OK - what makes you think that passengers have one particular decision model? In my experience passengers (and taxi drivers) have at least *two* parallel decision models and negotiation patterns to chose between. Actually thinking of it I know of at least *three* different models available in every day engagement with different pricing schemes. So before the question is investigated further - perhaps the underpinning assumptions about the research question should be reflected upon? How about looking into the question - what are the different types of pricing schemes available? Under what conditions can there be more than one scheme available to choose between? Under what conditions would there only be one? and so on. There may be a decision for passengers to make related to *choosing* which pricing scheme to request. Once we have a model of the different potential alternatives of pricing scheme it becomes interesting to see if the decision models within each pricing scheme is the same. Complexity. Perhaps this question would benefit from being explored through the use of *systems thinking*. Sources which might be useful as a starting point might be Gregory Bateson: Steps to an ecology of mind.

First, I would do a little homework on the elasticity of demand for taxis.  How responsive are people seeking taxis to price in the first place?  If the demand for taxis is highly price inelastic to begin with, then it is unlikely that changing the pricing system would change customers' responses to these different types of pricing systems.  I am presuming that by dynamic pricing system, you are referring to some sort of pricing by time of day, and/or date.  I think Peter Bednar might be missing your point, as I believe you are referring to the response of potetial passengers to a choice made by the taxi provider to use one pricing system or the other.  I think companies like Uber tend to use more dynamic pricing schemes.  You should probably be looking not only in psychology for your answer but you should recognize that economics has been doing research into pricing for quite a while now.  The disicpline is broken down to two main areas, microeconomics or price theory and macroeconomics, on monetary theory.  Pricing and static and dynamic pricing has been studied in volumes, as well as bundling, two-part and multi-part pricing systems...

While there may, at first, be more uncertainty over the changing prices, regular customers come to learn the pricing system.  So, demand will be more sensitive to price the longer the price and the pricing system is in place.  This is what economists call the second law of demand.  The greater knowledge that potential passengers have of the price and the prices of alternative suppliers of transportation, they greater this elasticity of demand (the more responsive buyers are to price variations).  The more independent suppliers (not controlled by regulators, not in cahoots--in a price-fixing arrangement) the greater the price elasticity of demand.  

However, the issues is how this would change or would it change if the suppliers went to a different scheme.  The change in responsiveness to price if the pricing method were to change.  This does give customers more choices or more substitutes available, so that customers would resond somewhat to time of day, day of week, pricing variation.  Some would change when they went somewhere by taxi.  But out of town travelors traveling from airports to city hotels would not change much.  Those traveling from apartments to the city to go to the theatre or to dinner would not change much.

If you are not familiar with the extensive work done by economists on pricing, I would suggest that you take a look at Pindyck and Rubinfeld's "Microeconomics" text (Pearson).  This is a junior level book, and not an intro book.  If you find that too challenging or too simple, respond to my answer or contact me by email (I am easy to find).  You should note that there has also been a lot of experimental work in such areas, modeled a bit from psychological experiments, but with slight modifications in methods (usually using actual monetary payments for participation and performance in the experiments).  You will find quite a few journals of transportation economics. If you have not done a google scholar search on dynamic pricing and taxis or just pricing and taxis, I think you will find a lot of work.  For instance, take a look at these articles:

http://www.sciencedirect.com/science/article/pii/S0965856406001297

Transportation Research Part A: Policy and Practice

Volume 41, Issue 7, August 2007, Pages 672–683

Success and Failure of Travel Demand Management: Is Congestion Charging the Way Forward?

Responses to complex pricing signals: Theory, evidence and implications for road pricing, Peter Bonsalla, Jeremy Shiresa,  John Mauleb, Bryan Matthewsa, Jo Bealec, 

Nonlinear pricing of taxi services

http://www.sciencedirect.com/science/article/pii/S0965856410000431

H Yang, CS Fung, KI Wong, SC Wong - Transportation Research Part A: …, 2010 - Elsevie

Public transport demand models and elasticity measures: An overview of recent British experience

PB Goodwin, H Williams - Transportation Research Part B:  1985

http://link.springer.com/article/10.1023/A:1005185421575#page-1

Elasticities for taxicab fares and service availability

B Schaller - Transportation, 1999 - Springer

http://link.springer.com/article/10.1007/BF00172614#page-1

Some evidence of transit demand elasticities

MA Kemp - Transportation, 1973 - Springer

A survey of recent estimates of price elasticities of demand for transport

TH Oum, WG Waters, JS Yong - 1990 - www-wds.worldbank.org

http://www-wds.worldbank.org/external/default/WDSContentServer/IW3P/IB/1990/01/01/000009265_3960928230924/Rendered/PDF/multi_page.pdf

I should note that in my intro economics class, I just discussed a study on choices of transportation modes, air and car, the demand elasticities and substitutability of modes and infant travel seats--why the FAA does not require infants in car seats on planes.  A matter of elasticities.

