Coordination in centralized and decentralized systems
- Centre d’economie de la Sorbonne, France
Figures
Mean of coordination in the centralized and the decentralized system.
Note: In the centralized system, each agent conveys its number to a central-coordinator. The central-coordinator orders the agents on a line segment. In the decentralized system, at each time step, pairs of neighbouring agents are randomly selected. Within each pair, agents share information about each other5 s numbers. If the agent on the left reports a number greater than the agent on the right, the agents swap positions, otherwise the agents remain in their present positions. Agents make errors in communicating their numbers, i.e. with some probability an agent conveys an incorrect number. Coordination is the negative mean of the absolute value of the differences between the numbers of agents and the numbers of their respective locations. The sum of these differences is divided by the total number of agents and multiplied by negative one to measure coordination. Zero indicates perfect coordination, lower values of C indicate lesser coordination.
Variance of coordination in the centralized and the decentralized system.
Note: In the centralized system, each agent conveys its number to a central-coordinator. The central-coordinator orders the agents on a line segment. In the decentralized system, at each time step, pairs of neighbouring agents are randomly selected. Within each pair, agents share information about each other5 s numbers. If the agent on the left reports a number greater than the agent on the right, the agents swap positions, otherwise the agents remain in their present positions. Agents make errors in communicating their numbers, i.e. with some probability an agent conveys an incorrect number. Coordination is the negative mean of the absolute value of the differences between the numbers of agents and the numbers of their respective locations. The sum of these differences is divided by the total number of agents and multiplied by negative one to measure coordination. Zero indicates perfect coordination, lower values of C indicate lesser coordination.
Boxplots of coordination in the centralized and the decentralized system.
Note: In the centralized system, each agent conveys its number to a central-coordinator. The central-coordinator orders the agents on a line segment. In the decentralized system, at each time step, pairs of neighbouring agents are randomly selected. Within each pair, agents share information about each other5 s numbers. If the agent on the left reports a number greater than the agent on the right, the agents swap positions, otherwise the agents remain in their present positions. Agents make errors in communicating their numbers, i.e. with some probability an agent conveys an incorrect number. Coordination is the negative mean of the absolute value of the differences between the numbers of agents and the numbers of their respective locations. The sum of these differences is divided by the total number of agents and multiplied by negative one to measure coordination. Zero indicates perfect coordination, lower values of C indicate lesser coordination.
Histograms of coordination of the centralized and decentralized systems with different probabilities of error.
Note: In the centralized system, each agent conveys its number to a central-coordinator. The central-coordinator orders the agents on a line segment. In the decentralized system, at each time step, pairs of neighbouring agents are randomly selected. Within each pair, agents share information about each other5 s numbers. If the agent on the left reports a number greater than the agent on the right, the agents swap positions, otherwise the agents remain in their present positions. Agents make errors in communicating their numbers, i.e. with some probability an agent conveys an incorrect number. Coordination is the negative mean of the absolute value of the differences between the numbers of agents and the numbers of their respective locations. The sum of these differences is divided by the total number of agents and multiplied by negative one to measure coordination. Zero indicates perfect coordination, lower values of C indicate lesser coordination.
Time steps necessary for decentralized system to exceed the mean coordination of the centralized system with ten percent probability of communication error.
Note: In the centralized system, each agent conveys its number to a central-coordinator. The central-coordinator orders the agents on a line segment. In the decentralized system, at each time step, pairs of neighbouring agents are randomly selected. Within each pair, agents share information about each other5 s numbers. If the agent on the left reports a number greater than the agent on the right, the agents swap positions, otherwise the agents remain in their present positions. Agents make errors in communicating their numbers, i.e. with some probability an agent conveys an incorrect number. Coordination is the negative mean of the absolute value of the differences between the numbers of agents and the numbers of their respective locations. The sum of these differences is divided by the total number of agents and multiplied by negative one to measure coordination. Zero indicates perfect coordination, lower values of C indicate lesser coordination.