```Date: Fri, 27 Jun 1997 09:23:47 -0700 Reply-To: Donald Peter Cram Sender: "SAS(r) Discussion" From: Donald Peter Cram Organization: Stanford University, CA 94305, USA Subject: Re: SAS Simulation In article , Dana Arnetta Maclaurin wrote: >I have a fairly complicated SAS question. I am using SAS essentially to >run a simulation. Here is the setup: I have two firms, each having its >own quality level between 0 and 1. Say there are ten quality levels (0.1, >0.2, 0.3, etc.), then I want to consider each possible combination of the >two firms' quality levels. For each pair, I have some equations that I >use to calculate prices and profits for each firm. Then I pick the combo >that maximizes profits (first for firm 2 given each possible quality of >firm 1, then for firm 1 overall). The result should be one "best" >combination. You have a two player game and you seek an equilibrium where each plays his/her best response (sets a product quality level) in response to the other's quality level setting. It seems possible that there exist more than one equilibrium. If the special nature of your equations somehow lets you know that there is only one equilibrium, then I wonder if the same information might be used to tailor a search strategy for it. Your approach is to do an exhaustive search over a grid. But certainly you can write a formula expressing Firm 1's best response as a fucntion of Firm 2's quality level. I assume that analytically solving that maximisation problem is not possible. But you could use PROC NLP or an NPL algorithm in PROC IML to solve numerically, for each possible play by Firm 2. Use PROC PLOT to portray Firm 1's best response to Firm 2 and also Firm 2's best response to Firm 1's possible plays. You can then see where the intersection(s) is(are) and examine more closely in those regions, assuming your problem is "well-behaved". (If it's not well-behaved your exhaustive search wouldn't work either.) Your dataset size would be 2 datasets of say 1000 plays and bestresponses, one for each firm. That would provide an equivalent solution to your searching over 1000x1000 = 1,000,000 combinations. To implement this you would run PROC NLP in a macro programming loop. Start by checking the PROC NLP manual ( you can borrow mine). Does anyone have sample code for plotting 2 best response funcitons? >The bottom line: is there any way to have the current observation >overwrite the previous observation if a certain condition is met? I don't think so, and don't expect that a 40percent improvement is enough for you anyhow. >Thanks, >Dana regards Don -- doncram at gsb dot stanford dot edu all lowercase http colon slash slash www hyphen leland dot stanford dot edu slash tilde doncram ```

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