Winning the Hardware Software Game Winning the Hardware-Software Game - 2nd Edition

Using Game Theory to Optimize the Pace of New Technology Adoption
  • How do you encourage speedier adoption of your product or service?
  • How do you increase the value your product or service creates for your customers?
  • How do you extract more of the value created by your product or service for yourself?


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Mapping apps, such as Waze and Google Maps, have created enormous value for users by helping them get to where they’re going faster. As least initially, when few people were using mapping apps, the apps were particularly helpful for individual users in rerouting them around traffic problems. However, now that a large portion of drivers has adopted mapping apps, we’re seeing problems with side routes becoming congested, as everyone is being rerouted through the same detours. So not only is there congestion on the original route -- from where drivers have been re-routed – but there is now congestion in many more additional locations in society – to where drivers have been re-routed.

It turns out that mapping apps are most beneficial to users for dealing with congestion problems when only a few users have adopted them. But they become less useful to users as more people adopt them. That is, the mapping apps exhibit negative network externalities for users when it comes to congestion. At the same time, as more people adopt mapping apps, other members of the community – those who live on the routes through which mapping app users are being re-routed – also suffer, yet another negative externality.

What we have is a game:

  • Providers of mapping apps want as many Users as possible to adopt
  • Users of mapping apps want as few Users as possible to adopt
  • Local Drivers want as few Users as possible to adopt
  • Freeway Drivers are happy if Users of mapping apps divert to local roads, if it reduces congestion on the freeway.

This analysis examines mapping apps and other types of resource allocation games.

The Mapping Apps Game

Overview of the Game

At any moment in time, the capacity on the roads is fixed. Drivers compete for space on the roads. Each driver wants to get to where he’s going as quickly and efficiently as possible, and he chooses the route he thinks will achieve this. As roads have become more congested, drivers have continued to use traditional (default) routes: freeways for longer, more direct trips, and local areas for shorter trips.

Mapping apps are data driven arbiters of road space. They use information on current traffic patterns to re-route drivers to get them to where they’re going more quickly (in theory). In other words, instead of relying on traditional, ad hoc patterns of commute, mapping apps use data on real-time traffic patterns to route drivers more efficiently.

The nature of the mapping apps is to re-route drivers away from more congested roadways (say, freeways) onto less congested roadways (say, local roads) (see Figure 1). This helps the re-routed driver (i.e., app user), to the benefit of other freeway drivers, and at the expense of other local drivers. So mapping apps create the following benefits for the different groups of players:

  • Mapping App Provider: Gain
  • Re-routed Driver: Gain
  • Freeway Drivers: Gain
  • Local Driver: Lose

The net benefit to society will depend on the relative magnitudes of the gains and losses to each group.

Figure 1

1 game 

More specifically, the net impact on society of the routing depends on the following factors (see Figure 2).

  • The degree of congestion on freeways before and after re-routing (n/N): Provides a measure of the amount of relief non-diverted freeway drivers enjoy from the diversion
  • The portion of freeway drivers diverted onto local roads [(n’ + n*)/N*]: Provides a measure of the increase in the amount of congestion local drivers suffer due to the diversion.
  • The degree of congestion on local roads before and after re-routing (n*/N*): Provides a measure of the increase in the amount of congestion local drivers suffer from the diversion.
  • The Number of apps developers: Provides a measure of the level of inefficiency in re-routing diverted drivers due to lack of coordination.

Figure 2

2 def variables 


Winners and Losers

The gains and losses to each player at different levels of congestion are presented in Figures 3 and 4. Figure 3 shows the utility to each set of drivers when there is ample road capacity, while Figure 4 shows the utility to each set of drivers with insufficient road capacity.

The payoffs to each of the players before mapping apps are introduced into the market are designated as B(efore) payoffs. The payoffs to each of the players after mapping apps are introduced into the market are designated as A(fter) payoffs. More specifically, the net gains to each set of players after mapping apps have been introduced are:

Total Gain to All Drivers:                  Solid black line – Dashed blacked line

Gain to Mapping Apps Users:          Blue line – Solid orange line

Gain to Local Drivers:                       Solid green line – Dashed green line

Gain to Freeway Drivers:                  Solid orange line – Dashed orange line

Figure 3

Ample Road Capacity

(B: Before use of App, A: After use of App)

3 100 100 9 1.1 

Figure 4

Too Little Road Capacity

4 25 50 9 1.1 

Comparisons of pre- and post-app payoffs indicate the following.

  • At relatively low rates of diversion, mapping apps make Apps Users better off (difference between blue and solid orange lines), at the expense of Local Drivers (difference between dashed and solid green lines).
  • At moderate rates of diversion, Apps Users are somewhat better off, but at a greater cost to local drivers.
  • And at high levels of diversion, Apps Users and Local Drivers are all worse off, while Freeway Drivers may be a bit better off, due to freed-up congestion on the freeways.

So, if society as a whole is better off with mapping apps, it is when only a small portion of people use them. More generally, however, mapping apps only re-route drivers away from traditional routes after some threshold (i.e., moderate) level of congestion has been reached. In other words, at the point mapping apps are introduced into the market and play a role in diverting users from their traditional routes, use of mapping apps is likely to make society as a whole worse off.

