# Flow Allocation Games

## TL;DR

This paper introduces a game-theoretic model of flow allocation in networks, analyzing equilibrium existence, complexity, and efficiency, with implications for financial network incentives.

## Contribution

It provides new insights into equilibrium properties and computational complexity in flow allocation games, highlighting differences between ranking strategies.

## Key findings

- Pure Nash and strong equilibria existence results
- Complexity classifications for equilibrium computation
- Bounds on prices of anarchy and stability

## Abstract

We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the chosen allocation strategies evolves in the network. Each agent wants to maximize the amount of flow through her node. Flow allocation games can be used to express strategic incentives of clearing in financial networks. We provide a cumulative set of results on the existence and computational complexity of pure Nash and strong equilibria, as well as tight bounds on the (strong) prices of anarchy and stability. Our results show an interesting dichotomy: Ranking strategies over individual flow units allow to obtain optimal strong equilibria for many objective functions. In contrast, more intuitive ranking strategies over edges can give rise to unfavorable incentive properties.