arXiv subjects

Philip R. Neary

Publications and source records attributed to Philip R. Neary.

12 recordsLinked to original sources

arXiv2026

Note on the size of a stable matching

Consider a one-to-one two-sided matching market with workers on one side and single-position firms on the other, and suppose that the largest individually rational matching contains $n$ pairs. We show that the number of workers employed and positions filled in every stable matching is bounded from below by $\lceil\frac{n}{2}\rceil$ and we characterise the class of preferences that attain the bound. We then identify the minimum number of equilibrium pairings that must be ``sacrificed'' when maximising the employment rate is the objective; if each stable matching is of size $\ceiling{\frac{n}{2}}$, then no such pairs appear when all vacancies are filled.

econ.TH↗

arXiv2025

Public Goods Games in Directed Networks with Constraints on Sharing

In a public goods game, every player chooses whether or not to buy a good that all neighboring players will have access to. We consider a setting in which the good is indivisible, neighboring players are out-neighbors in a directed graph, and there is a capacity constraint on their number, k, that can benefit from the good. This means that each player makes a two-pronged decision: decide whether or not to buy and, conditional on buying, choose which k out-neighbors to share access. We examine both pure and mixed Nash equilibria in the model from the perspective of existence, computation, and efficiency. We perform a comprehensive study for these three dimensions with respect to both sharing capacity (k) and the network structure (the underlying directed graph), and establish sharp complexity dichotomies for each.

cs.GT↗

arXiv2024

Speeding up deferred acceptance

A run of the deferred acceptance (DA) algorithm may contain proposals that are sure to be rejected. We introduce the accelerated deferred acceptance algorithm that proceeds in a similar manner to DA but with sure-to-be rejected proposals ruled out. Accelerated deferred acceptance outputs the same stable matching as DA but does so more efficiently: it terminates in weakly fewer rounds, requires weakly fewer proposals, and final pairs match no later. Computational experiments show that these efficiency savings can be strict.

econ.TH↗

arXiv2024

Finding all stable matchings with assignment constraints

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm, based on the iterated deletion of unattractive alternatives, that determines if assignment constraints are compatible with stability. Whenever there is a stable matching that satisfies the assignment constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.

econ.TH↗

arXiv2024

Tiebout sorting in online communities

This paper proposes a stylized, dynamic model to address the issue of sorting online. There are two large homogeneous groups of individuals. Everyone must choose between two online platforms, one of which has superior amenities (akin to having superior local public goods). Each individual enjoys interacting online with those from their own group but dislikes being on the same platform as those in the other group. Unlike a Tiebout model of residential sorting, both platforms have unlimited capacity so there are no constraints on cross-platform migration. It is clear how each group would like to sort themselves but, in the presence of the other type, only the two segregated outcomes are guaranteed to be equilibria. Integration on a platform can be supported in equilibrium as long as the platform is sufficiently desirable. If online integration of the two communities is a desired social outcome then the optimal policy is clear: make the preferred platform even more desirable. Revitalizing the inferior platform will never lead to integration and even increases the likelihood the segregation. Finally, integration is more elastic in response to an increase in platform amenities than to reductions in intolerance.

econ.GN↗

arXiv2023

Some coordination problems are harder than others

In order to coordinate players in a game must first identify a target pattern of behaviour. In this paper we investigate the difficulty of identifying prominent outcomes in two kinds of binary action coordination problems in social networks: pure coordination games and anti-coordination games. For both environments, we determine the computational complexity of finding a strategy profile that (i) maximises welfare, (ii) maximises welfare subject to being an equilibrium, and (iii) maximises potential. We show that the complexity of these objectives can vary with the type of coordination problem. Objectives (i) and (iii) are tractable problems in pure coordination games, but for anti-coordination games are NP-hard. Objective (ii), finding the best Nash equilibrium, is NP-hard for both. Our results support the idea that environments in which actions are strategic complements (e.g., technology adoption) facilitate successful coordination more readily than those in which actions are strategic substitutes (e.g., public good provision).

