When an experiment requires many rounds and complicated matching schemes it is easiest done on a computer network. A typical example is the Bertrand duopoly game where it is best to use two different types of matching (fixed/random) and/or two different group sizes.
A large selection of computerised experiments is available via Charlie Holt’s Veconlab, Econport and our own FEELE website. Typing any of these keywords into Google will lead you directly to the relevant site. Veconlab offers the most information and help for a beginner. Once this system is familiar, it is easy to switch to our site which is deliberately of a similar design. Econport offers the best market experiment software, in particular for some experiments on financial markets. It is well-documented and easy to understand. How well it works in your computer lab depends on the ingenuity of your university IT group. The more complex and convoluted their firewall system, the less likely it is that the JAVA applets Econport uses will work and communicate without problems. This system has to be tested in every room where you intend to use it, preferably by your computing officers and IT services.
Many of the most popular classroom experiments are offered via the Internet for free. Apart from this, the big advantage of computerised experiments is their availability and the ease at which beginners can get started. The student experience tends to be uniform. The results are available immediately and can easily be distributed to students for evaluation. In many cases, there are tools provided for simple analysis of the results. A large number of rounds can be run as well as several treatments. An experienced instructor or teaching assistant can handle a computer classroom alone, although it is easier, particularly if there are more than ten students, if one instructor concentrates on the software and another on the students.
One main disadvantage is that the experiments are standardised. While there are some parameters a lecturer can change, there is not the broad opportunity for drastic innovation that a hand run experiment offers.
A second problem is the requirement to have a special computer room (and it helps to have a projection screen for the instructor’s computer). There is the usual hassle of reserving the room and organising the students to meet there. On a practical level, there is a limit to how many students can fit in the room. When there is a large class, you may have to split it up into several groups. This creates an additional teaching burden. The alternative is to use tutorials, which may have a higher opportunity cost.
Another problem is that in many cases the experiment tends to run as fast as the slowest student. You constantly have to control the monitor program to see how the experiment is progressing and may also have to check the screens of individual students. Students often check their email or Facebook accounts and therefore the experiment becomes stuck. If the experiment runs too slowly, boredom may set in, creating a free-rider problem for students paying attention. Once things are started and running smoothly, there is also the danger that the instructors may check their email as well and not realise that there is a delay. Luckily there is now a KIOSK program that keeps the computer locked in the experiment (see the hints).
Finally, there is a risk of technical problems, such as software bugs, network failure and IT-related problems. This is particularly true for experiments using technically more advanced software. However, such problems have only rarely occurred with our software and that of Veconlab, since they require only a standard web browser.
The hold-up problem is central to the theory of incomplete contracts. It shows how the difficulty in writing complete contracts and the resulting need to renegotiate can lead to underinvestment. We describe here the design of a simple teaching experiment that illustrates the hold-up problem. The model used is a simple perfect information game. The experiment can hence also be used to illustrate the concept of subgame perfect equilibrium and the problem of making binding commitments. In contrast to other perfect information games like the ultimatum or the trust game, the backward induction solution predicts well in our experiment. It is hence a good experiment to conduct in order to illustrate game theory before models where fairness considerations are discussed.
The hold-up problem (see Hart, 1995) results from situations where it is difficult to write complete contracts. When one party has made a prior commitment to a relationship with another party, the latter can ‘hold up’ the former for the value of that commitment. It is argued that the possibility of hold-up can lead to underinvestment in relationship-specific investments and hence to inefficiency. An often quoted (but also sharply disputed) historic example concerned the US car industry. Fisher Body had an exclusive contract to supply body parts for the cars of General Motors. They were the only ones who could deliver the parts according to the specifications needed by GM. In the 1920s there was a sharp increase in demand that exceeded all expectations that were held at the time when the contract was written. It is claimed that Fisher Body used this unforeseen development to hold up General Motors, amongst others, by increasing the price for the additional parts produced.
In our highly stylised game there are two players, the Buyer (aka GM) and the Supplier (aka Fisher Body). In a first stage, the Buyer makes a relationship-specific investment (i.e. decides to set up their line of production such that it depends on specific car body parts delivered by Fisher Body). Then (due to the unforeseen increased demand), the Supplier has the opportunity to raise the price (for the additional demand). In case the price is raised, the Buyer can, at their loss, change the Supplier.
