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Week 11_Part II_ECON 2101_S1_2010

# Week 11_Part II_ECON 2101_S1_2010 - ECON 2101 SESSION 1...

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ECON 2101, SESSION 1, 2010 GAME THEORY Part II Week 11 Repeated Games (Advanced Material) So far we have focused on single-shot interactions. Players play only once. While this might be relevant for some games, most players play the game repeatedly. Qantas and Virgin realise that each period they compete for price setting. Toyota and Honda understand that the competition among them is not for a week or for month but a more long-term one. First let us look at a simple game, solve for the Nash equilibrium and then look at equilibrium in repeated games. Example There are two pizza stores in the town – Donna’s Deep Dish (D hereafter) and Pierce’s Pizza pies (P hereafter). Each of these two pizza stores have loyal customer base of 2000 pizzas per week. There is a floating demand for 4000 pizzas – i.e. whoever charges the lower price sells those 4000 pizzas. If both stores charge the same price, each store sells 2000 pizzas. The profit margin is \$12 per pizza if price is high (H), and 10 if the price charged is low (L). (a) Draw the pay-off matrix for this game and find the Nash equilibrium. PPP DDD If P chooses Low price, D is better off choosing Low price as well (40 > 24) If P chooses High price, D is better off choosing Low price (60 > 48) So choosing Low is a dominant strategy for Donna. Similarly one can show that

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Week 11_Part II_ECON 2101_S1_2010 - ECON 2101 SESSION 1...

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