A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

Learning in peer-to-peer markets: evidence from Airbnb

Peer-to-peer markets are highly uncertain environments due to the constant presence of shocks. As a consequence, sellers have to constantly adjust to these shocks. Dynamic Pricing is hard, especially for non-professional sellers. We study it in an accommodation rental marketplace, Airbnb. With scraped data from its website, we: 1) describe pricing patterns consistent with learning; 2) estimate a demand model and use it to simulate a dynamic pricing model. We simulate it under three scenarios: a) with learning; b) without learning; c) with full information. We have found that information is an important feature concerning rental markets. Furthermore, we have found that learning is important for hosts to improve their profits.