One difficulty that might arise in doing empirical work examining this issue in the US is that pricing of taxis in most cities is highly regulated.  Many believe that Uber and other "app" taxi services are illegal.   

Yes I might have misunderstood the question and I agree that we can inquire into this from an economic point of view. But the question was specifically asking for links to social sciences and or behavioural psychology.

From my point of view: We should most likely ask ourselves what is the purpose of the research, what is the assumed problem we are investigating (from whose point of view and why) and who is the target audience for our potential *solution*. Important points from my perspective:

1. We can have more than one taxi company available to any one passenger to chose between.

2. A taxi company can have more than one pricing scheme for a passenger to chose between.

3. If the two points above are true it might be a good idea to broaden the inquiry to include the larger decision space available to the passenger as opposed to if the passenger only dealt with one company with one pricing scheme.

4. Regulation of taxi - we should not forget competitors to regulated taxi companies which are providing a similar service but are not included in the same regulatory framework. For the passenger these may be looked upon as *equally valid* alternatives. These non-taxi companies tend to have different pricing models compared to those who are formally regulated as taxi. This situation will potentially influence the decision space taken into consideration by a passenger.

Peter, Economics is a social science.  It deals with decision making by people, the choices that people make. It exactly studies behavior of people (mostly, but some have used rats in studies).  Take a look at this wikipedia entry on economics:

http://en.wikipedia.org/wiki/Economics

Especially look at microeconomics.

Pricing and how people respong to prices is what economics is about.  This includes issues of dergrees of uncertainty and risk.  But issues of price and the role of prices in decision making and the social role of prices has been studied far more, I would suggest, in economics than in psychology.  It is central to all of economics.

I do not mean to suggest that psychology has nothing to say about this question, but since this is just the sort of phenomena economists have been studying the behavior of individuals and groups of individuals for a very long time, I am suggesting that he look into it. The question and its answer has little to do with the point of view or the perspective of the person answering the question.

Yes, we aways need to ask about the purpose of the research.  We should first get to the real question that the research is supposed to answer.  That would have something to do with the project that Mr. Certicky is working on.  So, to better answer his question, we need to know why he is asking it in the first place.  I would suggest that whether we can ignore or assume away a particular difference is something we could do in some situations, but not in others.  I suggested that it would make less difference, however, in cases where people, in their decision to take a taxi or not, or to take a taxi at a particular time, if potential taxi customers are rather unresponsive to price in the first place.  If people happen to be highly responsive to price changes in their behavioral choices, then changing that pricing method is more likely to make a difference.

Dynamic prices vs. flat charges is something that has been studied in many ways by economist.   One type of dynamic pricing system is known as peak-load pricing, and it has been studied and used in many different situations, particularly in electricity and natural gas retailing.  Charging higher prices in peak times moves use toward off-peak times.  I suggested (in print) that universities use such a scheme when classroom use has major peak to off-peak swings.  This reduces the need to build new classroom space.  Utilities do it to reduce the need for new generating facilities.

#1.  Of course, and again, economics is always looking at competition and degrees of competition.  This has been studied for over a century now.

#2.  Yes, while a company could give passengers a choice between a flat rate and dynamic charge, this is quite unlikely.

#3. #2 is doubtful, but still, most economists would approach this by looking at real choices available to people in real situations.  Some would use stuctured choices in experimental settings, which is somewhat artificial, making them harder to generalize.  

#4.  Yes, Uber and Lyft and others exist as well as non-app type competitors.  But, decision making among different products, at different prices and different competitors is again what economists have been doing since Alfred Marshall, Principles of Economics (1890): http://en.wikipedia.org/wiki/Price_elasticity_of_demand . Most empirical work in these areas is done with experienced situations, where prices are recorded, actual behavior of buyers is recorded, other variables taken into account.  

I did not mean to suggest that psychology had nothing to say about this, but since this is just the sort of phenomena economists have been studying the behavior of individuals and groups of individuals for a very long time, I am suggesting that he look into it.  The question and its answer has little to do with the point of view or the perspective of the person answering the question.  

Sorry, I thought I moved that last paragraph, but I copied it instead.

Let me see if I understand what Mr. Certicky means.  By static pricing, I am assuming he means a fixed charge per mile or per minute, whereas by dynamic, I assume he means that the price per mile (or per minute) changes depending on the time or the date.  Is this correct?

