We study a general preferential attachment and Pólya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not disconnected, it joins an existing pioneer vertex with...

We study a general preferential attachment and Pólya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not disconnected, it joins an existing pioneer vertex with...

We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a...

We consider a team of agents with limited problem-solving ability facing a disjunctive task over a large solution space. We provide sufficient conditions for the following four statements. First, two heads are better than one: a team of two agents will solve the problem even if neither agent...

We study the evolution of trading strategies in double auctions as the size of the market gets larger. When the number of buyers and sellers is balanced, Fano et al. (2011) show that the choice of the order-clearing rule (simultaneous or asynchronous) steers the emergence of fundamentally...

Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly b children, with b = 3. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the root. Notice that it is still unknown if vertex-reinforced...

We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in...