Working Papers Alexander Gaigl

Observational Learning & Strategic Externalities

working paper, 2009

I 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

This 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

The prisoner’s 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

Mimeo, 2005

In 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 often faced with severe uncertainty (e.g. the impact of the climate change or the long-run health effects of new pharmaceutical products).