On other matters, Mr. Certicky explains: 

"By "passenger's decisions" we understand their reasoning about accepting the taxi trips based on prices, delays, travel times, etc. We suspect they will think about those things in almost the same way, regardless of whether the taxi company uses dynamic or static pricing scheme." 

Here is a crucial question to better understand the question that has been posed by Mr. Certicky:   By passenger's decisions, do you (Mr. Certicky) mean decision to take the taxi or not OR decision to take a taxi at one time rather than another.  Without performing an experiment it would be difficult to say, at least from an economist's perspective, except that if this demand has a low price elasticity in the first place, that customers are unresponsive to taxi prices, then it is unlikely that people will change whether they take a cab or not, but it still may make a difference as to when they take a taxi.  

Interesting that you make all these assumptions about me and also the research question and *reality*. Perhaps it is a cultural thing, never mind you say:

#2. Yes, while a company could give passengers a choice between a flat rate and dynamic charge, this is quite unlikely.

Actually it is quite common practice where I grew up. And the choices are actually *three* which are available to the customer. Both flat rate, time based and journey specific etc. The different alternatives are available for negotiation and depends on both context, situation and type of journey and so on. But that has also been studied. So there you go. Also people can choose which company they use when they *take a taxi*. it is not exactly the case that there is only one available  or that the way you decide which one to take is universal globally.

When it comes to passenger decisions

1) if we compare wether or not to take a taxi - or

2) if we compare wether or not to take one taxi instead of another one - or

3) if we compare wether or not a passenger selects one price model vs another (in the same taxi).

These are example of questions may or may not be relevant - dependent on the purpose of the research. Also it is possible that the price (total cost of a journey) may or may not be relevant for the passenger - as mentioned earlier in this thread - but there might be other aspects which are relevant and influence the choice made by the passenger - for example in Sweden people might prefer to take a *green* taxi for a journey as opposed to a normal (petrol or diesel) version. Additionally you still have all the other things already mentioned about delays, travel times etc.

It is also possible that some pricing models incur different travel times compared to others (due to economic driving, route selected, etc). Then there are pricing models which include *sharing* of taxi etc. These are all existing models that are practiced and available for customers in some cities already. No need to be including imaginary alternatives...

Wether or not we wish to ignore any of this matters perhaps, But that does certainly depend on the research question and the purpose the researcher has with it.

Anyway - we are still within exploring the question from within social sciences. 

I have been re-reading the question a few times now and thought about what it is that concerns me. This section:

***By "passenger's decisions" we understand their reasoning about accepting the taxi trips based on prices, delays, travel times, etc. We suspect they will think about those things in almost the same way, regardless of whether the taxi company uses dynamic or static pricing scheme. Is that so? And if so, what research supports this belief?***

When I read the question it seems to me as if there is an assumption that the passenger only have one taxi company to engage with. Now perhaps this is a special case which can be justified for some particular place. I personally would have some concerns about the potential trap of looking at it as if any taxi company can be looked upon in isolation from other companies. I am sure that I am not the only person who when I need to take a taxi I normally have quite a few different taxi companies to choose between. Also it is the case that some companies have different price models from others - this can (and sometimes in my case does) influence the choice of *which* taxi company. These models can have different complexity and in my experience some passengers prefer *simple* (but perhaps more expensive) alternative pricing model - while others are quite happy to choose a company with a more complex model (potentially cheaper). I think people are different and so it is likely that we can identify categories of passengers with different decision making patterns and preferences. Especially if we are taking into consideration taxi companies who have a larger variety of customers.

Some sources of potential value to complement the suggestions made earlier in the thread:

1. If the question of passenger choice is of significant importance one discussion of interest might be: Choices, Values, and Frames by Daniel Kahneman and Amos Tversky

2. If the question of passenger adaptation to new practices and the spread of a new behaviour (diffusion of social innovation) is of interest the following might be worth having a look at: Diffusion of Innovations by Everett M. Rogers

Thank you both for your comments, we appreciate your responses. To clarify, the general question we are interested in knowing is how an individual’s price preferences (i.e., their type) will differ when using a static pricing scheme (i.e., fixed $/km as in standard taxis) and a dynamic scheme (e.g., Uber’s approach) in a long term (we're only interested in the situation, when given pricing system has been in place for a longer time). Note that dynamic pricing will depend on the instantaneous supply and demand for the service; that is, the other passengers that seek a journey at that time and the drivers that are available. This will typically depend on the time of day, but also potentially on short-term fluctuations in either supply or demand, which are not regular or periodic.

For our purposes, we need to model the maximum price-rate of each passenger, which is the maximum $/km that a passenger is prepared to pay. We assume that a passenger will reject a journey offer if the price-rate offered exceeds this value. In particular, we consider a probability distribution of the price-rate over the population of passengers, where each passenger’s maximum price-rate is a realization from this distribution.