Presumably, Freeway Drivers prefer taking the freeway over taking local routes; otherwise, they would be Local Drivers to begin with, and not Freeway Drivers. So there must be some amount of disutility to Freeway Drivers if they divert from using the freeway to using local roads. The greater is the disutility from diverting, then the greater is the loss to society when apps users divert. More specifically, in Figure 5, the costs diverted drivers impose on local drivers is the same, regardless of the benefits the diversion brings to diverted drivers. But when there’s greater disutility of diverting, diverted drivers generate lower benefits, themselves, from diverting, but they impose the same costs on local drivers. So the combined utility of diverted drivers and local drivers after the diversion is lower when there’s a greater disutility of diverting.

Figure 5

Too Little Road Capacity, High Disutility of Being Re-Rerouted

5 25 50 5 1.1 


The Resource Allocation Game

Examples of Games

Road Traffic

Scarce Resource: Roadways

Competing Users: Freeway Drivers, Local Drivers

Solution Providers: Mapping Apps Developers


Scarce Resource: Student acceptances to good colleges

Competing Users: Students

Solution Providers: SAT prep tutors and coaches

Consumer Attention

Scarce Resource: Consumers’ attention

Competing Providers: Content Providers

Solution Providers: Persuasion Techniques

Event Tickets

Scarce Resource: Event (e.g., concert, sporting event, theater) Tickets

Competing Users: Ticket Buyers

Solution Providers: Ticket Scalpers


Overview of the Game

1. Users compete for a scarce resource. The game generally evolves organically, as users adopt heuristics or ad hoc methods for making allocation decisions. For example, drivers may decide to use local roads only when staying in town and freeways only when going out of town. Students do the best they can with the SAT on their own.

2. More users enter the game, and congestion develops.

3. At some point, ad hoc methods no longer provide optimal actions for every user. Some users might start to adapt to increases in congestion on their own, creating new heuristics. For example, drivers might use local roads to bypass certain freeway entrances during rush hour. Or ticket buyers might queue up in advance of ticket sales. Students may study extra hard for the SAT.

4. Eventually a new player enters the game, offering select users a more systematic (e.g. data-driven) method for determining actions. The new method provides select users an advantage over other users. However, because the resource at issue is scarce, the users who benefit from the new method do so at the expense of other users. For example, mapping apps providers enable freeway users to bypass freeway congestion using local roads. But the diversion of freeway users to local roads increases congestion for local drivers. Ticket scalpers help people with (i) high time costs and/or (ii) high event valuations buy tickets more readily, at the expense of people with lower time costs or lower valuations. SAT coaches help people with lower time costs and or higher ability to pay to spend more time and resources prepping for the SAT, at the expense of students with higher time costs and/or less ability to pay for tutors.

Because the resource at issue is scarce, any benefits early users of the new method enjoy from the new method quickly dissipate as more users adopt the new method.

5. Gains by early users of the new method attract (i) new providers of similar methods, as well as (ii) more users. Early success with the new method thus inevitably leads to over-use of the new method. Too much traffic diversion. Too many scalpers foreclosing the market. Too many students getting extra coaching for SAT exams.

6. Multiple providers for and excessive users of the new method may lead to less coordination and/or more congestion than there would have been without the new method. That is, excessive adoption may lead society to be worse off as a whole.



Players in the Game Have Competing Interests

Benefits to users from adopting re-allocation methods generally decrease as more users adopt. Users of resource allocation solutions thus want as few other users as possible to also adopt the solution.

Profits to solutions providers generally increase as more users adopt. Solutions providers thus want as many users as possible to adopt.

In zero- and negative-sum games, society generally wants as little adoption as possible.

Initial Success Creates Overuse

If the reallocation solution initially increases benefits for early adopters, then other providers and other users will be attracted into the market. New entry by users leads societal benefits to decrease as moderate numbers of user adopt (as we saw in Figures 3 and 4). New entry by providers leads to less coordinated actions of users, which can decrease societal benefits (see next section).

Multiple Solutions Providers Create Coordination Problems

Currently, there are several different providers of mapping apps. Presumably, each has its own algorithm for routing drivers. Algorithms often reroute drivers in non-organic (unintuitive) ways. As more drivers are re-routed using different algorithms, traffic flows become much more unnatural or unintuitive, which creates chaos for all drivers. With uncoordinated re-routing across different providers, there is thus more chaos in the system than there would be either with a single provider or with no providers at all. Said differently, each provider is creating externalities for other providers by increasing the uncertainty in traffic flows.


Possible Solutions

Solutions Providers Incorporate Social Costs: The private costs to users of reallocation solutions are less than the social costs. One way to mitigate the problem is for solutions providers to incorporate the social costs into their solutions. In particular, mapping apps providers can design their solutions so that drivers are only re-routed when doing so does not increase congestion (unduly) on alternative roads. Of course, this is not likely to happen in free markets.

Coordination of Solutions: Solutions providers can coordinate their actions to create less chaos in the system. Again, this is not likely to happen in free markets.

Education: Solutions providers and users can be made aware of the costs they’re imposing on society by their actions. Perhaps shaming can be invoked in particularly egregious situations.

Transparency: In many cases, there’s a lot more uncertainty in the system than solutions providers are letting on and/or that users are aware of. If users are made aware of the extent of uncertainty, they may choose not to use re-allocation solutions that may not actually end up helping them, but that will still impose costs on others.

Increase Costs of Diversion: Alternatively, society (or those who stand to lose) can make it more costly for users (diverters) to re-allocate or divert. Ideally, society would like impose costs on users but not on non-users. Unfortunately, that’s difficult to do. Examples of raising the costs of diversion include decreasing speed limits on local roads or putting up stop signs or speed bumps to slow through traffic.

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