econ.TH↗

arXiv2023

Unique Stable Matchings

In this paper we consider the issue of a unique prediction in one to one two sided matching markets, as defined by Gale and Shapley (1962), and we prove the following. Theorem. Let P be a one-to-one two-sided matching market and let P be its associated normal form, a (weakly) smaller matching market with the same set of stable matchings, that can be obtained using procedures introduced in Irving and Leather (1986) and Balinski and Ratier (1997). The following three statements are equivalent (a) P has a unique stable matching. (b) Preferences on P* are acyclic, as defined by Chung (2000). (c) In P* every market participant's preference list is a singleton.

econ.TH↗

arXiv2023

Ignorance is Bliss: A Game of Regret

An individual can only experience regret if she learns about an unchosen alternative. In many situations, learning about an unchosen alternative is possible only if someone else chose it. We develop a model where the ex-post information available to each regret averse individual depends both on their own choice and on the choices of others, as others can reveal ex-post information about what might have been. This implies that what appears to be a series of isolated single-person decision problems is in fact a rich multi-player behavioural game, the regret game, where the psychological payoffs that depend on ex-post information are interconnected. For an open set of parameters, the regret game is a coordination game with multiple equilibria, despite the fact that all individuals possess a uniquely optimal choice in isolation. We experimentally test this prediction and find support for it.

econ.TH↗

arXiv2023

Complexity Dichotomies for the Maximum Weighted Digraph Partition Problem

We introduce and study a new optimization problem on digraphs, termed Maximum Weighted Digraph Partition (MWDP) problem. We prove three complexity dichotomies for MWDP: on arbitrary digraphs, on oriented digraphs, and on symmetric digraphs. We demonstrate applications of the dichotomies for binary-action polymatrix games and several graph theory problems.

cs.DM↗

arXiv2023

Complexity of Efficient Outcomes in Binary-Action Polymatrix Games with Implications for Coordination Problems

We investigate the difficulty of finding economically efficient solutions to coordination problems on graphs. Our work focuses on two forms of coordination problem: pure-coordination games and anti-coordination games. We consider three objectives in the context of simple binary-action polymatrix games: (i) maximizing welfare, (ii) maximizing potential, and (iii) finding a welfare-maximizing Nash equilibrium. We introduce an intermediate, new graph-partition problem, termed Maximum Weighted Digraph Partition, which is of independent interest, and we provide a complexity dichotomy for it. This dichotomy, among other results, provides as a corollary a dichotomy for Objective (i) for general binary-action polymatrix games. In addition, it reveals that the complexity of achieving these objectives varies depending on the form of the coordination problem. Specifically, Objectives (i) and (ii) can be efficiently solved in pure-coordination games, but are NP-hard in anti-coordination games. Finally, we show that objective (iii) is NP-hard even for simple non-trivial pure-coordination games.

cs.GT↗

arXiv2022

Preference Swaps for the Stable Matching Problem

An instance $I$ of the Stable Matching Problem (SMP) is given by a bipartite graph with a preference list of neighbors for every vertex. A swap in $I$ is the exchange of two consecutive vertices in a preference list. A swap can be viewed as a smallest perturbation of $I$. Boehmer et al. (2021) designed a polynomial-time algorithm to find the minimum number of swaps required to turn a given maximal matching into a stable matching. We generalize this result to the many-to-many version of SMP. We do so first by introducing a new representation of SMP as an extended bipartite graph and subsequently by reducing the problem to submodular minimization. It is a natural problem to establish the computational complexity of deciding whether at most $k$ swaps are enough to turn $I$ into an instance where one of the maximum matchings is stable. Using a hardness result of Gupta et al. (2020), we prove that this problem is NP-hard and, moreover, this problem parameterised by $k$ is W[1]-hard. We also obtain a lower bound on the running time for solving the problem using the Exponential Time Hypothesis.

cs.DS↗

arXiv2021

The Effect of Social Distancing on the Reach of an Epidemic in Social Networks

How does social distancing affect the reach of an epidemic in social networks? We present Monte Carlo simulation results of a capacity constrained Susceptible-Infected-Removed (SIR) model. The key modelling feature is that individuals are limited in the number of acquaintances that they can interact with, thereby constraining disease transmission to an infectious subnetwork of the original social network. While increased social distancing always reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network. Our results also reveal the importance of coordinating social distancing policies at the global level. In particular, the public health benefits from social distancing to a group (e.g., a country) may be completely undone if that group maintains connections with outside groups that are not following suit.

q-bio.PE↗