A more precise formulation of our question is then: will the distribution of the maximum price-rate a passenger is prepared to pay significantly change when we use a dynamic pricing scheme instead of a fixed one?

To simplify and make our actual problem more tractable (which is routing/scheduling/pricing algorithm design for these services), we have (for the moment) assumed that there is only one provider and that the key preference is price. We understand that competition and demand elasticities in quality of service will probably also play a role, but believe that this will only change the actual prices the dynamic pricing generates, not qualitatively how passengers respond to the prices. If you have an argument that would indicate otherwise, we would be interested in knowing it.

While equilibrium demand elasticities play an important role in evaluating taxi services, we are more interested in how individual passengers respond to the changes (i.e., a microfoundations approach). As such, we believe that individual decision processes are the key factor here. We would like to thank Prof. Coats for the reference to the paper by Bonsalla et al., which seems to address a related problem.

Thank you again for your helpful discussion. If you have any more comments, we would be grateful for your help.

Of course  there can be more than one company available and that one company may use one system and another May use another.  Yes, this widens the choices set available.  But really to answer his question appropriately, we really need a better understanding or the problem under consideration, rather than both of us guessing at the problem.  Still, if the elasticity of demand is minute and/or price "explains" only a small proportion of the overall variability in use (cab ride choices). And these are not the same things, while other factors seem to explain much more, then price is playing a very small role in the decision.  

Yes, the choices available under monopoly, which may occur in certain times and places, is not at all the general case, but might be a good starting point in understanding the decisions involved.  From there, one may consider the case where the choice set is expanded to two competing selers.  Then it might be instructive to consider the choices of the competitors seeking customers and revenues (what they are really after) and then the "competitive game" between the two sellers.  From there, the choice set can be expanded and then finally generalized to many sellers.  

I would think hick that two sellers would probably adopt similar policies as is suggested by the work of Harold Hotelling, 1929, "Stability in Competition." Others have shown that if competition plays out in multiple dimensions, this result may not hold, so if competition is in both a price system dimension and a greeness dimension, then the stability is lost.  With odd numbers of competitors, stability is also lost.  

You are right that I was presumptive about the choices of pricing systems being just a seller choice, but unless forced to give such choices among pricing schemes to customers, it seems that giving customers such a choice of schemes is a decision made by the seller.  I would think that if the rate schedules are the choice of the sellers, not regulators, then in rates will be adjusted so that the expected value (EV) is the same across pricing systems--same  expected value from the seller's perspective,  from any one buyer's perspective, the EV may not be the same.

Peter, what I had said at first to Mr. Certicky was that he should look not just to psychology for answers but to other social sciences as well.  The answer to his question depends less on the discipline perspective than on the ultimate rem

Michal, the distribution of maximum prices (economists call them reservation prices), if examined as a cummulative distribution, from highest to lowest values, is exactly what economists mean be a "Demand Curve."  Yes, certainly examine from a microfoundations approach, a cross-section of individual buyers, The dynamic pricing, I would think, would do more to sort buyers into time elastic and time inelastic groups than to change that overall demand.  Think of one demand for the entire period over which prices may vary,say a day.  I think it would be very reasonable to assume that the overall day demand for the static and the dynamic cases would be largely the same.  People may change their choices of time of day for the travel in response to the peak pricing, but I would think would change very little else.  However, you should note (and this only matters depending on how you collect your data, you may experience more buyers overall with dynamic pricing, because there is almost constant equilibrium between supply and demand.  For a static pricing system, you will find that there will be shortages and surpluses more severe and more frequently as the price is not adjust to peak and off peak uses, so with a constant price, cabs will be idle some times and at other times there are not enough cabs for all of the riders who want rides at the going static price.

I would think that there may be other differences between ordinary taxi service and Uber and Lyft services that would overwhelm any differences caused by the pricing system.  If the dynamic system has been in existence for a while and people have no reason to be surprised, the is little to change the reservation prices, except perhaps, people turn to those services more often because they are more certain that they can get a taxi.  

I can also imagne a spatial pricing system, where prices are higher if picked up in high crime neighborhoods.  That would create a host of social and political problems.  I just don't know wihich is worse, higher prices in high crime heighborhoods or refusal to pick up a customer in a bad neighborhood.  That is a tough ethical problem.

Peter, yes, the work of Kahneman and Tversky is classic decision theory, no matter what one's discipline.  That is certainly a must.  

as i know discrete choice models are vastly used to prove such that assumptions.

search for mixed logit and probit or discrete choice modeling as key words I am pretty sure you will find very significant paper