# Tag Info

25

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 ...

6

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 ...

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

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 ...

1

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 ...

1

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 ...

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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 ...

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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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