Stop Falling Off the Cliff: Experimental Tests for Reducing the Temptation to Overload a Network

Stop Falling off the Cliff: Experimental Tests for Reducing the Temptation to Overload a Network

John L. Hartman* Department of Economics University of California Santa Barbara Santa Barbara, CA 93106 email: [email protected]

January 2011

Abstract This paper experimentally tests the effectiveness of two methods to try to ensure that quantity demanded remains below capacity in an electricity distribution grid. The first method involves taxing high-use consumers and rebating this money to low-use consumers. The second method involves allowing a communication period to coordinate efforts to decrease the quantity demanded. During the communication period, subjects make non-binding agreements to conserve electricity. The first method works better than the second, since subjects do not always adhere to their agreements.

Keywords: electricity grid, congestion, tax, rebate

JEL Classification Codes: C9, D4, H2, L1, Q3

* I would like to thank Gary Charness, Kelly Bedard, Philip Babcock, and participants at the 2008 International Economic Science Association conference for helpful comments. I am grateful for funding by a University of California Santa Barbara Non-Senate Faculty Professional Development Fund grant. 1. Introduction and Background

Electricity markets are unlike most other markets in many ways, due to the fact that most electricity consumption occurs as it is produced.1 Since storage is costly in an electricity market, the idea of dynamic pricing,2 based on hourly market conditions, has been proposed and tested

(Sanghvi 1989 and Faruqui and George 2005).3 The focus here is not on how much electricity to deliver to consumers in total, but on how to deliver the available electricity in an efficient manner without overloading the system or requiring forced blackouts.4 More specifically, is pricing a better mechanism to more efficiently distribute electricity than voluntary coordination?

For each experimental session, subjects start off without a mechanism to keep the quantity demanded from exceeding capacity. Later in the session, one of two methods is used to entice subjects to keep the grid from overloading. The first is the use of a tax5 in which the only equilibria prevent the grid from overloading. Tax money paid by high-level consumers is used to rebate low-level consumers. The second method involves allowing subjects to communicate and make non-binding conservation agreements. In the use of this method, subjects may be interested in issues dealt with by behavioral economists, such as fairness and reciprocation.6

1 See Bohn, Caramanis, and Schweppe (1984) for a thorough analysis of pricing electrical networks over space and time. 2 Without dynamic pricing, pricing does not coincide with the marginal cost of production. This leads to inefficient consumption, with some users of electricity implicitly subsidizing others. 3 Economists have looked at other markets that may benefit from dynamic pricing. For experimental examples with automobile congestion, see Selten et al. (2007) and Hartman (2009). For an analysis of internet congestion, see MacKie-Mason and Varian (1994). 4 In the long-run, capacity on congestible networks like electricity grids can be altered. For arguments for and against different approaches of electricity transmission expansion, see Rosellón (2003). 5 This can be looked at as being equivalent to a paying a higher marginal cost for electricity use above a given consumption level. 6 For more on reciprocity, see Fehr and Gächter (2000).

2 2. The electricity grid, equilibrium, taxes, and communication

Eighteen people are consumers of electricity. On any given day, each person can consume at one of two levels, high use or low use. The grid overloads when there are more than

10 people at high use. For high users, the payout is +90 points when the grid does not overload, while it is –45 points when the grid overloads. For low users, the payouts are +0 points and –90 points, respectively.

Under this payout structure, there are two types of pure-strategy Nash equilibria.7 The first is efficient, given the capacity of the grid. When exactly 10 people consume at high use, nobody can be made better off by switching their choice, and the highest total payout of +900 occurs. Figure 1 shows total payout as a function of the number of high users.

When consumption exceeds 10 people at high use, the gain “falls off the cliff,” becoming a substantial loss. This is due to the system overloading, leading to a major inconvenience to users, since electricity must be shut off to some customers in order to prevent the system from overloading.8

The second type of Nash equilibrium occurs when the grid overloads. Given that the grid overloads, everyone will prefer high use to low use, leading to an equilibrium of all 18 people consuming at high use.

