Learning without Recall by Random Walks on Directed Graphs

We consider a network of agents that aim to learn some unknown state of the world using private observations and exchange of beliefs. At each time, agents observe private signals generated based on the true unknown state. Each agent might not be able to distinguish the true state based only on her private observations. This occurs when some other states are observationally equivalent to the true state from the agent's perspective. To overcome this shortcoming, agents must communicate with each other to benefit from local observations. We propose a model where each agent selects one of her neighbors randomly at each time. Then, she refines her opinion using her private signal and the prior of that particular neighbor. The proposed rule can be thought of as a Bayesian agent who cannot recall the priors based on which other agents make inferences. This learning without recall approach preserves some aspects of the Bayesian inference while being computationally tractable. By establishing a correspondence with a random walk on the network graph, we prove that under the described protocol, agents learn the truth exponentially fast in the almost sure sense. The asymptotic rate is expressed as the sum of the relative entropies between the signal structures of every agent weighted by the stationary distribution of the random walk.Comment: 6 pages, To Appear in Conference on Decision and Control 201

Spatial Mobility in the Formation of Agent-Based Economic Networks

We extend the model of spatial social network formation of Johnson and Gilles (Review of Economic Design, 2000, 5, 273-299) by situating each economic agent within one of a set of discrete spatial locations and allowing agents to maximise the utility that they gain from their direct and indirect social contacts by relocating, in addition to forming or breaking social links. This enables the exploration of scenarios in which agents are able to alter the distance between themselves and other agents at some cost. Agents in this model might represent countries, firms or individuals, with the distance between a pair of agents representing geographical, social or individual differences. The network of social relationships characterises some form of self-organised persistent interaction such as trade agreements or friendship patterns. By varying the distance-dependent costs of relocation and maintaining social relationships we are able to identify conditions that promote the formation of spatial organisations and network configurations that are pairwise stable and efficient. We also examine the associated patterns in individual and aggregate agent behaviour. We find that both relative location and the order in which agents are allowed to act can drastically affect individual utility. These traits are found to be robust to random perturbations