Don't Overwhelm the Power Grid - A Simplified Congestion Game

This course is appropriate for principles or intermediate microeconomics courses. Students must be familiar with game theory. They should understand how to set up and read a payoff matrix. They should further be able to define and identify Nash Equilibria. There is no class size limitation for the exercise. One half to one whole class period is sufficient time for completion.

Overview

In this activity, students are given information to construct a simplified congestion game depicting usage of a power grid. We imagine two towns on the same grid with the strategies "use most power at peak time" and "use most power at off-peak time." We see that if both agents choose "peak" the grid is overwhelmed and there is a blackout. The options which avoid a black out are when they choose opposite strategies or when they both choose "off-peak." Students are then asked about regulatory solutions to the problem to avoid a blackout.

Expected Student Learning Outcomes

In this exercise students will set up a game theory payoff matrix based on a concrete situation, then propose methods to change the payoff matrix to avoid a suboptimal outcome for all.

Information Given to Students

Imagine there are two towns, Town A and Town B, on the same power grid. The grid services the two towns and no others. The power company designates the day into two periods. One is "peak" hours (the middle of the day) when a lot of power typically gets used. The other period is "off-peak" (mornings, evenings, and weekends) when there is generally less power usage.

The power company has found that if both Town A and Town B use most of their power during peak times, the grid gets overwhelmed and there is a blackout. If only one town uses most of its power during peak times but the other uses most of its power during off-peak times, the grid is fine. The grid is also fine if both towns use most of their power during off-peak times.

Part 1

Construct a payoff matrix which illustrates the situation above. Imagine that "peak time" is worth a payoff of 2 to each town, while "off-peak" is worth a payoff of 1. If both towns choose "peak", however, they both get a payoff of 0.

Part 2

Now, imagine your group is the city council in the town and you oversee the power company. Below are some strategies of how you could respond to the blackout issue. Pick a strategy and be prepared to defend your answer. Show how it would change the payoffs in your matrix.

A.) Stay hands-off and let the market decide. People know better for themselves when they need the power.

B.) Put an extra tax on peoples' power bills for usage during peak time. This will discourage them from using power then.

C.) Pay people a rebate if they use most of their power during off peak time. This will encourage them to switch to off-peak time as much as possible.

D.) Mandate that one town at a time is allowed to heavily use the grid during peak time. The towns can alternate days so they each have a turn with unrestricted peak time usage.

Before groups start debating regulatory choices, the instructor should confirm they all reached a correct payoff matrix. Given the information in the above section, the payoff matrix should look like this:

                              B
                        Peak Off-Peak
A   Peak            0,0 | 2,1
      Off-Peak     1,2 | 1,1

Both towns have an incentive to choose "peak." If they both choose "peak," however, the grid fails. If only one chooses "peak," everything is fine. The problem is we don't know who will choose it. If they both choose "off-peak" they are both fine, but that is not a Nash Equilibrium and it is not Pareto optimal.

Once students are confident in constructing and interpreting the matrix, they can move on to debating the choices.

Explanation of Choices

A.) Stay hands-off and let the market decide. People know better for themselves when they need the power.

This choice is probably not very realistic given the information provided. We can confidently say the town will be plagued by blackouts. A group arguing this choice would have to say that that is just the price of freedom and freedom must be protected.

B.) Put an extra tax on peoples' power bills for usage during peak time. This will discourage them from using power then.

Choices B and C will likely be the popular choices among the groups. If you are from an area where power grid issues are a common real-life occurrence (like I am here in California), the options will be familiar to you.

The benefits of the tax are that it will discourage consumers from using power during peak time, thereby alleviating the strain on the grid. It would also generate revenue for the town which could be used in other productive ways.

There are some issues associated with this choice as well. It could be that the tax disproportionately affects low income people in the town but high income residents can go about their lives still heavily using the power grid. Additionally, because power is a necessity and an inelastic good, it could be that people end up paying high taxes but crash the grid anyway as they still need the power.

Payoff matrices which incorporate a tax could lower the payoff of "peak" and look something like this:

                                B
                        Peak Off-Peak
A   Peak            0,0 | 1,1
      Off-Peak     1,1 | 1,1

                                B
                           Peak Off-Peak
A   Peak               0,0 | 0.5,1
      Off-Peak     1,0.5 | 1,1

C.)Pay people a rebate if they use most of their power during off peak time. This will encourage them to switch to off-peak time as much as possible.

This option is the flip side of option B. Option B is the stick, option C is the carrot. Instead of penalizing consumers for choosing the problematic option, the regulators can incentivize the desired one. If the incentive was successful, the strain on the grid could be averted without having to resort to painful taxes which would harm consumers' pocket books.

Some issues with this option include the fact that it may not end up working. People may just need to use the power more during peak time. Also, assuming a sizable enough rebate to adequately incentivize consumers to switch could be found, the town could find itself with a very large financial burden paying out the rebates. There would have to be other revenue raising programs to cover the rebates which would mean taxes or bonds that the townspeople would end up paying.

Payoff matrices which incorporate a rebate could increase the payoff of "off-peak" and look something like this:

                                B
                        Peak Off-Peak
A   Peak            0,0 | 2,2
      Off-Peak     2,2 | 2,2

                                B
                        Peak Off-Peak
A   Peak            0,0 | 2,3
      Off-Peak     3,2 | 3,3

D.) Mandate that one town at a time is allowed to heavily use the grid during peak time. The towns can alternate days so they each have a turn with unrestricted peak time usage.

This option will likely not be popular among the groups. It is anathema to the reasoning in our textbooks, but students might be able to find plausible examples of it working. For example, China achieved notable success controlling air pollution in large cities by mandating alternating days when only cars with either even or odd numbered license plates could drive.

Instructors can assess that students are understanding a basic level of understanding of game theory concepts by the students ability to set up matrices and correctly define and identify Nash Equilibria. Instructors will be able to assess when students surpass a basic understanding when students can demonstrate they are able to think critically about the assumptions for a game.