vote
1 answer
579 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 ...
Vee's user avatar
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