Capturing pattern bi-stability dynamics in delay-coupled swarms

Swarms of large numbers of agents appear in many biological and engineering fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been observed in many models of large population swarms. However, many reduced models for analysis, such as mean-field (MF), do not capture the bifurcation structure of bi-stable behavior. Here, we develop a new model for the dynamics of a large population swarm with delayed coupling. The additional physics predicts how individual particle dynamics affects the motion of the entire swarm. Specifically, (1) we correct the center of mass propulsion physics accounting for the particles velocity distribution; (2) we show that the model we develop is able to capture the pattern bi-stability displayed by the full swarm model.Comment: 6 pages 4 figure

The Agents-are-Substitutes Property in Continuous Generalized Assignment Problems

The VCG mechanism has some nice properties if the agents-are-substitutes property holds.For example, for combinatorial auctions the property assures that the VCG mechanism is supported by a pricing equilibrium. The existence of such a pricing equilibrium is a necessary condition for the existence of ascending auctions that are equivalent to the VCG mechanism.Although it is known that the agents-are-substitutes property is important in several settings few problems or subclasses of problems are proven to have the property.In this paper we show for a class of problems that the agents-are-substitutes property holds. Moreover we give two rather natural and small extensions that do not have this property in general.Furthermore we show that in our simple problem class we need the possibility of price discrimination.operations research and management science;