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 :
Suppose that after you graduate you have two options when applying for a position at a firm: You can either use your undergraduate diploma or pursue graduate studies for two years and receive an MA diploma and send it as part of your application. Your skill level is either High or Low. You learn your skill level but the employer does not know your skill level. The employer only knows that your it is High with probability 1/4. After you learn your type you either apply for the job with your undergraduate diploma or get an MA degree and apply with master’s diploma. Thus you have two possible messages. You already have a BA degree, so its cost is zero. The cost of MA degree is 2 if you are High type and 5 if you are Low type. The employer, observing the message you send but not your type, decides what kind of job to offer you. There are two possible jobs: job1 pays 10 and job2 pays 6. The net payoff of the employer is 10 if you are High type and employed at job1, 5 if you are High type and employed at job2, 0 if you are Low type and employed at job1, and 3 if you are Low type and employed at job2. Is this game a cheap talk game?
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