Taxes can encourage conservation so that the grid does not overload. When taxes are introduced, the high users pay the tax and the low users receive an equal share of the tax money collected. This tactic has appeal, since some tax amounts lead to an equilibrium in which all players receive net payoffs that are positive and equal. Two taxes are examined here. In the case

7 Note that high use is not a dominant strategy. 8 This payout structure can be viewed such that high users get some benefit (relative to the low users) before rotational blackouts occur.

3 of the 40-point tax, equilibrium occurs with 10 people consuming at high use, paying 400 points total in taxes. A 45-point tax is also examined, with equilibrium at 9 people at high use.

Another mechanism to encourage conservation is to let people communicate with each other. People can determine in advance who consumes at high use on any day, but cheating can occur if these agreements are not binding. If the 18 people agree on 10 people at high use, then an efficient outcome occurs, with a total payout of +900. However, low-use consumers may deviate, especially if they believe that other low users will deviate, too.

3. Experimental Design

Each experimental group of 18 subjects goes through two parts of an experimental session, each with 30 rounds.9 Part 1 involves the experimental set-up described in the previous section without taxes or communication. Part 2 adds a 40-point tax, a 45-point tax, or the ability to communicate with each other for five minutes. Two sessions are run with each of the taxes, with each subject starting with a point endowment of 2000 points. Three sessions are run with the communication treatment, and each subject starts with a 3000-point10 endowment.11

Subjects are also told one other aspect related to their payoffs. At the end of the experimental rounds, a 30-sided die is rolled twice. From the number on the die, subjects receive an extra 10 times the gain or loss from the respective rounds in each part of the experiment. This is done in order to keep subjects from thinking that they will necessarily be bankrupt at the end of the experiment and to motivate their efforts through every round of the experiment.

9 This experiment was programmed and conducted using z-Tree (Fischbacher 2007). Full instructions are available from the author upon request. 10 Communication sessions are given a higher point endowment, due to the higher expected point loss during the experiment. 11 Six additional sessions are run with different point endowments and/or fewer subjects. The results of these sessions are similar to those presented here.

4 At the end of the experiment, each subject receives cash at a conversion rate of one dollar per 100 points for any remaining points. Each subject also receives a $5 show-up fee.

4. Results

In the first part of each session, subjects are not told which treatment they receive in Part

2. Figure 2 shows that all seven sessions are similar in the first 30 rounds. Of all 210 rounds in the figure, all but four resulted in the grid overloading. In most of the early rounds, 12 to 16 subjects choose high use. Subjects likely realize that the grid always overloads, and adjust their choices accordingly in later rounds.

In the second part of each session, subjects are told of one of the three treatments. In the sessions with taxes, subjects quickly adjust their behavior so that most of the rounds have 10 or fewer at high use (see Figures 3 and 4). All of the groups using communication agree to have half of the subjects at high use and the rest at low use in the first round. They also agree to have each person alternate between high use and low use during the 30 rounds. If subjects follow the agreement, then there are nine at high use in every round, leading to one or more of the low users to be tempted to improve their payout by deviating from the agreement. If there is enough deviation from the agreement, a similar result to Part 1 can occur. Some of this occurs in the three communication sessions (see Figure 5). The results vary, from the grid never overloading

(Session 7) to the agreement breaking down from the beginning (Session 1).

Another way to analyze the results is to look at relative efficiency. Table 1 shows that the sessions with taxes generally do well. Although the 40-point tax predicts equilibrium with greater efficiency than in the 45-point tax case, the 45-point tax works better than the 40-point tax. This is probably due to the lower tax leading to an equilibrium that is too close to the

5 “cliff.” Sessions with communication have no enforcement mechanism, and so there is more variance in the results. In fact, although the communication sessions do worse on average, the session with the highest average payout involves communication.

