# The Bakers and Millers Game with Restricted Locations

arXiv: https://arxiv.org/abs/2501.05334 · HTML: https://mlsanity.com/paper/2501.05334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 14 of 14)

- [Fractional Hedonic Games](https://mlsanity.com/paper/1705.10116/) (2017)
- [Schelling Segregation with Strategic Agents](https://mlsanity.com/paper/1806.08713/) (2018)
- [Schelling Games on Graphs](https://mlsanity.com/paper/1902.07937/) (2019)
- [Convergence and Hardness of Strategic Schelling Segregation](https://mlsanity.com/paper/1907.07513/) (2019)
- [Individual-Based Stability in Hedonic Diversity Games](https://mlsanity.com/paper/1911.08669/) (2019)
- [Two-Stage Facility Location Games with Strategic Clients and Facilities](https://mlsanity.com/paper/2105.01425/) (2021)
- [Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games](https://mlsanity.com/paper/2204.12599/) (2022)
- [Hedonic Diversity Games](https://mlsanity.com/paper/1903.00303/) (2019)
- [From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation](https://mlsanity.com/paper/1903.04265/) (2019)
- [Stable Outcomes in Modified Fractional Hedonic Games](https://mlsanity.com/paper/1804.05040/) (2018)
- [Strategic Facility Location with Clients that Minimize Total Waiting Time](https://mlsanity.com/paper/2211.14016/) (2022)
- [Strategic Resource Selection with Homophilic Agents](https://mlsanity.com/paper/2305.00843/) (2023)
- [Location Games on Networks: Existence and Efficiency of Equilibria](https://mlsanity.com/paper/1601.07414/) (2016)
- [Equilibria in Two-Stage Facility Location with Atomic Clients](https://mlsanity.com/paper/2403.03114/) (2024)

## Abstract (arXiv)

We study strategic location choice by customers and sellers, termed the Bakers and Millers Game in the literature. In our generalized setting, each miller can freely choose any location for setting up a mill, while each baker is restricted in the choice of location for setting up a bakery. For optimal bargaining power, a baker would like to select a location with many millers to buy flour from and with little competition from other bakers. Likewise, a miller aims for a location with many bakers and few competing millers. Thus, both types of agents choose locations to optimize the ratio of agents of opposite type divided by agents of the same type at their chosen location. Originally raised in the context of Fractional Hedonic Games, the Bakers and Millers Game has applications that range from commerce to product design. We study the impact of location restrictions on the properties of the game. While pure Nash equilibria trivially exist in the setting without location restrictions, we show via a sophisticated, efficient algorithm that even the more challenging restricted setting admits equilibria. Moreover, the computed equilibrium approximates the optimal social welfare by a factor of at most 2left(fracee-1right). Furthermore, we give tight bounds on the price of anarchy/stability. On the conceptual side, the location choice feature adds a new layer to the standard setting of Hedonic Games, in the sense that agents that select the same location form a coalition. This allows to naturally restrict the possible coalitions that can be formed. With this, our model generalizes simple symmetric Fractional Hedonic Games on complete bipartite valuation graphs and also Hedonic Diversity Games with utilities single-peaked at 0. We believe that this generalization is also a very interesting direction for other types of Hedonic Games.