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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 ...
Herr K.'s user avatar
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6 votes
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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 ...
Giskard's user avatar
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6 votes
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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 ...
Bayesian's user avatar
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6 votes
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Adverse selection problem

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 ...
Herr K.'s user avatar
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6 votes
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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 ...
tdm's user avatar
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5 votes
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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 ...
Regio's user avatar
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5 votes
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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 ...
Regio's user avatar
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5 votes
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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 ...
Herr K.'s user avatar
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5 votes
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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 ...
Ubiquitous's user avatar
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5 votes
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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 ...
Regio's user avatar
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5 votes

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 ...
Herr K.'s user avatar
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5 votes
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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 ...
Michael Greinecker's user avatar
5 votes
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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 ...
Michael Greinecker's user avatar
5 votes
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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 ...
djsteve's user avatar
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5 votes
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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, ...
Walrasian Auctioneer's user avatar
5 votes
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Is the following claim written with the right way?

Would be strange to write it that way. If you had to define something like that, just do the following: Start with a type space $(T,\mu)$ with probability measure $\mu$. Let $\sigma: T \rightarrow \...
Walrasian Auctioneer's user avatar
5 votes

In games of Bayesian Persuasion, under what conditions is Receiver better off than under uninformative signals?

A receiver can always ignore any additional information and do what they would have done in the absence of informative signals. If they react optimally, they can therefore never be worse off. It is a ...
Michael Greinecker's user avatar
4 votes
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Game theory with rational and irrational players

Yes, a whole book has been written on Behavioral Game Theory. More specifically, standard solution concept such as Nash equilibrium requires that players best respond to a correct belief about other ...
Herr K.'s user avatar
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4 votes
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Bayesian game and the set of types

Sure. In the two type case there is an alternate solution that is frequently used. If $a \neq c$ and $b \neq d$, that is the types are really different in both attributes, then you can define a ...
Giskard's user avatar
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4 votes
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Are there multiple equilibria in the second price auction?

Sure. An example: if both valuations are drawn from the $[0,1]$ interval then the strategies $$ b_1(v_1) = v_1 $$ and $$ b_2(v_2) = \left\{\begin{array}{cc} v_2 & \text{ if } v_2 < 1 \\ 5 & ...
Giskard's user avatar
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4 votes
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Bayesian Nash Equilibria in Battle of Sexes

Yes, you are correct. All types $t_{1}$ choose O (B) and all types $t_{2}$ choose O (B) are both Bayesian equilibria. Note that there are other Bayesian equilibrium in this game, if you are interested ...
Ali's user avatar
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4 votes
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How to prove the WPBE is SE in signaling game?

Claim: If choice sets $T, M,$ and $A$ are finite, then an assessment $\{\beta^*_{r}, \beta^*_{s}, \mu^*\}$ is a WPBE (weak perfect Bayesian equilibrium) of the two-stage signalling game between ...
Kenneth Rios's user avatar
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4 votes

Mixed Strategies in Bayes Nash Equilibrium (Bayesian Battle of the Sexes). Shouldn't it depend on $p$?

Given game also has one pure-strategy Nash equilibrium besides the two you mentioned: Row player plays $C$, Column player (left) plays $C$ and right plays $H$ i.e. $C,H$. Also, when player 1 chooses a ...
Amit's user avatar
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4 votes
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What does 'continuation' as in continuation games, strategies, plays, etc. exactly mean?

Consider a game with private information such as a privately known willingness-to-pay or any other type. We usually model this as a game in which at first "Nature" draws the type and then ...
Bayesian's user avatar
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4 votes
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Strong sequential equilibria and the existence of others

There are three classes of equilibria of this game. The first class is sequential: \begin{equation} (s_1,s_2)=(y,r) \end{equation} and the beliefs are \begin{equation} \mu_1(a)=\mu_1(b)=\mu_2(a\mid y)...
Herr K.'s user avatar
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4 votes

Bayesian Nash Equilibrium in a Duopoly Cournot Competition

If the capacities $q_1$ and $q_2$ are the same, say $\overline{q}$ you can rule out some cases. The best response functions are given by: $$ \begin{align*} \hat q_1 &= \min\left\{\frac{M - (1-\...
tdm's user avatar
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4 votes
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Alternative way to calculate the symmetric BNE of the game

There is another way to compute the symmetric BNE in increasing strategy. Let $U(v)$ denote the expected utility of a player in equilibrium when his type is $v$: Given that the bidding strategy is ...
Lorenzo Castagno's user avatar
4 votes
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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 ...
Michael Greinecker's user avatar
4 votes
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Bergemann and Morris information designer and decision rule concept

Bayes Correlated Equilibrium characterizes (by Theorem 1 in the paper) what can happen in a Bayes Nash Equilibrium in which the players might have more information than is specified in the Bayesian ...
Michael Greinecker's user avatar

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