# What conditions characterise “cheap-talk” games

I've looked all over the internet but couldn't find a simple answer. My claim is that if none of the players utility functions depend on the messages being sent, then the game is a cheap talk. Consider this :

We can clearly see that for the employee the messages (whether choosing a MA or BA degree) will have an effect on her payoffs. Therefore I conclude that the game is not cheap talk. But I'm not sure since this kind of games are characterised under cheap talk games, what makes a game cheap talk? How I can explain whether the game above is a cheap talk or not

Your general question is in my opinion far more interesting than the course problem, so I will answer that.

What conditions characterise “cheap-talk” games?

1. As you have noted yourself, the talk needs to be cheap, meaning signals/messages should have no direct effect on the players' utility. Indirect effects are allowed. Even in cheap talk games it is possible that the beliefs of a player are updated by a cheap message, hence his response changes altering the outcome. Simple examples include coordination problems.

2. A second necessary condition is that all messages are available to all types. hence there are no type specific message spaces $M_i$, only a shared message space $M$ from which all types of the sender can freely choose their message. Without this, a signal, though costless, could carry information, as certain types are incapable of sending it.

It's a cheap-talk game, so what?

If these two conditions are met then the game is a cheap-talk game. Why is that important?

Let us call a version of the cheap-talk game where we leave out the signal round the simple variant. For any equilibrium of the simple variant there is a payoff equivalent equilibrium of the cheap-talk game. Similarly, for any equilibrium of the cheap-talk game there is a payoff equivalent equilibrium of the simple variant. Hence it seems that the ability to signal did not fundamentally alter the set of equilibrium outcomes. The reason for this is that the signal did not carry any information, as it was easily imitable by other types, it was 'cheap'.

• How can I make a distinction between direct/indirect effect of messages on the outcomes? For instance I believe in the game I gave as an example would have a direct effect. – Xenidia May 21 '17 at 10:16
• Not sure what you mean by "effect of messages on the outcomes". If message $m$ has a direct effect on a player's utility then the utility function has $m$ among its variables. – Giskard May 21 '17 at 10:25
• I see, an approach towards my question would have made everything clear. – Xenidia May 21 '17 at 14:07
• @Xenidia I am sorry but I do not understand your comment. – Giskard May 21 '17 at 15:54