# 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 ...
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/...
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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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### 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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### 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 ...
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### 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 $L$....
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### 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 ...
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. ...
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 ...
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### 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 ...
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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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### 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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### 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 ...
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### 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....
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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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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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### 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 ...
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### 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 ...
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### 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. ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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. ...
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### 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 ...
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### 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 ...
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1 vote
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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 ...
1 vote
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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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### 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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1 vote
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### 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 (...
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### 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 ...
1 vote
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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 ...
1 vote
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 ...
1 vote
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### 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 ...
1 vote
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