# Tag Info

Accepted

### Questions of the type "What do you think other people would think?"

Epistemic game theory would be the closest (sub-)field that deals with questions involving higher order beliefs among interacting agents. The introductory article by Dekel and Siniscalchi is a good ...
• 15.4k
Accepted

### Bayesian-Nash equilibrium in a first-price auction

It is actually assumed that $b_i(v_i)$ is of the form $\alpha_i+\beta_i \cdot v_i$. So it is an affine function. Linearity only works if the bottom of the uniform distribution is 0. A somewhat ...
• 29.2k
Accepted

### Why is it called Bayesian Persuasion?

In a standard cheap-talk setting, a sender (S) has better information on a state of the world and wants to communicate this information to a receiver (R) who then takes an action. However, S and R ...
• 5,291
Accepted

Signaling is the informed side taking actions to reduce (or maintain, depending on the private types) the information asymmetry. For example, high skill workers getting certifications to signal their ...
• 15.4k
Accepted

### Difficulty in understanding the notation related from probability theory with game theory

We have that ${\cal I} = ((X^i)_i, \mu)$​ and ${\cal J} = ((Y^i)_i, \nu)$​ are two information structures. An Interpretation mapping for player $i$​​ is a mapping $\phi^i: X^i \to \Delta(Y^i)$​ so it ...
• 12.2k
Accepted

### Bayes Correlated Equilibrium: obedience

To understand the "Obedience" inequality, notice that the player is "integrating out" everything that she is uncertain about, this is why the sum runs over the actions of other players, $a_{-i}$, the ...
• 4,188
Accepted

### Definition of Bayesian Nash equilibrium

Bayesian Nash equilibrium is a set of strategies $\{\sigma_i\}$ one for each player and some beliefs $\{\mu_i\}$ also one for each player such that $\sigma_i$ is a best response for player $i$ given ...
• 4,188
Accepted

### Social Welfare and Pareto Optimality in a Bayesian Game

While it is a bit unusual to describe a strategy profile as being Pareto optimal, especially in the context of Bayesian games, I guess you can still define Pareto optimality in different stages of ...
• 15.4k
Accepted

### Confusion about multiple information Sets

You could represent the game in extensive form like this: The dashed lines enclose player 2's information set. This encompasses all of player 2's nodes because player 2 observes neither nature's nor ...
• 16.9k
Accepted

### Finding Bayesian Nash Equilibrium

The Key to BNE is that players that know something (about the state of the world or their type) can condition their strategies with their information. That is, for example, in question 3, type A could ...
• 4,188

### I cannot understand Sobel & Crawford 1982 (cheap talk)

$U^S(\bar y,\bar m,b)=\max_{y\in Y}U^S(y,\bar m,b)$ is standard notation that says $\bar y$ is the action (taken by receiver) that would maximize sender's utility given message $\bar m$ and bias ...
• 15.4k
Accepted

### When should my beliefs be a martingale?

The expected posterior is the prior. But for this to hold, you have to take the expectation with respect to the prior. In your example, you describe a Bayesian but ev aluate their update with respect ...
• 13.3k
Accepted

### Correlation device that induces a specific transition probability

The common prior $p\in\Delta L$ and the transition probability $q:L\to\Delta A$ induce a joint distribution on $L\times A$ in which the pair $(l,a)$ is selected with probability $p_l\cdot q_l(a)$. You ...
• 13.3k
Accepted

### What is the intuition behind Blackwell's Equivalence Theorem on Information Structures?

To answer the first part of your question, we do not need any more assumptions for the comparison of experiments (besides some measurability issues). Before going on, I'll fix some notations to ones ...
• 66
Accepted

### Why does the belief over information sets with probability zero matter in Perfect Bayesian Equilibrium?

The key is that "since both equilibria satisfy sequential rationality" is no longer true when you consider weak sequential equilibria. Both concepts satisfy sequential rationality on-path, ...
• 1,899
Accepted

Accepted

### Bayes correlated equilibrium of Bergemann and Morris

Suppose you are an analyst studying a Bayesian game. You know the players, the possible states of nature, the common prior, the action spaces, the payoff functions, and you know about some information ...
• 13.3k