Econ 488: Experimental Economics
Experiment Report
Topic/Question: What is the expected observed price and quantity change for Cancun air tickets in the 6 weeks leading up to the Spring Break?
Group Members: Cecilia and Danye
Professor: Shyam Sunder
TA: Foong Soon Cheong
Date of Experiment: Oct. 30, 2007
Date of Presentation: Nov. 27, 2007
I. Background
We have observed that airfare fluctuate significantly in the weeks or months before departure. We are interested in exploring if there is a trend for prices and quantity, and what might be the best time for buyers to purchase airplane tickets. We believe that the trend would indicate a Nash Equilibrium between airlines and passengers, who each play their Best Responses (by changing price – airlines, or by changing time and amount of transactions – passengers). Since it would be difficult to gain empirical information of prices and quantity from airlines, we believe that an experiment would be a useful way to observe price and quantity under certain constraints.
II. Hypotheses
We know that the observed price and quantity is a reflection of demand and supply in the market. If the buyers believe the seller’s pricing strategy is going up, they will buy at the beginning, and when sellers see more transactions at the beginning, they will raise the price, so the buyers will then tend to buy later. So the game is based on the interaction between buyers and sellers, and the results will be:
1. We expected prices to fluctuate, but stay close to 200. In other words, the price line will be rather flat.
2. We expected to observe upward sloping general trend, and a decrease in prices towards the end as sellers are concerned that they are incurring a cost at the “bundles of 5”.
3. We expected that the number of transactions will be greater closer to the end.
III. Procedure
We utilized a zTree program to conduct our experiment. We have 15 participants, 3 acting as Sellers and 12 acting as Buyers. Sellers are randomly chosen by the first three zLeaf who get accessed. Participants are unaware of the context (the airplane ticket scenario) of the game, so we may focus our experiment and observations on prices and quantities. Instructions for Sellers and Buyers were given separately (refer to the Appendix). We conducted 11 trials in total. After trial 5, we made the Sellers’ “bundles of 5” selling constraint public.
In terms of programming, we adjusted the double auction demo zTree program, we solved major problems by adding new parameters, implementing new constraint to “check boxes”, disabling the Bid option for buyers, adding cancel option for sellers so they can buyback their own goods without showing the transaction prices on the plotting scene, and etc.
IV. Results
1. Results of all transactions for each period.
And we have 11 periods all together. The X axis represents Time, and Y axis represents Price.
Trial 1-4.1
Trial 2-4.2
Trial 3-4.3
Trial 4-4.4
Trial 5-4.5
Trial 6-4.6
Trial 7-4.7
Trial 8-4.8
Trial 9-4.9
Trial 10-4.10
Trial 11-4.11
2. Results of Prices, Quantities, and Payoffs for each of the 3 sellers respectively
(These charts were not included in the initial Presentation made to the class, but are important to our analyses)
For Seller 1-4.12
For Seller 1-4.13
For Seller 2-4.14
For Seller 2-4.15
For Seller 3-4.16
For Seller 3-4.17
V. Analyses
1. Price
In the first 3 periods, price remained relatively flat with a small standard deviation. Prices stayed close to 200, which was in line with our expectation. We treat the first 3 trials as “practice runs”. Periods 4-11 saw a general downwards trend in price, with a much higher standard deviation. The large range in prices was due to many downwards “spikes” in prices.
Trial / Mean / Median / Std Dev / Max / Min1 / 195.6 / 196.0 / 2.9 / 200 / 190
2 / 196.4 / 197.0 / 2.8 / 200 / 185
3 / 193.5 / 194.0 / 2.3 / 200 / 189
4 / 182.5 / 189.0 / 11.8 / 196 / 160
5 / 163.0 / 161.5 / 18.9 / 195 / 134
6 / 168.9 / 171.5 / 11.5 / 187 / 145
7 / 174.0 / 174.0 / 11.3 / 200 / 115
8 / 164.5 / 170.0 / 21.8 / 200 / 101
9 / 173.4 / 175.0 / 9.5 / 200 / 156
10 / 151.5 / 145.0 / 18.9 / 185 / 120
11 / 160.2 / 155.0 / 16.8 / 198 / 100
The result of our experiment contradicts our original expectation for a general upward trend in price, with a possible downward spike at the very end. There are two possible explanations: (1) Decreasing marginal utility of buyers and (2) Competition between sellers causing “price war”.
