# Modelling transfer profits as externalities in a cooperative game-theoretic model of natural gas networks

## TL;DR

This paper introduces a novel game-theoretic method to model transfer profits as externalities in natural gas networks with regulated third-party access, addressing limitations of traditional characteristic function form models.

## Contribution

It proposes a new iterative flow-based approach to incorporate externalities into cooperative game models of gas networks with TPA, converting PFF games into CFF games for analysis.

## Key findings

- Method effectively captures externalities in gas networks with TPA
- Application to Central Eastern Europe network illustrates the approach
- Highlights the impact of Ukraine's transit role on bargaining power

## Abstract

Existing cooperative game theoretic studies of bargaining power in gas pipeline systems are based on the so called characteristic function form (CFF). This approach is potentially misleading if some pipelines fall under regulated third party access (TPA). TPA, which is by now the norm in the EU, obliges the owner of a pipeline to transport gas for others, provided they pay a regulated transport fee. From a game theoretic perspective, this institutional setting creates so called "externalities," the description of which requires partition function form (PFF) games. In this paper we propose a method to compute payoffs, reflecting the power structure, for a pipeline system with regulated TPA. The method is based on an iterative flow mechanism to determine gas flows and transport fees for individual players and uses the recursive core and the minimal claim function to convert the PPF game back into a CFF game, which can be solved by standard methods. We illustrate the approach with a simple stylized numerical example of the gas network in Central Eastern Europe with a focus on Ukraine's power index as a major transit country.