We run two treatments of this game which differ only by one parameter. We sketch here the computerised version available via our FEELE website. More details, and a hand run version, are discussed in (Balkenborg, Kaplan and Miller, 2009a, b). In both treatments it is optimal for the Supplier to hold up the Buyer and for the Buyer to accept the hold-up. In the first treatment it is optimal to invest even if there is a hold-up while in the second treatment it is better not to invest due to the hold-up. We choose this set-up because it allows students first to learn that there will be a hold-up and then to experience the economic consequence of underinvestment caused by the hold-up problem. We tend to run 8–10 rounds of each treatment with a different random pairing for each round. An even number of players is needed.
The first game is given in game tree form in the following graph.
If no investment is made, both players get zero. The investment costs 500 and the gross value produced is 1500. In the initial contract all surplus goes to the Buyer and they get 1000 while the Supplier makes zero profit. The Supplier can hold up the Buyer by raising their price by 750 and leaving the Buyer with 250. The Buyer could change the Supplier, but this hurts everybody. The Buyer loses their investment and the Supplier loses all their business with the Buyer.
Once the number of players is determined, we can complete the set-up of the experiment and give the students the access code to log in to the experiment via our website. They are then assigned the roles of Buyers and Suppliers and can work through the computerised instructions. In each period the program randomly matches Buyers and Suppliers. Sequentially the game is then played, with first the Buyer deciding whether to invest, followed, if applicable, by the Supplier’s decision whether to raise the price and the Buyer’s decision whether to change the Supplier
In the following screenshot the Supplier is asked to keep or raise their price. The design of the screen is very simple to keep the emphasis on the basic decision.
Typically subjects learn quickly to play the backward induction equilibrium. This means that the Buyer learns that their threat to change the Supplier is ineffective because it is too costly, and therefore the Buyer is held up, i.e. the price is raised. It still pays for the Buyer to make the investment.
This changes in the second treatment. The only number we alter is the cost of the investment which is raised to 1000. As a consequence, the Buyer loses from the investment if they are held up. The payoffs are now illustrated in the following game tree.
In part 2 of the game the Suppliers are typically held up when possible, and the investment is made much less often.
The next figure shows how often each possible outcome arose in the experiment.
Notice that there is a minority of Buyers who switch Supplier after the price has been raised. (This did not happen in all the sessions we ran.) The rationality of these Buyers is an important point for class discussion: what were they trying to achieve?
The second figure shows the development from period to period.
One of our favorite computerised experiments is on Bertrand competition (available on both Veconlab and FEELE). We have had success running this experiment with students from sixth form level up to corporate executives. Students act as firms in a market. Each period in time, they choose prices. The customers (played by the computer) go to the firm with the lowest price (in the event of a tie, the demand is split equally). Each firm has constant marginal cost and, given the demand of the consumers, the Nash equilibrium is for firms to charge a price equal to their marginal cost, leading to zero profits (see Kaplan and Wettstein, 2000).
You can see the results of the experiment in the figure below. These results are typical. With two firms in a repeated situation, the prediction of perfect competition fails. Even without explicit communication, firms can collude. To quote an anonymous student:
‘I learnt that collusion can take place in a competitive market even without any actual meeting taking place between the two parties.’
This changes quite drastically for a larger number of firms and random matching. Here, the competition is fierce and the profits are driven out of the market. To quote another student:
‘Some people are undercutting bastards!!! Seriously though, it was interesting to see how the theory is shown in practice.’
It is especially important in this experiment to display the selling price in addition to the average price chosen since that indicates the profits in the market. Only by seeing the selling price can one clearly see the strength of the equilibrium prediction.
A lecture on industrial organisation will discuss the advantages and disadvantages of different market structures. A counter-intuitive concept is that more competition is not always better. Duopoly may be worse than monopoly. This is the case when a monopoly sells two complementary goods and is then split into two firms to sell each good separately. The theoretical analysis shows that consumers pay a higher price for a pair of commodities after the split. In a crude analogy, being robbed twice is worse than being robbed once for the consumer. The analysis is clearly relevant for competition policy: for instance, the decision on whether to split Microsoft up into two separate companies, one that sells the Windows operating system and one that sells Microsoft Office (Excel, Word, etc.) Krugman (2000) argues just this in his column entitled ‘Microsoft: What Next?’ In agreement with the economic analysis, the US government agencies decided against such a split.
