Adeline and Bani are a team in a consulting firm. Once a task is assigned, Adeline...
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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. Let ea and en denote the level of effort exerted by Adeline and Bani respectively where e; € (0, 1) and i = a, b. If Adeline chooses S, each individual i's payoff is If Adeline chooses T U₁ = ei + ej - ei. - 2 U₁ = v min{e, ej} - ei, where i, je (a, b) but ji2 and min{e,, ej) = e(ej) if e; ≤ (>)ej. Assume u 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. 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. Let ea and en denote the level of effort exerted by Adeline and Bani respectively where e; € (0, 1) and i = a, b. If Adeline chooses S, each individual i's payoff is If Adeline chooses T U₁ = ei + ej - ei. - 2 U₁ = v min{e, ej} - ei, where i, je (a, b) but ji2 and min{e,, ej) = e(ej) if e; ≤ (>)ej. Assume u 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.
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i If Adeline chooses S the corresponding payoff matrix is Bani chooses eb0 Bani chooses eb1 Adeline ... View the full answer
Related Book For
Practical Management Science
ISBN: 978-1305250901
5th edition
Authors: Wayne L. Winston, Christian Albright
Posted Date:
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