Wealth inequality and the price of anarchy

Kurtuluş Gemici

National University of Singapore

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Elias Koutsoupias

University of Oxford

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Christos Papadimitriou

Columbia University

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Barnabé Monnot

Singapore University of Technology and Design

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Georgios Piliouras

Singapore University of Technology and Design

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Pricing induces optimal flow, PoA = 1 in Pigou

Equilibrium: stable, but inefficient

Optimum: unstable, but efficient

For heterogeneous agents x

Cost = type(x) * latency + price

Impact of game on income

• [Börjesson et al., 2012] Travel time / travel price elasticity equal to income.

Latency: time

Money

Price: money

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• Players have income q(x), play a routing game, income is now q

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Optimal toll induces highest inequality!

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• Pigou, q(x) = x, ℓ(x) = x

Latency

Inequality in symmetric routing games

Routing in Singapore

• Data collected by providing sensors to students in Singapore.�Records location during morning commute. (+ environmental factors)

(Figure by F. Benita)

Routing in Singapore

• Rental price dataset mapped with subjects’ home location.�(Rental price ~ income)�
• Latency correlates negatively with rental price.

Routing in Singapore

• With the precision of the sensors and associated algorithms, we can unpack further.

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• Pricier options correlate positively with rental price.

Many open questions!!

• Effect a tradeoff between efficiency and inequality.

Efficient algorithm to find tolls doing so.�

• Redistribute income.

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• Network design, using money raised from tolls to improve network links.

Done in practice, now and in the future.