ECON5111 Practice problem 3
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ECON5111
Practice problem
1. In the classic Bertrand competition game, 2 firms each have a per-unit cost of C and simultaneously decide what price to set: whichever firm sets the lower price captures the entire market, and if the firms charge the same price, they split the market equally. Consider a variant of the Bertrand game in which, instead of being able to choose any nonnegative number for price, firms can only choose prices 1, 2 or 3. Both firms have a per-unit cost of 1. There are 10 consumers, each of which will buy 1 unit from whichever firm charges the lowest price (and will flip a coin to decide who to buy from if the prices are the same).
(a) Represent this game in a payoff matrix, and find all Nash equilibria. Are any of the NE inadmissible? Is any NE payoff dominant? Which might emerge as a focal point?
(b) Suppose both firms can also price at 4. Modify the payoff matrix accordingly. Does the addition of this extra strategy change the set of NE? Does it change which are inadmissible?
2022-06-20