Our original design of the experiment was such that sellers face increasing costs and buyers face decreasing value per unit. Due to programming difficulties we had to forego increasing costs. Therefore supply curve remains the same, but the demand curve continuously shifts downwards with time, as buyers purchase more units. This would naturally lead to a fall in prices. Failure to control for this factor likely affected our result.
We also observed many downwards “spikes” that occur at various times during each trial, not just at the very end. These spikes appear to be uncorrelated to the number of transactions that have occurred (thus uncorrelated to the decreasing marginal utility of buyers). Careful observation of price graphs also reveals that price immediately following a downward spike is almost always lower or equal to the price immediately preceding the spike. These downward spikes behave as if they “pull” the price downwards.
Our hypothesis is that competition among the three sellers causes these spikes. Seller 2 in particular caused most of the downward spikes. When we conducted post-experiment evaluation, one seller mentioned that he tried to keep prices up by signaling to other sellers, through inputting many high “asks” into the system to alert to other sellers his desirable price level. Although all sellers would benefit if they maintained a higher price level together, this attempt was unsuccessful. Once price has been pulled down, a downward spiral (price war) begins. This experiment is an excellent example of competition and price wars in oligopolies.
2. Quantity
Our hypothesis was that number of transactions would increase with time (as close to departure date as possible). In our experiment, we observed a significantly higher number of transactions towards the end, especially the last 60 seconds, which supports our hypothesis.
Seconds / #Transactions / %Total0-30 / 55 / 7.9%
31-60 / 95 / 13.7%
61-90 / 99 / 14.3%
91-120 / 133 / 19.2%
121-150 / 157 / 22.6%
151-180 / 161 / 23.2%
(If transactions were evenly spread, each 30 seconds should have 16.7% of total transactions)
Another crucial factor we wanted to explore was the effect of the “bundle of 5”. Our hypothesis was that sellers would tend to sell in multiples of 5 to ensure that the recover their fixed costs. Out of 33 instances (3 sellers x 11 periods) only in 5 instances were sellers able to achieve a total transaction per period that is a multiple of 5 (excluding 2 instances when sellers had 0 transactions in the period), a success rate of merely 15%. This may be due to time lag in the program that slowed sellers’ responses.
3. Seller “Personality” Factor
By “personality” we mean individual pricing strategies each seller has. As shown in Graph 4.12 to 4.17, when we combine the elements of price, quantity, payoff for each period for different sellers respectively, some other observations become apparent.
Seller ID / Mean Price / Total Tickets Sold1 / 161.7246 / 167
2 / 176.6853 / 448
3 / 176.9878 / 82
First we come to realize that seller 2 is doing the best among the 3 sellers because he has sold the highest number of tickets, without sacrificing for too low a price. When we look at his individual price chart at 4.14, we learn that he has been adopting a rather consistent strategy of starting off at a high price and steadily going downward within that period. He has been very active putting up prices at the transaction board for all periods, and thus seizing most of the quantities. When we look at graph 4.15, we learn that except for the first 2 periods and the last period, seller 2 has been making significantly large payoffs, which means his strategy has been rather successful.
Second when we look at seller 1 at graph 4.12 and 4.13, we learn that seller 1’s pricing strategy is very flat for the first 3 periods and last 2 periods, and those are the periods he makes good amount of positive payoffs. His pricing strategy in other periods, however, is to jump the prices all over the place, with low prices immediately following high ones, which lead to rather negative effects on his payoff and his overall mean price.
Third when we look at seller 3 and compare his behavior with seller 1 and 3, we learn that seller 3 is the one who’s trying the hardest keeping the prices up, but he sacrificed his quantities significantly. And because he was too focused on keeping prices up, so he hardly kept up with the “bundles of 3” factor, which makes him even worse-off when it comes to payoff analysis. As we can see in graph 4.17, for 5 out of 10 periods (he skipped period 10), seller 3 incurred a rather huge negative payoff.
