Talk:Bertrand competition
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[edit] A technical issue on best responses
The article correctly sates that:
Firm 1s optimum price (which will be a best response) depends on what it believes firm 2 will set prices at.
However there is a misconception on the continuing lines, namely:
If firm 1 expects firm 2 to price below marginal cost, then its best strategy is to price higher, at marginal cost.
According to Wikipedia a best response is the strategy (or strategies) which produces the most favorable immediate outcome for the current player, taking other players' strategies as given.
Therefore, in the context of Bertrand interaction when firm 1 prices below marginal cost firms' 2 best response will be to not sell any positive amount. However price equal to cost is just oneway of achieving this outcome, any price above the price of firm 1 will be a best response.
The original idea of a best response is a correspondence, i.e. given the action of player i, player j may react in various different ways (as opposed to a function). Consequently the graphs of the best responses are flawed.
This does not affect the main outcome or the general presentation of the article.
--I agree with the above. Even though it does not affect the outcome, I still think it is an important point which may lead to misunderstandings. —Preceding unsigned comment added by 131.111.220.6 (talk) 22:14, 28 April 2008 (UTC)
