Design
The experiment has three parts. The first part is a one-shot game. In the second part, after a surprise restart, the same groups of two participants repeat the game for 10 announced periods. In the third part, after another surprise restart, constant groups of two participants are exposed to a regime change.
In the first part of the experiment, participants are randomly assigned to be “firms” or “regulators”, and randomly matched into economies of one firm and one regulator. In line with the experimental literature on monopoly and oligopoly, we thus use a market frame, rather than just exposing participants to the opportunity structure. We do so for reasons of internal and external validity. It is much easier to understand the opportunity structure if it is framed as the interaction between a firm and a regulator. With the frame we thus have less reason to fear that participants do not understand the task. Moreover, if regulators know they are setting the stage for a firm, they learn that they are responsible for governing an industry. Behavioral effects of knowing that one has this task might affect their choices, as well as the reactions of firms to such intervention.
The firm holds a monopoly. The regulator receives 50% of welfare as her incentive. In the instructions, we explain how welfare is calculated, and that consumer rent is factored in. We do so in the interest of making participants understand the nature of the normative conflict. Inverse demand is given by \(p = a - q\). Supply is characterized by \(p = q\). Consequently, welfare \(w\) is given by
$$w = pr + cr = p\left( {a - p} \right) - \frac{1}{2}\left( {a - p} \right)^{2} + \frac{1}{2}\left( {a - p} \right)^{2} = p\left( {a - p} \right)$$
(1)
where the first two terms define producer rent \(pr\), and the third term defines consumer rent \(cr\).
The intercept \(a\) of demand is randomly drawn from the uniformly distributed interval \(\left[ {1,201} \right]\).Footnote 3 The regulator moves first. She has power to impose any price cap she deems fit. The firm moves second. She chooses price \(p\), but may not exceed the price cap.
Note that we implement a market without fixed cost. In reality most regulated markets are characterized by high (if the market is a natural monopoly: prohibitively high) fixed cost that can moreover be sunk cost. High fixed cost shields incumbents from market entry, especially since incumbents have an incentive to bid aggressively to deter entry and to protect their upfront investment. In the interest of cleanly identifying the behavioral effect we are interested in, we abstract from this additional source of inefficiency and exclude market entry by design. This is analogous to a legally protected monopoly (which, in the past, was characteristic for many utilities). Consequently, additional welfare loss from “ruinous” competition and the duplication of investment is outside the scope of this paper.
We have a Baseline and two treatments. In the Baseline, the regulator knows \(a\). In the Upfront treatment, the regulator only knows the distribution. In the Signal treatment, she receives a signal that is correct with probability 50%. With a counterprobability of also 50%, the actual intercept of the demand function is (another) random draw from the distribution.
In our experiment, marginal cost increases in quantity (we set \(c = \frac{1}{2}q^{2} )\), which means that the firm makes a positive profit even if it sets the market clearing price \(p^{**} = \frac{1}{2}a\). The main reason for this specification of the supply function is experimental. Had we chosen constant marginal cost, or marginal cost decreasing in quantity, if regulators maximize welfare firms make zero profit. We would have had to compensate experimental firms by a substantial show-up fee. Profit would only have had a negligible impact on their payoff.Footnote 4 In the field, regulating firms in markets with increasing marginal cost is not infrequent either. The social benefit from regulation results from the difference between monopoly price and the welfare-maximizing price. A practical illustration is monopoly resulting from the fact that one firm has superior access to the scarce input that causes marginal cost to increase in quantity. This is characteristic for an “essential facility”, a frequent object of regulatory oversight.Footnote 5
In regulatory practice, the authority does not pocket in half the welfare. But the authority knows full well that it is in charge of balancing out consumer and producer interests. This is why we explicitly tie the authorities’ payoff to consumer and producer rent. We want to incentivize regulators so that their choices are credible. And we want to make sure that they earn approximately the same amount as firms to minimize fairness concerns. It is not far-fetched that actual regulators have an incentive to care about the performance of regulated industries. The more they visibly do a good job, the more they are likely to maintain, if not increase, their powers, and to be better equipped. This design feature has the additional advantage that we need not be concerned about collusion between the regulator and the firm. (In expectation) the regulator has nothing to gain from being overly generous with the firm. The design also excludes side-payments, so that there is no room for bribery.
If unregulated, the firm sets monopoly price \(p^{*} = \frac{2}{3}a\).Footnote 6 In anticipation, the regulator imposes cap \(c^{b} = p^{**} = \frac{1}{2}a\). The regulator prevents the firm from exceeding the welfare-maximizing price. At the expected value of \(a\), i.e., at \(a = 101\), the regulator sets \(c = 50.5\). Since the monopoly price is strictly above this price, the regulatory constraint binds.
