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A concise, completely informal way of putting it is this: The intuitive criterion rules-out any out-of-equilibrium beliefs that can only be correct if some player did something stupid. Below is a slightly more long-winded explanation with an informal example. In many signalling games (that is, games in which one player—the sender—can communicate information ...


7

I don't believe those two terms are used in the same spheres. To me, an economic theorist, signaling plays a role in models with asymmetric information when the informed party moves first and the uninformed player reacts, treating the first action as a signal about the private information. This idea goes back to Spence, and also plays a role in biology with ...


7

Here's a simple model to complement my less formal answer: A worker is of (privately known) type $H$ or $L$, each with probability $1/2$. The marginal product of the two types is $\pi_H>\pi_L$. The labour market is competitive so that workers are paid their (expected) marginal product. The worker can invest in education; doing so costs type $i$ $c_i$, ...


5

A comment on the number of players in signaling games in general. Signaling games need not have only two players. In the cheap talk literature, there are papers that study signaling games with multiple informed senders and one uninformed receiver (e.g. Krishna & Morgan, 2001), or one informed sender with multiple uninformed receivers (e.g. Farrel and ...


5

I'm not sure what exactly you're looking for, but here are some wild guesses: Bolton and Dewatripont (2005) Contract Theory, MIT Press. [Probably Chapters 5 and 6] Maskin and Tirole (1990) "The Principal-Agent Relationship with an Informed Principal: The Case of Private Values", Econometrica 58: 379-409. Maskin and Tirole (1992) "The ...


5

In my interpretation of the model, competitive firms imply that the wage always equals the expected productivity, which depends on the beliefs. Clearly, in any pooling equilibrium the on-path beliefs are equal to the prior such that the wage is simply $E[\theta]$. If, in your example, a worker sends the off-path messags $e=1$, the wage must be $w(e=1)=w_1=...


4

Contracting with an informed principal is not so easy because the agent can learn about the principal's type from the kind of contract offered. This introduces signaling, which can quickly get messy. The other answer already mentioned the three seminal papers in that literature. I think Myerson's paper fits best for your goal to understand moral hazard with ...


4

Responding to OP's comment For the babbling equilibrium, it's important to note that how S randomizes over his messages matters. In particular, the messages should be randomized in the same way across all states. For example, if S sends messages $\{o, g, m\}$ with probabilities $(p,q,r)$ (where $p,q,r\in(0,1)$ and $p+q+r=1$) when the state is $o$, he needs ...


4

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)=\mu_2(b\mid y)=\frac12. \end{equation} The second class is not sequential, but weak perfect Bayesian: \begin{equation} (s_1,s_2)=(x,l) \end{equation} and the ...


4

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 players make their moves. Such games do not have proper subgames because a proper subgame never splits up an information set and Nature's first move connects the ...


4

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 receiver $r$ and sender $s$ if and only if it is a SE (sequential equilibrium). Proof: SE $\implies$ WPBE is trivial since SEs are PBEs by construction, and thus are ...


4

I once wrote an example of Kreps criterion using the canonical signaling model and The Simpsons. I think it goes along the same lines as @Ubiquitous' answer while being much less precise and general. But I thought the Simpsons' context might help in a pedagogical setting. Suppose that Hank Scorpio must decide of a wage schedule for employees at Globex ...


3

Perhaps I have a counterexample! Let there be three messages, $m_1, m_2,$ and $m_3$, and three sender types $t_1,t_2,t_3$ where $\Pr(t=t_3)=\frac{1}{2}-\epsilon$, $\Pr(t=t_2)=\frac{1}{4}$ and $\Pr(t=t_1)=\frac{1}{4}+\epsilon$. Sending $m_3$ results in a payoff $0$ for senders, we can think of it as exiting the game. The set of receiver responses to a ...


3

I think this cannot happen with risk averse senders, risk neutral receiver, and $A$ rich enough. For example, and to stick to the canonical signaling model, suppose that $A$ is the positive real line and senders' utility $u$ is increasing in $a$ while receiver's have linear utility decreasing in $a$. (Admittedly, this is only a partial answer as the ...


