Revenue Volatility under Uncertain Network Effects

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Opher Baron, Ming Hu and Azarakhsh Malekian discusses the revenue volatility of a monopolist selling a divisible good to consumers in the presence of local network externalities among consumers.

Image courtesy of interviewee. March 28, 2024

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This video discusses research focused on understanding the volatility of monopolistic revenue in contexts where customers influence one another, particularly in social networks with network externalities. The study examines how uncertain network structures—both in terms of connections and their strengths—affect a seller's pricing and revenue management strategies.

The research considers two types of uncertainty: robust optimization, where a fixed uncertainty set for network parameters is assumed, and stochastic optimization, which incorporates distributions of noise affecting the network's performance. The findings highlight that revenue volatility is influenced by the network structure, with varying connectivity leading to differing revenue responses.

A notable insight is that while uncertainty generally harms average performance, it can also present opportunities for increased expected revenue. This video suggests that businesses can leverage network uncertainties to their advantage through innovative products and services. The implications of these findings extend to policymakers, emphasizing the need for transparency in network operations to mitigate negative revenue volatility effects and enhance social welfare for both consumers and sellers.

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Here are five key points from the video:

1. **Network Externalities and Volatility**: The work focuses on understanding how revenue volatility in monopolistic markets is influenced by the interactions among customers in a network, where their consumption of a product or service is affected by the presence and actions of others.

2. **Uncertainty in Network Structures**: The study examines scenarios where the structure of the consumer network and the strength of their relationships are uncertain. This uncertainty can impact both the sellers' pricing strategies and the revenue generated from their products or services.

3. **Modeling Approaches**: The researchers use two main approaches — robust optimization (dealing with defined uncertainty sets) and stochastic optimization (considering distributions of noise) — to analyze how sellers can respond effectively to uncertainties in network externalities.

4. **Impact on Revenue Management**: Ignoring uncertainties in network structures when making pricing and revenue management decisions can lead to inaccurate predictions and poor outcomes, emphasizing the need for a deeper understanding of these dynamics.

5. **Implications for Businesses and Policymakers**: The findings suggest that businesses may need to adapt their pricing strategies based on the underlying network uncertainties to mitigate risks. Policymakers should consider the influence of network structures on market stability and explore regulatory measures to encourage transparency and fair practices, which could enhance social welfare.

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Here are some key quotes extracted from the video you :

1. **Understanding Monopolistic Revenue:**
"Our work focused on understanding how volatile is the monopolistic revenue when they sell to a group of customers that impact each other through their relationship."

2. **Impact of Network Externalities:**
"You can think about it as a social network when there are some network externalities among consumers."

3. **Uncertainty in Network Structure:**
"Our focus was what happens when this network structure is uncertain."

4. **Seller's Commitment to Prices:**
"The model assumes that sellers need to commit to prices in advance, and the quantity of service or product they will provide depends on these customer's interaction."

5. **Influence of Opinion Leaders:**
"If you send something on social media, and you wanna improve the consumption, you can offer discounts to opinion leaders."

6. **Literature on Strategic Customers:**
"There is plenty of literature on strategic customers and what are the welfare implications in the convideo of a network externality."

7. **Ignoring Uncertainty Leads to Poor Results:**
"The revenue management and pricing decisions when ignoring these uncertainties may be inaccurate and lead to poor results in this convideo."

8. **Robust vs. Stochastic Optimization:**
"We examine two specific uncertainties structures and try to optimize the seller's response given those uncertainties."

9. **Revenue Volatility and Network Structure:**
"The revenue volatility depends on the structure of the network, but this is not a simple task in practice."

10. **Counterintuitive Results Regarding Uncertainty:**
"We also have some counterintuitive results that suggested the expected revenue increases in the level of uncertainty."

11. **Policy Implications:**
"Understanding the monopolistic behavior is essential... regulations that would encourage some transparency in the network operation will allow you to get better and fairer practices."

12. **Impact on Social Welfare:**
"This revenue volatility impacts the social welfare for everybody, consumers, and the sellers."

