Burkhard C. Schipper

A canonical model for interactive unawareness

Heifetz, Meier and Schipper (2006) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. We show that this generalized state-space model arises naturally if states consist of maximally consistent sets of formulas in an appropriate logical formulation.

The visible hand: finger ratio (2D:4D) and competitive bidding

In an experiment using two-bidder rst-price sealed bid auctions with symmetric independent private values, we scan also the right hand of each subject. We study how the ratio of the length of the index and ring ngers (2D:4D) of the right hand, a measure of prenatal hormone exposure, is correlated with bidding behavior and total prots.

Sex Hormones and Competitive Bidding

We correlate competitive bidding and profits in symmetric independent private value first-price auctions with salivary testosterone, estradiol, progesterone, and cortisol in more than 200 subjects. Bids are significantly positively correlated and profits are significantly negatively correlated with basal salivary progesterone, but only for females who do not use hormonal contraceptives. Surprisingly, we have null findings for basal testosterone, estradiol, and cortisol for both males and females. We show that our finding for progesterone is not mediated by risk aversion or bidding mistakes. No hormone responds to total profits in the auctions except for a small positive response of the stress hormone cortisol in males. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.1959 . This paper was accepted by Uri Gneezy, behavioral economics.

Submodularity and the Evolution of Walrasian Behavior

Vega-Redondo (1997) showed that imitation leads to the Walrasian outcome in Cournot Oligopoly. We generalize his result to aggregative quasi-submodular games. Examples are the Cournot Oligopoly, Bertrand games with differentiated complementary products, Common-Pool Resource games, Rent-Seeking games and generalized Nash-Demand games.

Cournot Competition between Teams: An Experimental Study

In the literature on market competition, firms are often modeled as individual decision makers and the internal organization of the firm is neglected (unitary player assumption). However, as the literature on strategic delegation suggests, one cannot generally expect that the behavior of teams is equivalent to the behavior of individuals in Cournot competition. Nevertheless, there are models of team-organizations such that team-firms and individual firms are behaviorally equivalent. This provides a theoretical foundation for the unitary player assumption in Cournot competition. We show that this assumption is robust in experiments, which is in contrast to experimental results on price competition.

Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of finite population evolutionary stable strategies.

Unawareness - A Gentle Introduction to Both the Literature and the Special Issue

This article provides a brief survey of the literature on unawareness and introduces the contributions to the special issue on unawareness in Mathematical Social Sciences. First, we provide a brief overview both about epistemic models of unawareness and models of extensive-form games with unawareness. Instead of introducing the approaches in full detail, we illustrate the main differences and similarities with the help of examples. Finally, we discuss the contributions to the special issue on unawareness.

Rage against the machines: how subjects learn to play against computers

We use an experiment to explore how subjects learn to play against computers which are programmed to follow one of a number of standard learning algorithms. The learning theories are (unbeknown to subjects) a best response process, fictitious play, imitation, reinforcement learning, and a trial & error process. We test whether subjects try to influence those algorithms to their advantage in a forward-looking way (strategic teaching). We find that strategic teaching occurs frequently and that all learning algorithms are subject to exploitation with the notable exception of imitation. The experiment was conducted, both, on the internet and in the usual laboratory setting. We find some systematic differences, which however can be traced to the different incentives structures rather than the experimental environment.

When is Tit-for-Tat Unbeatable?

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2