# Random Utility Theory relationship with markt simulations

Dear Sawtooth Team,

we handed in our research  which we did with your Sawtooth Lighthouse programme at a high ranked Journal and we got good feedback.  :-) Thanks for your great tool which enables us for interesting research.

However, one comment regarding our market simulation results confused us. In this analysis, we ran a market simulation with 2 products+non option and forecasted the share of preferences for 4 customer segments identified vis latent class clustering. We found that a certain percentage of respondents choose an option, which was more expensive and had no price discount, which seems counterintuitive.
The reviewer commented:
...even if one alternative is completely dominated by another alternative, the choice probability of the former is not zero since the random utility model is used in this study where an error term is included into the utility function. It is the limitation of the random utility models if the dominated alternative has zero choice probability in reality....

Is this comment true, because I do not fully understand the relationship between Random utility function and market simulations.  I thought a random utility function does not play a role in market simulations or does it? In the simulation, we use the part-worth utilities derived from the HB approach and simulate which product option would an individual choose based on the highest utility. What role could random utility function play in market simulations? What role does random utility function play in the HB approach?

We would highly appreciate a short comment since we are a little bit confused and would need some outside perspective. Maybe we oversee some obvious....

Thanks a lot and kind regards,

AP

Yes, the reviewer is correct.  Our market simulator, when using either the Share of Preference or the Randomized First Choice, is simulating respondent choices in a way appropriate to Random Utility Theory (RUT).

Under RUT, respondents have a non-zero probability of selecting a product concept, even if that product concept has lower utility than another concept in the simulation scenario.

If you were to change the simulation method to First Choice, then this is a deterministic rule that assumes the respondent chooses with 100% probability the alternative in the simulation scenario that has the highest utility.  First Choice does not follow from RUT.  (Unless the error is assumed to be zero).
answered Jan 31, 2019 by Platinum (169,915 points)
Thanks a lot! Very helpful! :-)