These quotes reflect the central themes and findings discussed within the video, emphasizing the relationship between consumer networks, seller pricing strategies, uncertainty, and the implications for both businesses and policymakers.

X-TIMESTAMP-MAP=LOCAL:00:00:00.000,MPEGTS:90000

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So, our work, focused on understanding how,

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vol volatile is the monopolistic, revenue

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when they sell to, group of

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customers that impact each other,

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through their relationship.

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You can think about it as a social network

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when there are some network externalities among consumers.

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They appreciate the products more or less,

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or the services more

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or less, given how many other, people in the network

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use this, product or service.

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There is a lot of literature, on how this,

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can be done effectively depending on the network structure.

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Uh, but our focus was

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what happens when this network structure is uncertain.

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So you can think about,

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either you are uncertain in the connections

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that a specific person has with others in the network,

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or you are uncertain about

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how strong these connections are, among people.

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So your, your connection

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with your significant other is stronger, your connection

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with someone else, but we don't always know exactly,

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how strong are these connections

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and how they impact your benefit

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and your consumption level from the service or product.

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We are, looking at the, the model assumes that the,

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and this is what happens in reality, that sellers need to

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commit to prices in advance,

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and they, the quantity of service or,

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or product they will provide depend on

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these customer's interaction.

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And, therefore, the externalities

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of the connections

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between customers impact the revenue of the seller.

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Uh, you can think just as an example of what can,

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when this happens, if you send something on social me,

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media, and you wanna improve the consumption,

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you can offer discounts to opinion leaders.

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And then these opinion leaders, when they consume something

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and they show it to everyone else, they influence others,

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increasing your, your, total, profits, essentially.

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Uh, but you need to know what is the true,

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what is their true influence.

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Uh, knowing that Taylor Swift has, millions of followers

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doesn't imply that her strength

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or connection with all of them is, significant enough

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to generate enough, profit after, of it.

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So, indeed, as you said, there is plenty

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of literature on, strategic customers.

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And what are the welfare implications, in the context

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of a network externality?

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The main thing that is, ignored in the vast majority

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of the SRE is, as I said, the,

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the uncertainty in the network, the, the structure

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and the strength of the impacts

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of people on, one another.

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Uh, so in contrast to this previous literature

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that assume a fixed

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and non-network structure, we

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examine two specific uncertainties structures,

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and try to optimize the seller's response given

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those uncertainties.

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Essentially, the first one is them, is

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what is called robust optimization.

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So we have a given uncertainty set

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for the parameters of the network.

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And the other one is,

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a stochastic optimization where we have, some,

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distribution on the noise.

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Uh, and we, we wanna work given this, the,

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given this distribution

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and try to find how to effectively respond.

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And what we try to characterize in this context is also

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what is the impact of this uncertainty given the seller's

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decision on the volatility of the

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revenue that the seller is going to get out of, selling

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to this, network, given the externalities

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among customers there.

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And the, the revenue management

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and pricing decisions when ignoring these uncertainties

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may be inaccurate and lead to poor results in this context.

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So the main idea is, as you said, we look at the,

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network and the, the local network externalities where our

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customers are influencing each other.

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Uh, you can think about, social media

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as a great example, as I said, where if I write something

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and people respond to it, there's a lot of externality.

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Uh, our model, as I said, kind of allows

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to capture also the uncertainties in these network

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externalities and not taking them as, as given.

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And we investigate the impact of this on the revenue, the

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analysis, again, from both, both different, types

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of uncertainty, the, the set of errors in the structure,

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or we if we have some stochastic understanding

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of the noise on the accuracy of things.

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And we investigate how,

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the revenue volatility is affected by those different,

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uncertainties in the network's externalities,

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relatively technical, work.

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And the idea here, the, what, what we started is

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by showing the worst case revenue fluctuations,

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the variability in the revenue

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of the sellers under different uncertainty

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set on the network

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Externalities.

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This is, directed

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to the largest agent value of the network.

