Bayesian Game - Signalling

Signalling

Signalling games constitute an example of Bayesian games. In such a game, the informed party (the “agent”) knows their type, whereas the uninformed party (the “principal”) does not know the (agent’s) type. In some such games, it is possible for the principal to deduce the agent's type based on the actions the agent takes (in the form of a signal sent to the principal) in what is known as a “separating equilibrium”.

A specific example of a signalling game is a model of the job market. The players are the applicant (agent) and the employer (principal). There are two types of applicant, skilled and unskilled. The employer does not know which the applicant is, but he does know that 90% of applicants are unskilled and 10% are skilled (type 'skilled' has a probability of 0.1 and type 'unskilled' has a 0.9 probability).

The employer's action space is the set of natural numbers, representing wages—these are used to form a contract based on how productive the applicant is expected to be. Paying larger wages to skilled workers will generate larger payoffs for employers, while wages given to unskilled workers will have a less pronounced effect. The payoff of the employer is determined thus by the skill of the applicant (if the applicant accepts a contract) and the wage paid. Crucially, the employer chooses his or her action (the wage offered) according to his or her belief as to how skilled the applicant is and this belief is largely determined through signals sent by the applicant.

The applicant's action space consists of two actions: either obtain a university education or abstain from university. It is less costly for a skilled worker to obtain an education, as he or she may receive scholarships, find classes less taxing, and so on. University education therefore serves as a signal, a means with which the applicant may communicate to the employer that he or she is, in fact, skilled.

One strategy the employer may use is to give all applicants a wage such that skilled applicants may attend university (due to its lower cost) but which is insufficient to provide university education for unskilled applicants. This creates a separating equilibrium: skilled applicants can now signify their skill by going to university, and unskilled applicants cannot. The employer can observe which workers are able to go to university, and can then maximize his or her payoff by providing high wages to skilled workers and low wages to unskilled.