On the Impact of Player Capability on Congestion Games

TL;DR

This paper investigates how varying player capabilities influence social welfare in congestion games, introducing a new complex game model and formalizing capability effects through program-based strategies.

Contribution

It introduces the Distance-bounded Network Congestion game (DNC), analyzes its computational complexity, and formalizes the impact of player capabilities on social welfare at equilibrium.

Findings

DNC is PLS-complete, unlike standard symmetric network congestion games.

Capability bounds can increase, decrease, or leave social welfare unchanged.

Four capability preference properties are characterized with necessary and sufficient conditions.

Abstract

We study the impact of player capability on social welfare in congestion games. We introduce a new game, the Distance-bounded Network Congestion game (DNC), as the basis of our study. DNC is a symmetric network congestion game with a bound on the number of edges each player can use. We show that DNC is PLS-complete in contrast to standard symmetric network congestion games which are in P. To model different player capabilities, we propose using programs in a Domain-Specific Language (DSL) to compactly represent player strategies. We define a player's capability as the maximum size of the programs they can use. We introduce two variants of DNC with accompanying DSLs representing the strategy spaces. We propose four capability preference properties to characterize the impact of player capability on social welfare at equilibrium. We then establish necessary and sufficient conditions for the four properties in the context of our DNC variants. Finally, we study a specific game where we derive exact expressions of the social welfare in terms of the capability bound. This provides examples where the social welfare at equilibrium increases, stays the same, or decreases as players become more capable.