|Working Papers Alexander Gaigl
Observational Learning & Strategic Externalities
working paper, 2009
introduce strategic externalities into a standard herding model. It is
assumed that such externalities only affect successors. I study the
interplay of informational and strategic externalities and I determine
how their relative magnitude affects the occurrence of herds and informational cascades.
If strategic externalities (measured by a parameter sigma) are
negative and sufficiently strong, an informational cascades arises but
there is no herding (’anti-herding’ occurs). This contrasts
with the existing literature which generally finds that an
informational cascade implies herding. In a continuous-signal version
of the model, I show that there exists an interval of sigma in which
learning is more efficient than in the sigma = 0 case. Moreover, there
always exists one value of sigma such that every individual reveals her
signal. I make different assumptions on the observability of actions
and I show that agents may engage in either imitative or contrarian
behavior, depending on the value of sigma. It is shown that some
previous results on herding and informational cascades are not robust.
Finally, I study the model under binary signals. It is shown that
negative strategic externalities always prevent herding and may lead to
a considerable increase in the efficiency of learning.
Learning under Incomplete Information
with Applications to Auctions
working paper, 2008
paper studies learning under incomplete information. Players sometimes
reveal their types and actions, which enables other players to learn
their strategies (i.e. the mapping from types to actions). Convergence
results in terms of best-reply graphs are derived for general n-player
games. Moreover, these results are applied to discrete first- and
second price auctions with either private or common valuations.
Attention is restricted to models with two bidders and a uniform
distribution of types. It is shown that small perturbations of players'
beliefs may lead to unique outcomes of the learning process. These
outcomes correspond to equilibria that are of particular interest in the different continuous benchmark models (in most
cases the symmetric outcomes are selected). It is argued that these
results justify some of the ad hoc approaches on equilibrium selection
taken by classical auction theory (such as the restriction to symmetric
equilibria in second-price auctions with common values).
On the Dynamics in a Market for long-term Relationships
joint with Heiner Schumacher, 2007
dilemma is played by many pairs simultaneously in a random matching
game in which players have the option to maintain or to quit
relationships. Hence, the population consists of fixed matches and a
“market for long-term relationships”. Agents learn their current
opponent’s strategy in finitely many periods. Further, they update
their subjective belief over the aggregate behavior of players in the
market. In a first step, we assume that there are infinitely many
agents in the population and impose structure on strategies and
updating rules. Analytically, and by simulating the model, we derive
conditions under which a significant degree of cooperation can be
expected. Then, we extend the model to finite populations and show that
thedynamics are similar to the infinite case if there are sufficiently many agents.
matlab code of the simulations (m-file)
Stochastic Evolution and Deterministic Approximation in Games
Diploma Thesis, 2006, Supervisor: Christoph Kuzmics
Stochastic processes which arise from the repeated interaction of
individuals in large populations are often approximated by systems of
differential equations (which are deterministic and therefore usually
more easy to handle). I review a recent branch of the game theory
literature which subjects this very common approach to a thorough
mathematical analysis. Most results are obtained asymptotically, by
taking the population size and/or time to infinity. I review the
literature, broaden several results and construct applications to some common games.
The Value of Information in the MaxMin Expected Utility Framework
situations where individuals face large uncertainty, it has
been shown by the Ellsberg paradox that individuals' choices might
violate Savage's paradigm (expected utility maximization with
respect to some (subjective) prior).
A conceivable explanation for this is that there is too little
information to form a prior and therefore individuals rather consider a set of possible priors. By introducing the concept of ambiguity aversion, Gilboa and Schmeidler axiomatized the MaxMin criterion (where the minimum is taken over the set of priors). I
construct a model which allows to determine the value of information of
an ambiguity averse decision maker. In particular, I find that
ambiguity aversion has two opposed effects on the magnitude of the value of information.
Applications can be found in the
fields of Political Economy and Medical Science, where decision makers are
faced with severe uncertainty (e.g. the impact of the climate change or
the long-run health effects of new pharmaceutical products).