4. Load Factor
Trial / Seller 1 / Seller 2 / Seller 3 / Total Sold / Total Incurred / Load Factor1 / 11 / 31 / 7 / 49 / 60 / 81.7%
2 / 15 / 26 / 13 / 54 / 60 / 90.0%
3 / 11 / 44 / 9 / 64 / 70 / 91.4%
4 / 23 / 30 / 8 / 61 / 65 / 93.8%
5 / 15 / 36 / 11 / 62 / 70 / 88.6%
6 / 9 / 50 / 7 / 66 / 70 / 94.3%
7 / 5 / 53 / 9 / 67 / 70 / 95.7%
8 / 5 / 47 / 5 / 57 / 60 / 95.0%
9 / 0 / 70 / 5 / 75 / 75 / 100.0%
10 / 24 / 44 / 0 / 68 / 70 / 97.2%
11 / 49 / 16 / 6 / 71 / 80 / 88.8%
694 / 750 / 92.5%
A more interesting point, however, is to look at the load factor, calculated by the number of occupied seats divided by the total number of seats flown. Higher load factor indicates higher efficiency and thus higher profitability. In our experiment, the sellers as a whole achieved a total load factor of 92.5%, which is very high.
5. Error
Two errors have been observed when we are doing data analysis, the first one is that although we constrained in the instruction that each buyer can only buy up to 5 tickets, but we did not put the constraint into the zTree program, and there is no error message when a buyer tries to buy more than 5 tickets within a given period.
So we have Buyer ID 9 challenged the rule and he purchased more than 5 tickets for many periods. The effect of his behavior is two folds. It might have explained why both seller 1 and seller 3 incurred huge payoff lost in period 6 and period 11, because the payoff is largely seized by the buyers. It might have also explained why the Load Factor has been so high, because buyer 9 has seized the quantities that would otherwise not able to be sold.
Period / Subject / Stock / Utility / Payoff1 / 9 / 2 / 226.7927 / 88.58548
2 / 9 / 5 / 244.2706 / 385.3528
3 / 9 / 6 / 218.5664 / 364.3987
4 / 9 / 5 / 182.0974 / 84.48699
5 / 9 / 7 / 146.7508 / 141.2555
6 / 9 / 13 / 149.8273 / 522.7551
7 / 9 / 7 / 171.4211 / 291.9479
8 / 9 / 7 / 142.8246 / 99.77255
9 / 9 / 13 / 163.5389 / 773.0055
10 / 9 / 11 / 114.4719 / 385.1906
11 / 9 / 14 / 148.2192 / 965.0687
Another error is that we observed that seller 1 did not participate in period 9 and seller 3 did not participate in period 10 at all. The effect of their absence is not obvious though.
6. Critique
We were unable to observe price trends within the “bundles of 5”. While it is possible that there would be no price trends observable, we believe that an adjustment to our experiment would yield different results. Since 5 is a small unit and it is difficult to observe trends within 5 units, except for very prominent trends. Increasing from “bundles of 5” to “bundles of 10” would allow easier observation of trends. Furthermore, the expected downward price spike at the very end would be more pronounced.
We were also unable to implement the buyer “cancel” their ticket option into the program, and this might be the reason why we did not observe a “last-minute” drop in prices as we normally see in real-life. The “last-minute” good deals are usually offered due to the fact that some people have cancelled their tickets last minute, but we eliminated this option in our experiment, so we did not see this phenomenon in our lab.
With regards to the overall price trend, we earlier mentioned a significant flaw in not programming in rising costs for sellers. Another factor we would improve on is the effect of time remaining until departure which was not sufficiently represented in the experiment. Since participants were unaware that our experiment is based on airfare, there is no significant incentive for buyers to buy as late as possible, as is common in real life. Implementing the flexibility option in our original design would cause buyers’ value per unit to increase with time. Making these two changes may alter the downward price trend that we have observed.