 J. Lorenz, M. Marciniszyn, A. Steger: Observational Learning in Random Networks. Proceedings of the 20th Annual Conference on Learning Theory (COLT), 2007. (Full version)
In the standard model of observational learning, n agents sequentially decide between two alternatives a or b, one of which is objectively superior. Their choice is based on a stochastic private signal and the decisions of others. Assuming a rational behavior, it is known that informational cascades arise, which cause an overwhelming fraction of the population to make the same choice, either correct or false. If agents are able to observe the actions of all predecessors, false informational cascades are quite likely. In a more realistic setting, agents observe just a subset of their predecessors, modeled by a random network of acquaintanceships. We show that the probability of false informational cascades depends on the edge probability p of the underlying network. If p=p(n) is a sequence that decreases with n, correct cascades emerge almost surely (provided the decay of p is not too fast), benefiting the entire population.
Wisdom of Crowds
 Nicla Bernasconi, J. Lorenz, R. Spoehel: Hand Development in the von Neumann and Newman Poker Models. Discrete Mathematics 311(21), 23372345, 2011.
The von Neumann and Newman poker models are simplifed twoperson poker models with Uniform(0,1)hands. We analyze a simple extension of both models that introduces an element of uncertainty about the final strength of each player's own hand, as is present in real poker games. Whenever a showdown occurs, an unfair coin with fixed bias q is tossed. With probability 1q, the higher hand value wins as usual, but with the remaining probability q, the lower hand wins. Both models favour the frst player for q=0 and are fair for q=1/2. Our somewhat surprising result is that the first player's expected payoff increases with q as long as q is not too large. That is, the first player can exploit the additional uncertainty introduced by the coin toss and extract even more value from his opponent.