5. Conclusion

Many states are already working on long-term plans to reduce electricity use,12 including various methods being used to try to conserve electricity during peak demand periods. The main contribution from this paper is that financial incentives appear to be the better way to improve efficiency.

The above results bring some insight to the debate toward implementing policies that could help to meet the goal of energy conservation. The structure of taxes and rebates appears to lead to results that are stable, with consumption that is close to efficient. Voluntary agreements are less stable. Therefore, methods related to pricing (such as the use of taxes in this experiment) appear to hold the most promise in efficient use of electricity.

12 To see efforts made by each state, see http://www.aceee.org/sector/state-policy. For example, authorities in Arizona have ordered a 20 percent reduction to most electricity providers by 2020.

6 References:

Bohn, Roger E., Micheal C. Caramanis, and Fred C. Schweppe. 1984. “Optimal Pricing in

Electrical Networks over Space and Time.” RAND Journal of Economics, 15(3): 360-

Faruqui, Ahmad and Stephen George. 2005. “Quantifying Customer Response to Dynamic

Pricing.” The Electricity Journal, 18(4): 53-63.

Fehr, Ernst and Simon Gäcther. 2000. “Fairness and Retaliation: The Economics of

Reciprocity.” Journal of Economic Perspectives, 14(3): 159-181.

Fischbacher, Urs. 2007. “z-Tree: Zurich Toolbox for Ready-made Economic Experiments.”

Experimental Economics, 10(2): 171-178.

Hartman, John L. 2009. “Special Issue on Transport Infrastructure: A Route Choice

Experiment with an Efficient Toll.” Networks and Spatial Economics, forthcoming, DOI

10.1007/s11067-009-9111-1.

MacKie-Mason, Jeffrey K. and Hal Varian. 1994. “Economic FAQs About the Internet.”

Journal of Economic Perspectives, 8(3): 75-96.

Rosellón, Juan. 2003. “Different Approaches Towards Electricity Transmission Expansion.”

Review of Network Economics, 2(3): 238-269.

Sanghvi, Arun P. 1989. “Flexible Strategies for Load/Demand Management Using Dynamic

Pricing.” IEEE Transactions on Power Systems, 4(1): 83-93.

Selten, Reinhard, Thorsten Chmura, Thomas Pitz, Sebastian Kube, Michael

Schreckenberg. 2007. “Commuters Route Choice Behaviour.” Games and Economic

Behaviour, 58(2): 394-406.

Table 1: Average payouts by session and treatment in Part 2 Average payout

Communication -556.5 (Session 1) 397.5 (Session 4) 819 (Session 7) Average: 220

40-point tax 403.5 (Session 2) 265.5 (Session 5) Average: 334.5

45-point tax 546 (Session 3) 529.5 (Session 6) Average: 537.75

8 Figure 1: Total points gained or lost as a function of number of high users

Total gain or loss based on number of high users

200 s s

o 0 l / n

i 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

a -200 G -400

-1200 Number of high users

Figure 2: First 30 rounds of each session

First 30 rounds of each session

e Session 1

s 12 u Session 2 h g i 10 Session 3 h

t Session 4 a

r 8 e Session 5 b

m Session 6 u 6 N Session 7 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Period

Note: Sessions 1, 4, and 7 are communication sessions; sessions 2 and 5 are 40-point tax sessions; sessions 3 and 6 are 45-point tax sessions.

9 Figure 3: Sessions with a 40-point tax

40-point tax sessions

s 12 u

h g i 10

h Session 2

t a Session 5 r 8 e b m

u 6 N 4

0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 Period

Figure 4: Sessions with a 45-point tax

45-point tax sessions

s 12 u

h g i 10

h Session 3

t a Session 6 r 8 e b m

u 6 N 4

0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 Period

Figure 5: Sessions with communication

Communication sessions

s 12 u

g Session 1 i 10 h

t Session 4 a

e Session 7 b m

u 6 N 4

0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 Round