arXiv subjects

Pál András Papp

Publications and source records attributed to Pál András Papp.

24 records · Page 2Linked to original sources

arXiv2020

Sequential Defaulting in Financial Networks

We consider financial networks, where banks are connected by contracts such as debts or credit default swaps. We study the clearing problem in these systems: we want to know which banks end up in a default, and what portion of their liabilities can these defaulting banks fulfill. We analyze these networks in a sequential model where banks announce their default one at a time, and the system evolves in a step-by-step manner. We first consider the reversible model of these systems, where banks may return from a default. We show that the stabilization time in this model can heavily depend on the ordering of announcements. However, we also show that there are systems where for any choice of ordering, the process lasts for an exponential number of steps before an eventual stabilization. We also show that finding the ordering with the smallest (or largest) number of banks ending up in default is an NP-hard problem. Furthermore, we prove that defaulting early can be an advantageous strategy for banks in some cases, and in general, finding the best time for a default announcement is NP-hard. Finally, we discuss how changing some properties of this setting affects the stabilization time of the process, and then use these techniques to devise a monotone model of the systems, which ensures that every network stabilizes eventually.

cs.CE↗

arXiv2020

On the Hardness of Red-Blue Pebble Games

Red-blue pebble games model the computation cost of a two-level memory hierarchy. We present various hardness results in different red-blue pebbling variants, with a focus on the oneshot model. We first study the relationship between previously introduced red-blue pebble models (base, oneshot, nodel). We also analyze a new variant (compcost) to obtain a more realistic model of computation. We then prove that red-blue pebbling is NP-hard in all of these model variants. Furthermore, we show that in the oneshot model, a $δ$-approximation algorithm for $δ<2$ is only possible if the unique games conjecture is false. Finally, we show that greedy algorithms are not good candidates for approximation, since they can return significantly worse solutions than the optimum.

cs.CC↗

arXiv2020

A General Stabilization Bound for Influence Propagation in Graphs

We study the stabilization time of a wide class of processes on graphs, in which each node can only switch its state if it is motivated to do so by at least a $\frac{1+λ}{2}$ fraction of its neighbors, for some $0 < λ< 1$. Two examples of such processes are well-studied dynamically changing colorings in graphs: in majority processes, nodes switch to the most frequent color in their neighborhood, while in minority processes, nodes switch to the least frequent color in their neighborhood. We describe a non-elementary function $f(λ)$, and we show that in the sequential model, the worst-case stabilization time of these processes can completely be characterized by $f(λ)$. More precisely, we prove that for any $ε>0$, $O(n^{1+f(λ)+ε})$ is an upper bound on the stabilization time of any proportional majority/minority process, and we also show that there are graph constructions where stabilization indeed takes $Ω(n^{1+f(λ)-ε})$ steps.

cs.DM↗

arXiv2020

Network-Aware Strategies in Financial Systems

We study the incentives of banks in a financial network, where the network consists of debt contracts and credit default swaps (CDSs) between banks. One of the most important questions in such a system is the problem of deciding which of the banks are in default, and how much of their liabilities these banks can pay. We study the payoff and preferences of the banks in the different solutions to this problem. We also introduce a more refined model which allows assigning priorities to payment obligations; this provides a more expressive and realistic model of real-life financial systems, while it always ensures the existence of a solution. The main focus of the paper is an analysis of the actions that a single bank can execute in a financial system in order to influence the outcome to its advantage. We show that removing an incoming debt, or donating funds to another bank can result in a single new solution that is strictly more favorable to the acting bank. We also show that increasing the bank's external funds or modifying the priorities of outgoing payments cannot introduce a more favorable new solution into the system, but may allow the bank to remove some unfavorable solutions, or to increase its recovery rate. Finally, we show how the actions of two banks in a simple financial system can result in classical game theoretic situations like the prisoner's dilemma or the dollar auction, demonstrating the wide expressive capability of the financial system model.

q-fin.RM↗

arXiv2019

Stabilization Time in Minority Processes

We analyze the stabilization time of minority processes in graphs. A minority process is a dynamically changing coloring, where each node repeatedly changes its color to the color which is least frequent in its neighborhood. First, we present a simple $Ω(n^2)$ stabilization time lower bound in the sequential adversarial model. Our main contribution is a graph construction which proves a $Ω(n^{2-ε})$ stabilization time lower bound for any $ε>0$. This lower bound holds even if the order of nodes is chosen benevolently, not only in the sequential model, but also in any reasonable concurrent model of the process.

cs.DM↗

arXiv2019

Stabilization Time in Weighted Minority Processes

A minority process in a weighted graph is a dynamically changing coloring. Each node repeatedly changes its color in order to minimize the sum of weighted conflicts with its neighbors. We study the number of steps until such a process stabilizes. Our main contribution is an exponential lower bound on stabilization time. We first present a construction showing this bound in the adversarial sequential model, and then we show how to extend the construction to establish the same bound in the benevolent sequential model, as well as in any reasonable concurrent model. Furthermore, we show that the stabilization time of our construction remains exponential even for very strict switching conditions, namely, if a node only changes color when almost all (i.e., any specific fraction) of its neighbors have the same color. Our lower bound works in a wide range of settings, both for node-weighted and edge-weighted graphs, or if we restrict minority processes to the class of sparse graphs.

cs.DM↗