Question

Group Work Game Setup

• Players: Three students
  • Students are named A, B, and C
• Strategies: Work or shirk
• Payoff: Group grade for the assignment
• Assume: Student A would like an A, student B would like at least a B, and student C would like at least a C
• Payoff will depend on how many of the students work on the project
  • Same skill level is assumed for all players

Outcomes

• If all three players work, they achieve an A
• If any two players work, they achieve a B
• If only one player works, they achieve a C
• If no player works, they get an F
• What is a Nash equilibrium to the game?

Answer 1

No one works is not a nash equilibrium because atleast player C has tendency to deviate and obtain C which is preferred to F.

One players working is not a nash equilibrium because player B has tendency to deviate and to work and obtain B which is preferred to C.

Two players working is not a nash equilibrium because player A has incentive to deviate to work and obtain A which is preferred to B.

Thus the nash equilibrium is one where all three work.