Final answer:
A perfect Bayesian equilibrium (PBE) is a refinement of the concept of Nash equilibrium. In a pooling equilibrium, both high-skilled and low-skilled individuals might choose to pursue the same job or career path, leading to a lack of distinction between the two types refers to pure-strategy pooling.
Step-by-step explanation:
In game theory, a perfect Bayesian equilibrium (PBE) is a refinement of the concept of Nash equilibrium. It is a strategy profile in which players' strategies not only result in a Nash equilibrium, but also satisfy beliefs held by each player about the actions of the other players.
In the given scenario, the question refers to pure-strategy pooling and separating equilibria. In a pooling equilibrium, all players choose the same action, regardless of their type. In a separating equilibrium, players with different types choose different actions. To identify the pure-strategy pooling and separating equilibria, you would need additional information about the scenario.
Your full question was
Scenario:
In a pooling equilibrium, both high-skilled and low-skilled individuals might choose to pursue the same job or career path, leading to a lack of distinction between the two types. For instance:
Suppose both high-skilled (H) and low-skilled (L) individuals choose to apply for entry-level positions or jobs that don't differentiate between their skill levels. They both apply for the same roles, leading to a lack of distinction between the two groups.
Employers, lacking information or means to differentiate between high and low skill, treat all candidates equally, offering similar job roles or salaries. This results in a pooling equilibrium where both skill types end up in the same positions or careers.
Identify (and state) all pure-strategy pooling and separating perfect Bayesian equilibria in the given scenario.