The Cost of Denied Observation in Multiagent Submodular Optimization

by   David Grimsman, et al.

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 blind (unable to observe others' choices) or 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.


page 1

page 2

page 3

page 4


Optimal Price of Anarchy in Cost-Sharing Games

The design of distributed algorithms is central to the study of multiage...

Distributed Submodular Maximization with Parallel Execution

The submodular maximization problem is widely applicable in many enginee...

Valid Utility Games with Information Sharing Constraints

The use of game theoretic methods for control in multiagent systems has ...

Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games

Residential segregation in metropolitan areas is a phenomenon that can b...

When Smoothness is Not Enough: Toward Exact Quantification and Optimization of the Price-of-Anarchy

Today's multiagent systems have grown too complex to rely on centralized...

Distributed resource allocation through utility design - Part II: applications to submodular, supermodular and set covering problems

A fundamental component of the game theoretic approach to distributed co...

Tracking Truth by Weighting Proxies in Liquid Democracy

We study wisdom of the crowd effects in liquid democracy when agents are...

Please sign up or login with your details

Forgot password? Click here to reset