arXiv subjects

Jorge Bruno

Publications and source records attributed to Jorge Bruno.

9 recordsLinked to original sources

arXiv2023

Efficient Public Good Provision Between and Within Groups

We generalize the model of Gallice and Monzon (2019) to incorporate a public goods game with groups, position uncertainty, and observational learning. Contributions are simultaneous within groups, but groups play sequentially based on their observation of an incomplete sample of past contributions. We show that full cooperation between and within groups is possible with self-interested players on a fixed horizon. Position uncertainty implies the existence of an equilibrium where groups of players conditionally cooperate in the hope of influencing further groups. Conditional cooperation implies that each group member is pivotal, so that efficient simultaneous provision within groups is an equilibrium.

econ.TH↗

arXiv2022

The graph minor relation satisfies the twin alternative conjecture

In 2006 Bonato and Tardif posed the Tree Alternative Conjecture (TAC): the equivalence class of a tree under the embeddability relation is, up to isomorphism, either trivial or infinite. In 2022 LaFlamme, et al. provided a rigorous exposition of a conter-example to TAC developed by Tetano in his 2008 PhD thesis. Also in 2022, the present author provided a positive answer to TAC for the topological minor relation. Along with embeddability and the topological minor, the graph minor relation completes the triad of the most widely studied graph relations. In this paper we provide a positive answer to TAC for the the graph minor.

math.CO↗

arXiv2022

Pricing and Electric Vehicle Charging Equilibria

We study equilibria in an Electric Vehicle (EV) charging game, a cost minimization game inherent to decentralized charging control strategy for EV power demand management. In our model, each user optimizes its total cost which is sum of direct power cost and the indirect dissatisfaction cost. We show that, taking player specific price independent dissatisfaction cost in to account, contrary to popular belief, herding only happens at lower EV uptake. Moreover, this is true for both linear and logistic dissatisfaction functions. We study the question of existence of price profiles to induce a desired equilibrium. We define two types of equilibria, distributed and non-distributed equilibria, and show that under logistic dissatisfaction, only non-distributed equilibria are possible by feasibly setting prices. In linear case, both type of equilibria are possible but price discrimination is necessary to induce distributed equilibria. Finally, we show that in the case of symmetric EV users, mediation cannot improve upon Nash equilibria.

econ.TH↗

arXiv2022

A Proof of the Tree Alternative Conjecture Under the Topological Minor Relation

We prove the Tree Alternative Conjecture for the topological minor relation: letting $[T]$ denote the equivalence class of $T$ under the topological minor relation we show that: $|[T]| = 1$ or $|[T]|\geq \aleph_0$ and $\forall r\in V(T)$, $|[(T,r)]| = 1$ or $|[(T,r)]|\geq \aleph_0$. In particular, by means of curtailing trees, we show that for any tree $T$ with at least one not eventually bare ray: $|[T]| \geq 2^{\aleph_0}$.

math.CO↗

arXiv2022

A Group Public Goods Game with Position Uncertainty

We model a dynamic public good contribution game, where players are (naturally) formed into groups. The groups are exogenously placed in a sequence, with limited information available to players about their groups' position in the sequence. Contribution decisions are made by players simultaneously and independently, and the groups' total contribution is made sequentially. We try to capture both inter and intra-group behaviors and analyze different situations where players observe partial history about total contributions of their predecessor groups. Given this framework, we show that even when players observe a history of defection (no contribution), a cooperative outcome is achievable. This is particularly interesting in the situation when players observe only their immediate predecessor groups' contribution, where we observe that players play an important role in motivating others to contribute.

econ.TH↗

arXiv2017

Locally finite trees and the topological minor relation

A well-known theorem of Nash-Williams shows that the collection of locally finite trees under the topological minor relation results in a BQO. Set theoretically, two very natural questions arise: (1) What is the number $λ$ of topological types of locally finite trees? (2) What are the possible sizes of an equivalence class of locally finite trees? For (1), clearly, $ω\leq λ\leq \mathfrak{c}$ and Matthiesen refined it to $ω_1 \leq λ\leq \mathfrak{c}$. Thus, this question becomes non-trivial when the Continuum Hypothesis is not assumed. In this paper we address both questions by showing that - entirely within ZFC - for a large collection of locally finite trees that includes those with countably many rays: the answer for (1) is $λ= ω_1$, and that for (2) the size of an equivalence class can only be either $1$ or $\mathfrak{c}$.

math.CO↗

arXiv2014

Metric axioms: a structural study

For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such $d$ naturally arise, such as separation, triangle inequality and symmetry. We present an order-theoretic investigation of various collections of weight structures, as naturally occurring subsets of $[0,\infty]^{X \times X}$ satisfying certain metric axioms. Furthermore, we exploit the categorical notion of adjunctions when investigating connections between the above collections of weight structures. As a corollary, we present several lattice-embeddability theorems on a well-known collection of weight structures on $X$.

math.GN↗

arXiv2014

Relaxed complete partitions: an error-correcting Bachet's problem

Motivated by an error-correcting generalization of Bachet's weights problem, we define and classify relaxed complete partitions. We show that these partitions enjoy a succinct description in terms of lattice points in polyhedra, with adjustments in the error being commensurate with translations in the defining hyperplanes. Our main result is that the enumeration of the minimal such partitions (those with fewest possible parts) is achieved via Brion's formula. This generalizes work of Park on classifying complete partitions and that of Rødseth on enumerating minimal complete partitions.

math.CO↗

arXiv2013

Pathological and Omega-transitive Representations of Free Groups

Given a linear order $Ω$ its automorphism group $\Aut(Ω)$ forms a lattice-ordered group via pointwise order. Assuming the continuum to be a regular cardinal, we show that \emph{pathological} and \emph{$ω$-transitive} (i.e. highly transitive) representations of free groups abound within \emph{large} permutation groups of linear orders. Consequently, under the Generalized Continuum Hypothesis it is then true that given any linear order $Ω$ for which $|Ω| = $ cof$(Ω) = \aleph_i$ ($i \in \N$) then any permutation group that is large in $\Aut(Ω)$ contains an $ω$-transitive representation of $G_{\aleph_{i}^+}$ (i.e. the free group of rank $2^{\aleph_i}$). In particular, and working solely within ZFC, we show that any large subgroup of $\Aut(\Q)$ (resp. $\Aut(\R)$) contains an $ω$-transitive and pathological representation of any free group of rank $λ\in [\aleph_0,2^{\aleph_0}]$ (resp. of rank $2^{\aleph_0}$). Lastly, we also find a bound on the rank of free subgroups of certain restricted direct products.

math.RT↗