In the Upfront regime, the regulator only knows that \(a \in \left[ {1,201} \right]\), and that all realizations of the intercept of the demand function are equally likely. In the face of this uncertainty, welfare is given by (2).Footnote 7
$$wu = \mathop \smallint \limits_{a = 1}^{{a = \left( {\frac{3}{2}} \right)c}} \frac{2}{9}a^{2} da + \mathop \smallint \limits_{{\left( {\frac{3}{2}} \right)c}}^{201} \frac{1}{4}a^{2} da$$
(2)
The first term captures welfare if the cap is not binding and the firm sets the monopoly price. The second term captures welfare for all realizations of \(a\) for which the given cap \(c\) binds. Maximizing this objective function leads to an optimal cap of \(c^{u} = 80.4\). With this cap, expected welfare is at 3248.24, while it would be 3383.58 in the first-best. Society loses (some) welfare since it lacks a technology for completely hindering the firm from earning a monopoly rent. The welfare loss results from the institutional constraint imposed by price cap regulation. With regulation, however, the economy is still better off than with laissez-faire. When unregulated, the firm would always set the monopoly price, and the economy would expect to earn only 3007.63.
From (1), and solving for \(p\), we learn that producer rent turns negative whenever \(p < \frac{1}{3}a\). Producers would have to serve a demand that is too large to leave them a profit. Negative profits of regulated firms are unlikely, if not illegal, in regulatory practice, and impractical in the lab. We therefore cut profit at 0 by imposing \(p = \hbox{max} \left\{ {p_{regulated} ,\frac{1}{3}a} \right\}\). However, we do not have to adjust the regulator’s problem (2) to this fact.Footnote 8 As we have seen, if she maximizes her payoff, the regulator sets \(p = 80.40\). With this cap, the firm never makes a negative profit. Hence in equilibrium the regulated price is never so low that it is replaced by \(\frac{1}{3}a\).
In the Signal regime, the regulator receives a signal \(a_{s}\) that is correct with probability 50%. With counterprobability 50%, the true value of \(a\) is a random draw from the uniform distribution. The regulator maximizes expected welfare
$$ws = \frac{1}{2}w + \frac{1}{2}wu$$
(3)
which leads to
$$p^{rs} = \frac{1}{2}\frac{1}{2}a_{s} + \frac{1}{2}\frac{402}{5}$$
(4)
The chosen price cap depends on the signal \(a_{s}\). If the signal is at the expected value of \(a\), i.e., at 101, the regulator sets \(p^{rs} = 65.45\).Footnote 9
Provided regulators are risk-neutral and maximize rent, we thus predict price caps as in Table 1.
Table 1 Predicted price caps per treatment predictions assuming \(a = 101\)
At the beginning of the experiment, we play this game one-shot. At the end of this period, participants receive feedback about choices, payoffs, welfare, and consumer rent. After a surprise restart, we repeat the experiment 10 announced times. In each period, ex post both the firm and the regulator are informed about the current realization of \(a\), and about payoffs. However in the Upfront and in the Signal treatments, the regulator may only once set a price cap, before the firm takes her first decision. At this point, in the Upfront treatment the regulator only knows the distribution of \(a\). In the Signal treatment, the regulator is informed that, initially, \(a = a_{s}\). The regulator further knows that in every period, with probability \(.1,\) there is a random shock, and \(a\) is replaced by a new draw from the distribution (which may, of course, also be \(a_{s}\)). It is common knowledge that, during these 10 periods, no more than one shock occurs. Provided both the firm and the regulator hold standard preferences and this is common knowledge, repetition does not change best responses and hence equilibria. However, comparing the one-shot experiment with the repeated experiment, we see whether having to decide for an extended duration has a separate effect.
After 10 periods, we have another surprise restart. We keep pairs fixed. Pairs that were in the Baseline are now either in the Upfront or in the Signal regime. Pairs that were in the Upfront or in the Signal regime are now in the Baseline. The intercept of the demand curve a is newly determined at random. It again changes once during the following 9 periods. After the regime change, money-maximizing regulators adjust to the new opportunity structure.
Demand is represented by the computer. This avoids the confound with the motivational effect of harming passive experimental participants.
We use three combined approaches to make sure that all participants understand the game. In the instructions, we explain the opportunity structure in words, equations, and graphs (see Appendix). In the control questions, we have participants calculate simple examples. They are only allowed to participate in the experiment after they have answered all questions correctly. In each period, each participant has access to a simulator.Footnote 10 Participants may try out as many combinations of parameters as they like. Participants heavily use the tool. In the first period, in the Baseline, firms on average use the tool 22.17 times, and regulators use it 13.96 times. In the Signal treatment, firms on average use the tool 17.42 times, and regulators 12.75 times. Finally, in the Upfront treatment, firms on average use it 20.42 times, and regulators 15.92 times. In the second period (and pooled over treatments), firms on average run 16.15 simulations, and regulators run 15.42 simulations. In period 12, i.e., after the second restart, these numbers are 10.69 and 9.02 simulation runs. The simulator calculates quantity, firm, and authority payoff and consumer rent for them.