3

Signaling games (games in which an informed "sender" moves first and an uninformed "receiver" second) typically have a plethora of Perfect Bayesian Equilibria which is not really appealing in terms of predictive power. However, as you already said, some equilibria may be "unreasonable". Refinements serve the purpose to formalize which of these equilibria are ...


2

There are many refinements of pooling equilibria. For starters, you want to make sure all your equilibria are Perfect Bayesian Equilibria. After that, you can also require any equilibrium to survive the intuitive criterion or other forms of forward induction. Lastly, you could also require things like efficiency or symmetry. The choice of refinements is ...


2

From the perspective of the buyer, he is receiving 1 two-dimensional signal. After observing a combination of the wholesale price and limit order, the buyer can update their beliefs about the supplier's capacity using Bayes rule. Let me show it: Let $c\in [0,1]$ be the supplier's capacity (just for simplicity of notation I assumed it is in the interval from ...


2

Both of these criteria refine equilibria where there is an unused message or action. Notice that if there is one action that is not used by any of the types, it can be either because they are all pooling on some other action, or because they are all separating, but there are more actions than types, or anything in between (for example some types are pooling ...


2

This is a common source of misunderstanding with regards to the concept of equilibrium. The specification of an equilibrium (at least in the standard theory of a one shot games) is agnostic about how the players figured out they are in that equilibrium, and, by definition, assumes players know the ex-ante strategies of their opponents. We do not need the ...


2

In signaling games, beliefs as well as strategies constitute an equilibrium. In other words, beliefs are a part of the equilibrium object. By deciding which equilibrium to focus on, you also (partially) determines the beliefs consistent with that equilibrium. The key restriction is that beliefs be derived from Bayes' rule using sender's strategy and the ...


2

The difference between signaling and screening stems from the fundamental difference in bargaining power- who offers the contract for which her utility is the highest. While in screening the uniformed party proposes the contracts, in signaling it is the informed party. For your general conjecture, I refer to Stiglitz and Weiss (1990): "Sorting Out the ...


2

Given that $T^i$ is $i's$ finite set of messages and the mechanism uses the signal function to map $T$ to a signal, the architects of the mechanism can use any arbitrary label for the individual messages. In simple game theoretical examples, the strategies of player 1 are often denoted $a_1,a_2...$ This does not tell us anything about what player 1 is ...


2

We cannot judge if your answer is correct because we don't see the game tree. First, I would not say that "we can rule out this equlibrium as a possible pooling PBE by the intuitive criterion" because the intuitive criterion is simply a refinement. The PBE is still an equilibrium - it's just that we can say that it appears "unreasonable" ...


2

First, you also have to check all possible separating equilibria. You only checked (MSc,BSc), not (BSc,MSc) with all possible reactions of the receiver. No separating equilibrium exists here. The pooling eq you find is correct. There is no pooling eq in which both types play MSc. The intuitive criterion is a refinement to rule out "unreasonable" ...


2

As suggested in the comments, there are many different signaling models with firms and workers, and also what is the "standard model" to differnt people differs in details. In most of those models, however, a firm does not make a profit in any equilibrium as the wage is equal to the expected productivity. In any separating equilibrium, the wage of ...


1

Can there be a PBE in which both types do not get any education (i.e. $e=0$ for both)? Yes, workers' strategies $e^*(\theta_L)=e^*(\theta_H)=0$ and a wage function $w^*(e)$ satisfying: (i) $w^*(0)=E[\theta]$ and (ii) for all $e\ge0$, $w^*(e)$ is no higher than $u_H^0$ --- the high-type's indifference curve crossing point $(0,E[\theta])$ --- form such a PBE. ...


1

I don't have a copy of Gibbons handy, so I cannot speak to the specific model presented there, but only generally. The intuition of the conclusion is based on the combination of the following factors: Whenever the firm can tell the high and low types apart, it's willing to pay a high wage to high type and a low wage to low type If the firm cannot tell the ...


1

If you have a game where both players are sender and receiver, then there is no asymmetric information and you do not have a signalling game, but a game with uncertainty. There are a lot of these games. E.g. bayesian games, global games etc. These types of games can also handle situations where some players no more about the state of the game than other ...


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