Repeated Games II
Week 2
Repeated Games II Backward Induction
Backward Induction
Can be used to analyse repeated games with finite repetitions
Process of reasoning backwards in time: • First consider the last stage of a game and determine the best action at that time • With this information, determine what to do in the penultimate stage • Continue until the best strategy for every stage of the game is found
Street Lights Recap
Installation takes 5 months, every month 100 street lights can be manufactured and installed
The contractor threatens the organizing committee:
If the organizing committee renegotiates the price in one month, they will deliver low quality in all subsequent months
The organizing committee threatens the contractor:
If the contractor delivers low quality in one month, they will renegotiate the price in all subsequent months
Payoffs in Month 5 Last month of interaction: No threat of retaliation in subsequent period
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Payoffs in Month 4 No cooperation in month 5 in any case: Threat of retaliation not credible
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Payoffs in Month 3 No cooperation in months 4 and 5 in any case: Threat of retaliation not credible
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Payoffs in Month 1 No cooperation in months 2 to 5 in any case: Threat of retaliation not credible
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Summary
Following backward induction • The contractor will deliver low quality in all months • The organizing committee will always renegotiate a lower price
The outcome is triggered by the fact that in the last stage of the game there is no further threat of retaliation
Endgame effect
This holds for any prisoners‘ dilemma with finite repetitions
Competitive Strategy Tobias Kretschmer Professor of Management, LMU Munich
© 2013 LMU Munich
Repeated Games II Backward Induction
Backward Induction
Can be used to analyse repeated games with finite repetitions
Process of reasoning backwards in time: • First consider the last stage of a game and determine the best action at that time • With this information, determine what to do in the penultimate stage • Continue until the best strategy for every stage of the game is found
Street Lights Recap
Installation takes 5 months, every month 100 street lights can be manufactured and installed
The contractor threatens the organizing committee:
If the organizing committee renegotiates the price in one month, they will deliver low quality in all subsequent months
The organizing committee threatens the contractor:
If the contractor delivers low quality in one month, they will renegotiate the price in all subsequent months
Payoffs in Month 5 Last month of interaction: No threat of retaliation in subsequent period
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Payoffs in Month 4 No cooperation in month 5 in any case: Threat of retaliation not credible
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Payoffs in Month 3 No cooperation in months 4 and 5 in any case: Threat of retaliation not credible
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Payoffs in Month 1 No cooperation in months 2 to 5 in any case: Threat of retaliation not credible
Contractror
Organizing Committee Accept price
Renegotiate price
High quality
£15,000 / £15,000
£5,000 / £25,000
Low quality
£18,000 / £0
£8,000 / £10,000
Summary
Following backward induction • The contractor will deliver low quality in all months • The organizing committee will always renegotiate a lower price
The outcome is triggered by the fact that in the last stage of the game there is no further threat of retaliation
Endgame effect
This holds for any prisoners‘ dilemma with finite repetitions
Competitive Strategy Tobias Kretschmer Professor of Management, LMU Munich
© 2013 LMU Munich
