Question
Waitrose and Tesco are quick-delivery shopping apps launched by Woolworths and Checkers, respectively. Each supermarket can decide whether to charge a high price or a
Waitrose and Tesco are quick-delivery shopping apps launched by Woolworths and Checkers, respectively. Each supermarket can decide whether to charge a high price or a low price. This interaction is represented in normal form below, where payoffs represent monthly profits in thousands of dollars.
| Tesco | ||
| High | Low | |
Waitrose | High | 320, 320 | 100, 625 |
Low | 625, 100 | 180, 180 |
2.1 Assume that this interaction is repeated every month forever, and that both supermarkets discount the future at a rate of 6.25% per month. Both supermarkets adopt the Tit-for-Tat
contingent strategy, where they copy the strategy chosen by their opponent in the previous period. Redraw the game table above including a row and column for the contingent strategy.
Showing all calculations, complete the game table with the payoffs that each supermarket will receive under each strategy profile. Hint: Remember that the payoffs received by each supermarket should represent the present value of income streams obtained under a given strategy profile.
2.2 Solve for all the pure strategy Nash equilibria of the game above.
2.3 What type of game are the two supermarkets playing now? Will this new game, including the contingent Tit-for-Tat strategy, help maintain cooperation? Why or why not?
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