Adeline and Bani are a team in a consulting firm. Once a task is assigned, Adeline first decides whether to work separately (S) or work together (T). Subsequently, Adeline and Bani choose their effort levels. We assume that effort choices are made separately but simultaneously. 1 Let ea and eb denote the level of effort exerted by Adeline and Bani respectively where ei{0,1} and i=a,b. If Adeline chooses S, each individual i 's payoff is Ui=2ei+ejei If Adeline chooses TUi=vmin{ei,ej}ei where i,j{a,b} but j=i2 and min{ei,ej}=ei(ej) if ei(>)ej. Assume v equals the largest digit in your student ID. (i) (2 marks) Suppose Adeline chooses S. Consider the subgame associated with that choice (i.e. the one that arise following S ). - Write the corresponding payoff matrix. - Identify all pure strategy Nash equilibria. - Is there a Nash equilibrium in mixed strategies where at least one player chooses both effort levels with strictly positive probability? Explain. (ii) (2 marks) Suppose Adeline chooses T. Consider the subgame associated with that choice (i.e. the one that arise following T ) and answer the three questions stated in part (i). (iii) (2 marks) Now consider the entire game - Identify a pure strategy profile that is a Subgame Perfect Nash equilbrium (SPNE). Explain why it is SPNE. - Identify a pure strategy profile that is a Nash equilbrium (NE) but not SPNE. Explain why it is a NE but not SPNE..

1. Adeline and Bani are a team in a consulting firm. Once a task is assigned, Adeline first decides
whether to work separately (S) or work together (T). Subsequently, Adeline and Bani choose
their effort levels. We assume that effort choices are made separately but simultaneously. 1 Let
ea and eb denote the level of effort exerted by Adeline and Bani respectively where ei{0,1} and
i=a,b. If Adeline chooses S, each individual i 's payoff is Ui=2ei+ejei If Adeline chooses
TUi=vmin{ei,ej}ei where i,j{a,b} but j=i2 and min{ei,ej}=ei(ej) if ei(>)ej. Assume v equals the
largest digit in your student ID. (i) (2 marks) Suppose Adeline chooses S. Consider the subgame
associated with that choice (i.e. the one that arise following S ). - Write the corresponding payoff
matrix. - Identify all pure strategy Nash equilibria. - Is there a Nash equilibrium in mixed
strategies where at least one player chooses both effort levels with strictly positive probability?
Explain. (ii) (2 marks) Suppose Adeline chooses T. Consider the subgame associated with that
choice (i.e. the one that arise following T ) and answer the three questions stated in part (i). (iii)
(2 marks) Now consider the entire game - Identify a pure strategy profile that is a Subgame
Perfect Nash equilbrium (SPNE). Explain why it is SPNE. - Identify a pure strategy profile that
is a Nash equilbrium (NE) but not SPNE. Explain why it is a NE but not SPNE.