The Price of Selfish Stackelberg Leadership in a Network Game

TL;DR

This paper investigates how a selfish leader in a network routing game can influence overall social cost by committing to a flow allocation, often increasing total costs while improving their own.

Contribution

It introduces the concept of a selfish Stackelberg leader in network games and analyzes its impact on social cost and individual costs, providing bounds in the two-player case.

Findings

The leader can reduce their own cost by sacrificing social welfare.

In simple networks, selfish leadership often increases total social cost.

Bounds on the worst-case additional cost are established for two-player scenarios.

Abstract

We study a class of games in which a finite number of agents each controls a quantity of flow to be routed through a network, and are able to split their own flow between multiple paths through the network. Recent work on this model has contrasted the social cost of Nash equilibria with the best possible social cost. Here we show that additional costs are incurred in situations where a selfish ``leader'' agent allocates his flow, and then commits to that choice so that other agents are compelled to minimise their own cost based on the first agent's choice. We find that even in simple networks, the leader can often improve his own cost at the expense of increased social cost. Focusing on the 2-player case, we give upper and lower bounds on the worst-case additional cost incurred.