Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2009.05018

The Cost of Denied Observation in Multiagent Submodular Optimization

David Grimsman·Joshua H. Seaton·Jason R. Marden·Philip N. Brown
View original source ↗Read source document ↗Export metadata ↓

Abstract

A popular formalism for multiagent control applies tools from game theory, casting a multiagent decision problem as a cooperation-style game in which individual agents make local choices to optimize their own local utility functions in response to the observable choices made by other agents. When the system-level objective is submodular maximization, it is known that if every agent can observe the action choice of all other agents, then all Nash equilibria of a large class of resulting games are within a factor of $2$ of optimal; that is, the price of anarchy is $1/2$. However, little is known if agents cannot observe the action choices of other relevant agents. To study this, we extend the standard game-theoretic model to one in which a subset of agents either become \emph{blind} (unable to observe others' choices) or \emph{isolated} (blind, and also invisible to other agents), and we prove exact expressions for the price of anarchy as a function of the number of compromised agents. When $k$ agents are compromised (in any combination of blind or isolated), we show that the price of anarchy for a large class of utility functions is exactly $1/(2+k)$. We then show that if agents use marginal-cost utility functions and at least $1$ of the compromised agents is blind (rather than isolated), the price of anarchy improves to $1/(1+k)$. We also provide simulation results demonstrating the effects of these observation denials in a dynamic setting.

Explore related subjects

cs.GTcs.DCcs.SYeess.SY

Keep this discovery

BibTeXRIS

David Grimsman, Joshua H. Seaton, Jason R. Marden, Philip N. Brown. 2020-09-10. The Cost of Denied Observation in Multiagent Submodular Optimization. https://arxiv.org/abs/2009.05018

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT↗
arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗
arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