Hypotheses
With common knowledge of rationality, we predict
H
1
Regulators and firms play best responses.
Despite all the safeguards for making sure participants understand the structure of the game, a first potential qualification is cognitive. Regulators and firms might nonetheless need experience to find their preferred choices. Moreover, the standard framework assumes that the firm maximizes profit under the constraint of the cap. In reality this need not be true either. Consequently, the regulator not only faces stochastic, but also strategic uncertainty. The regulator would benefit from gaining a sense of the firm’s behavioral traits, and adjusting its intervention. For these reasons, the Baseline may have the advantage of easing regulatory learning. A motivational effect points in the same direction. It may be couched in fairness terms: the more an agent is powerful, the more she may feel the urge to respect the legitimate interests of others under her spell. In all fairness, power comes with responsibility. It has been shown that this effect is quite pronounced (Engel and Zhurakhovska 2017). In the Upfront and Signal treatments, the regulator has the power to expose the firm to a risk of not making any profit that neither of them overlooks. This yields
H
2
In the Baseline, caps are closer to the prediction from standard theory than in the Signal and in the Upfront treatments.
The standard framework assumes all agents to be risk-neutral. In reality this need not be the case. Since in our design firms can directly adjust to any new development, risk preferences do not lead to the prediction of treatment differences for firms. Regulators might, however, dread two risks: By setting a cap that is too stringent, from an ex post perspective they may have reduced welfare, and hence their own payoff. Moreover, the cap may have cut into the firm’s profit (down to forcing the firm to make zero profit). The risk may materialize in the Signal treatment provided the signal is below \(a_{s} = 107.2\). This leads to
H
3
In the Signal treatment, caps are more lenient than predicted by standard theory.
In the standard framework, conditional on the realization of \(a\), the regulator can predict the firm’s choices with certainty. If the regulator sets a generous cap, or no cap at all, the regulator knows the firm will exploit the opportunity. Experimental work on the “hidden costs of control” suggests that this might not be true (Falk and Kosfeld 2006). If the regulator gives the firm more leeway than it must, the firm might feel obliged to reciprocate by not abusing this freedom. Hence regulators might succeed in transforming the interaction into a gift-exchange relationship. In the Baseline, the regulator has enough information to impose perfectly the solution that is best for her. In the remaining treatments, the regulator is unable to observe the current state of the world. If the regulator sets a generous cap, this may be an attempt at creating a trust relationship. Yet for the firm this signal is more difficult to interpret. A generous cap may also result from a lack of understanding, or from risk aversion. In anticipation, investment into a trust relationship is a less attractive strategy in the Signal and Upfront regimes. Moreover, if firms abuse the trust regulators put on them, in the Baseline regulators can strike back in the next period by reducing the cap, potentially even by imposing an overly severe cap as a punishment. None of this is possible in the remaining regimes. This leads to a competing hypothesis:
H
4
In the Baseline, the regulator is most likely to set an overly generous cap. In the Baseline, firms are most likely to react to a generous cap by setting a price below the monopoly price.
Post-experimental tests
The main experiment is followed by a standard trust game (Berg et al. 1995), with money sent by the trustor to the trustee tripled. Participants first play this game with authorities in the role of trustor, but participants newly matched to groups of two. At this point they do not know that another trust game is to follow with roles swapped, and again new partners. We rematch participants, since otherwise we would not measure their general propensity to trust, or to be trustworthy, but a lasting reaction to experiences made with a concrete interaction partner. We further administer the standard test for risk aversion by Holt and Laury (2002) and a questionnaire with demographic questions, the Big5 personality test (Rammstedt and John 2007) and a measure for justice sensitivity (Schmitt et al. 2005).
The experiment was conducted in the Bonn EconLab. It was fully computerized, using the software zTree (Fischbacher 2007). Participants were invited using software ORSEE (Greiner 2004). 96 students of various majors participated. In each sequence of treatments (Baseline-Signal, Baseline-Upfront, Signal-Baseline, Upfront-Baseline), we had 24 participants, i.e., 12 randomly composed groups of one firm and one regulator.Footnote 11 55 participants (57.29%) were female. The mean age was 24.40 years. The experiment lasted approximately 2 hours. Participants on average earned 22.27 € (28.66 $ on the days of the experiment), range [4.64, 45.68 €].