To convey this concept, FEELE provides a computerised experiment based upon a similar hand-run experiment by Beckman (2003).
Looking at the following graph of results, we started students in a monopoly situation facing a demand of 15p and a constant marginal cost of 3p. The profit maximising price is 9p. Students found this price fairly rapidly. When we broke up the company into two separate companies producing complements and competing in a duopoly, there was a clear increase in the price to over 10p (the equilibrium price is 11p).
It is of particular teaching and learning value that the model is just a seemingly minor variation of the standard model of price competition which we use in microeconomics. (The standard model uses perfect substitutes instead of perfect complements.) For the standard model one observes sharp cut-throat competition which erodes profit possibilities: a completely opposite result.
One can run a combination of both Bertrand games against former subjects with the following:
Once relegated to cinema or history lectures, bank runs have become a modern phenomenon that captures the interest of students. Now a simple classroom experiment based upon the Diamond-Dybvig Model (1983) can demonstrate how a bank run, a seemingly irrational event, can occur rationally. The computerised version of this experiment is available from our FEELE website.
This model captures elements of what a bank does. We will focus on the conversion of long-term loans (mortgages) into short-term deposits. It is this conversion that leads to the fundamental problem of bank runs.
In the model there are depositors and a bank. There are three time periods: yesterday, today and tomorrow. Depositors placed money (say £1000) in a bank (yesterday) before learning when they need the money. Depositors either need their money today (impatient) or tomorrow (patient). There is a 50% chance of being either type. The depositors that need money today get relatively little utility for the money tomorrow. The depositors that need their money tomorrow can always take the money today and hold onto it.
The bank has both a short-term and a long-term investment opportunity for the money. The short-term investment (reserves) is locking the money in the vault. This investment returns the exact amount invested. The long-term investment returns an amount R tomorrow. It is illiquid and returns only L<1 today. The depositors that invested £1000 yesterday have a contract with the bank. They can withdraw their money today and receive £1000 or wait until tomorrow and receive R*£1000. The bank meets these potential demands by taking half as reserves and half in the long-term investment.
If all the depositors withdraw the money according to their types, then the bank will meet all the demands. In this case, each depositor has an incentive to indeed withdraw according to their type. Hence, all impatient depositors withdrawing today and all patient depositors withdrawing tomorrow is a Nash equilibrium.
While the contract is fulfilled in this Nash equilibrium, in other cases the bank cannot always remain solvent. If too many depositors try to withdraw today, it will not be able to meet the contract tomorrow. It is then optimal for all depositors to withdraw today. This other equilibrium is a bank-run equilibrium.
The experiment is then to see under which conditions a particular equilibrium arises.
The following figure shows the results of a classroom experiment run in Exeter on a single group of 18 students.[note 2] Investor types (roles) were randomly re-allocated at the start of every round, with 9 students being type A (impatient) investors and 9 students type B (patient) investors. The experiment lasted 23 rounds and there were 3 treatments. In the first treatment, lasting 8 rounds, conditions were set for R=2 and L=.5 (we call this ‘normal conditions’). Toward the last few rounds of this treatment, the students settled into the normal equilibrium. Type As withdrew today and type Bs withdrew tomorrow. In the second treatment, lasting 10 rounds, we had R=1.1 and L=.11. We might refer to this as a ‘credit crunch’. Tight conditions for the bank: not much leeway if depositors try to withdraw early. In this treatment, there was a run on the bank. In the third treatment, lasting 5 rounds, we also had R=1.1 and L=.11, but payments were halted after 9 depositors withdrew from the bank early. This suspension stopped the run on the bank. There was an instant effect that steadily improved.
There are many topics for lively discussion. Obviously, it is worthwhile to connect the experiment to current events. Another topic is to discuss various ways to help avoid a bank run (suspension, deposit insurance, the government stepping in). While not in the experiment or model, this leads to discussion about moral hazard.
 There were 18 computer terminals and the students were paired up with an average of 2 to a computer.