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Uh, metrics. Uh, we, this tells you that networks that are,

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that have different level of connectivity among them,

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essentially responds, differently.

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Uh, and it it suggests that, specific

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structure of network has less variability in the

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revenue than others.

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Uh, we, this is related to the robust,

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uncertainty that we investigate in the context

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where we looked at the uncertainty,

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with, with some, with normal noise,

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essentially Gaussian noise.

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Uh, we show that the revenue volatility depend on the

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network, which has less, uncertainties,

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but the revenue

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and its uncertainty may, increase.

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Uh, so the revenue may increase in the level

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of uncertainty in those less connected network.

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There is, the more connected networks are,

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to some extent, a little bit more robust.

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And there the, the volatility in the

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revenue is, smaller.

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Uh, the striking difference between those two mechanisms

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that the robust opt, the robust approach

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and this astic approach is that,

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they suggest different, different structure of networks are,

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increasing the volatility of the revenue

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or decreasing the volatility in their revenue.

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Uh, and that suggests that in reality,

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really all network structure are exposed to

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significant revenue volatility for the seller.

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So they need to create, to pick up their, prices

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with some sort of, some sort of

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awareness to the potential risk.

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And the revenue volatility depend the structure

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of the network, but,

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and the structure of uncertainty, as I said.

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But this is not a simple tasking practice.

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And so I started to touching a little bit on

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that when I answered your previous question.

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So basically, depending on the uncertainty, if it's robust

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or, or stochastic, businesses, need

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to think of different ways of controlling,

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their pricing.

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And also if they can impact the network structure,

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that is something that they need to consider

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and try to impact it in a way

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that would reduce uncertainties.

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Uh, effectively, we also have some counterintuitive results

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that suggested the expected revenue

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increase in the level of uncertainty.

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Uh, and this is something quite surprising

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'cause typically we think of uncertainty as something

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that harms your average performances.

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So that's certainly something interesting.

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Um, there is, this gives businesses some opportunity to,

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to leverage the uncertainty in the networks to their,

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to their, advantage essentially by, by using innovative,

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product and services that kind of take advantage

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of these network externalities

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and the uncertainty, the network externality externalities.

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Finally, for policy makers, it, I think it's important

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to understand the impact of,

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the network structure also on the market stability.

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And in this kinda, in this case, the monopolistic

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behavior, understanding the

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monopolistic behavior is essentials.

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We think of regulations

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that would encourage some transparency in the network

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operation, will allow you to get, better

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and fairer practices that will, mitigate,

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negative effects of revenue volatility.

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Because at the end of the day,

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this revenue volatility impacts, the social welfare

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for everybody, consumers, and, the sellers.

Understanding Revenue Volatility in Monopolistic Markets

00:00:00 - So, our work, focused on understanding how, vol volatile is the monopolistic, revenue when they sell to, group of customers that impact each other, through their relationship. You can think about it as a social network when there are some network externalities among consumers. They appreciate the products more or less, or the services more
00:00:34 - use this, product or service. There is a lot of literature, on how this, can be done effectively depending on the network structure. but our focus was what happens when this network structure is uncertain. So you can think about, either you are uncertain in the connections that a specific person has with others in the network,
00:01:07 - how strong these connections are, among people. So your, your connection with your significant other is stronger, your connection with someone else, but we don't always know exactly, how strong are these connections and how they impact your benefit and your consumption level from the service or product. We are, looking at the, the model assumes that the, and this is what happens in reality, that sellers need to
00:01:38 - and they, the quantity of service or, or product they will provide depend on these customer's interaction. And, therefore, the externalities of the connections between customers impact the revenue of the seller. you can think just as an example of what can, when this happens, if you send something on social me,
00:02:10 - you can offer discounts to opinion leaders. And then these opinion leaders, when they consume something and they show it to everyone else, they influence others, increasing your, your, total, profits, essentially. but you need to know what is the true, what is their true influence. knowing that Taylor Swift has, millions of followers
00:02:41 - or connection with all of them is, significant enough to generate enough, profit after, of it. So, indeed, as you said, there is plenty of literature on, strategic customers. And what are the welfare implications, in the context of a network externality? The main thing that is, ignored in the vast majority of the SRE is, as I said, the,

