Arms Race

David Levinson

The Onion

• A study by the American Public Transportation Association reveals that 98 percent of Americans support the use of mass transit by others.” They reported on a campaign supposedly kicked off by APTA "Take The Bus... I'll Be Glad You Did."

Richardson Arms Race Model

• Lewis Frye Richardson, a Quaker physicist, suggested that an arms race can be understood as an interaction between two states with three motives. 

• Grievances between states cause them to acquire arms to use against one another. 

• States fear each other and so acquire arms to defend themselves against the others’ weapons. 

• Because weapons are costly, their expense creates fatigue that decreases future purchases. 

Example

• ArmsRace.xls

How Does This Relate To Transport/Land Use

• Arms Races• Bicycle vs. Car• Bus vs. Car• SUV vs. Car• Communities fighting for development, • Communities building infrastructure

(competitive advantage/disadvantage)

Caveat Planner

• Richardson’s (or any abstract) model is obviously a simplification. We can relax assumptions and make it more realistic (e.g. (dis)economies of scale associated with arms … does fatigue per unit of armament increase or decrease with total level of armaments?)

Prisoner’s Dilemma

Player B

Player A

Cooperate

Defect

Cooperate

[10,10] [-15,15]

Defect [15,-15] [5,5]

Repeated Prisoner’s Dilemma

• If 2 players, and game repeated indefinitely, the incentive is to cooperate.

• However if the end is known, the incentive is to defect on the previous turn.

• Also, if there are multiple players, cooperation becomes much more difficult to achieve

Modal Arms Races

Modal Arms Races (payoffs are time, try to minimize)

Commuter 2

Commuter 1

Bus Car

Bus [10,10]Good bus service

[20, 5]Poor bus service

Car [5,20]Car takes advantage of empty roads

[15,15] congestion sets in

Travel Time as Mode Share Changes

Private vs. Social Effects

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Auto Mode Share

Travel Time

System Average Time Auto Time Bus Time

Model 1

• Here we assumed the following:

• MA = Auto Mode Share

• MB = Bus Mode Share = 1 – Auto Mode Share

• TA = Auto Travel Time

• TB = Bus Travel Time

€

TA = 1+ 0.15MA

0.75

⎛

⎝ ⎜

⎞

⎠ ⎟4

€

TB = TA +MA + 0.1

OR (Note Total Time Drops as Car Use Rises)

Alternate Model of Bus and Auto

0

1

2

3

4

5

6

7

8

9

10

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Auto Mode Share

Travel Time

Auto Time Bus Time System Average Time

• D = Schedule Delay

€

TB = TA +D + 0.1

Model 2

€

D =0.5

MB

Implications

• Driving is always faster than riding the bus.

• Total travel time would be minimized if everyone rode the bus. Buses could operated frequently and more directly.

• However, in the absence of cooperation, the rational outcome is for everyone to drive.

• Cooperation is difficult to achieve in multi-player games.

Cooperation

• How can cooperation be achieved?

Beijing: Cars vs. Bikes

Individual Rationality

• Assumption: Individuals will do what is in their own long term interest.

• This can’t always be measured.• Max U = f( time, money,

socioeconomics, demographics, etc.)• Probability of taking a mode: Pm =

eUm/∑eUm

Conclusions

• Mode share must be understood as a system involving competition.

• This competition, under certain circumstances (without subsidies for positive feedback industries, and without penalties for negative externalities), may result in socially sub-optimal results.

• The degree to which the results are sub-optimal, and subsidies are justified, depends on (1) belief that government can actually figure out where to direct subsidy (the pork problem), (2) understanding the dynamics of the system under question.

• Not all subsidies are warranted, though many are justfied wrongly based on this logic.