Optimizing Seller Responses to Network Uncertainties

00:03:10 - and the strength of the impacts of people on, one another. so in contrast to this previous literature that assume a fixed and non-network structure, we examine two specific uncertainties structures, and try to optimize the seller's response given those uncertainties. Essentially, the first one is them, is what is called robust optimization. So we have a given uncertainty set
00:03:41 - And the other one is, a stochastic optimization where we have, some, distribution on the noise. and we, we wanna work given this, the, given this distribution and try to find how to effectively respond. And what we try to characterize in this context is also what is the impact of this uncertainty given the seller's
00:04:15 - revenue that the seller is going to get out of, selling to this, network, given the externalities among customers there. And the, the revenue management and pricing decisions when ignoring these uncertainties may be inaccurate and lead to poor results in this context. So the main idea is, as you said, we look at the,
00:04:48 - customers are influencing each other. you can think about, social media as a great example, as I said, where if I write something and people respond to it, there's a lot of externality. our model, as I said, kind of allows to capture also the uncertainties in these network externalities and not taking them as, as given. And we investigate the impact of this on the revenue, the
00:05:20 - of uncertainty, the, the set of errors in the structure, or we if we have some stochastic understanding of the noise on the accuracy of things. And we investigate how, the revenue volatility is affected by those different, uncertainties in the network's externalities, relatively technical, work. And the idea here, the, what, what we started is by showing the worst case revenue fluctuations,
00:05:52 - of the sellers under different uncertainty set on the network Externalities. This is, directed to the largest agent value of the network. metrics. we, this tells you that networks that are, that have different level of connectivity among them, essentially responds, differently. and it it suggests that, specific structure of network has less variability in the

Revenue Volatility in Network Structures

00:06:23 - we, this is related to the robust, uncertainty that we investigate in the context where we looked at the uncertainty, with, with some, with normal noise, essentially Gaussian noise. we show that the revenue volatility depend on the
00:07:00 - but the revenue and its uncertainty may, increase. so the revenue may increase in the level of uncertainty in those less connected network. There is, the more connected networks are, to some extent, a little bit more robust. And there the, the volatility in the revenue is, smaller. the striking difference between those two mechanisms that the robust opt, the robust approach and this astic approach is that,
00:07:34 - increasing the volatility of the revenue or decreasing the volatility in their revenue. and that suggests that in reality, really all network structure are exposed to significant revenue volatility for the seller. So they need to create, to pick up their, prices with some sort of, some sort of
00:08:05 - And the revenue volatility depend the structure of the network, but, and the structure of uncertainty, as I said. But this is not a simple tasking practice. And so I started to touching a little bit on that when I answered your previous question. So basically, depending on the uncertainty, if it's robust or, or stochastic, businesses, need to think of different ways of controlling, their pricing. And also if they can impact the network structure,
00:08:39 - and try to impact it in a way that would reduce uncertainties. effectively, we also have some counterintuitive results that suggested the expected revenue increase in the level of uncertainty. and this is something quite surprising 'cause typically we think of uncertainty as something that harms your average performances. So that's certainly something interesting. there is, this gives businesses some opportunity to,
00:09:12 - to their, advantage essentially by, by using innovative, product and services that kind of take advantage of these network externalities and the uncertainty, the network externality externalities. Finally, for policy makers, it, I think it's important to understand the impact of, the network structure also on the market stability. And in this kinda, in this case, the monopolistic behavior, understanding the monopolistic behavior is essentials.

Encouraging Transparency to Mitigate Revenue Volatility

00:09:59 - that would encourage some transparency in the network operation, will allow you to get, better and fairer practices that will, mitigate, negative effects of revenue volatility. Because at the end of the day, this revenue volatility impacts, the social welfare for everybody, consumers, and, the sellers.

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Revenue Volatility under Uncertain Network Effects

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