Stephan Jagau

Working Papers

Selection Pressure in Repeated Contests. (with John Duffy, Ethan Holdahl, and Francisco Klapp) Working Paper

Abstract: Competition for scarce resources in the face of birth and death (the struggle for survival) has shaped social and economic interaction since the beginnings of mankind. This research is the first to induce selection pressure in controlled strategic decision-making experiments using performance-based replacement of participants over time. Strategic decision-making with and without selection pressure is considered in repeated Tullock-type rent seeking contests. Tullock contests’ incentive structure drives a wedge between profit maximization and survival. Moreover, there is a large number of past experiments without selection pressure demonstrating a willingness to compete that cannot be justified by profit maximization alone and thus seemingly supports evolutionary game-theoretic predictions. Surprisingly, we find that the intensity of competition in repeated contests does in fact decrease once selection pressure is added. Participants’ behavior under selection pressure is well-approximated by the finite population evolutionarily stable strategy (ESS) of the stage game. This happens because a significant share of contestants quickly adapt to survive under selection pressure at the expense of new entrants. By contrast, when selection pressure is absent, we observe a large variance in competitiveness and frequent competition far beyond profit-maximizing levels. Selection pressure has a disciplining effect on contestants’ decision-making, boosting not only the lifespans of successful contestants but also average round payoffs across the entire population.

Context-Dependent Expected Utility. Working Paper, Slides  
Abstract: Understanding people’s diverse monetary and non-monetary motivations in strategic interactions is key for applying social science theories to real-life situations such as contracting and negotiations, collective action and teamwork, and electoral- and market-competition. However, methods to empirically identify individuals’ strategic goals based on observable data are lacking. In particular, it is currently unknown how expected utility in games can be theoretically justified based on in-game decision-making. This paper presents novel foundations for expected utility in games based on context-dependent preferences. Crucially, these behavioral foundations do not require empirically implausible comparisons of alternatives across different contexts. Moreover, they relax previous diversity-type assumptions, paving the way for a general context-dependent expected utility representation for any normal-form game. Next to direct utility measurement in games, the representation developed here has other useful applications to (e.g.) individual decision-making and social choice.

The Fundamental Theorem of Epistemic Game Theory.
Reject & resubmit, Econometrica. Working Paper, Slides
Abstract: In many applications of game theory, infinite strategy sets stand in for large finite strategy sets. It is then expected that results back-translate from infinite to finite. Transfinite non-best reply eliminations in infinite games raise concerns whether this always works. In response, a measure-theoretic characterization of common belief in rationality via two alternative procedures is developed. Procedure one is transfinite non-best reply elimination. Procedure two, elimination of non-best replies and supporting beliefs, avoids all transfinite iterations. Thus, transfinite non-best reply eliminations never require infinite reasoning depths, and infinite-game results always back-translate to the finite. The real cause of transfinite eliminations turns out to be non-best reply elimination itself. That procedure ignores belief-based information that is critical for strategic rationality in infinite games.

An Additive Equilibrium Theory for Admissibility in Games. (with Christian Bach) Extended Abstract, Slides  
Abstract: Admissibility (the elimination of weakly dominated strategies) is the most common tool for refining equilibrium predictions in normal form games. Curiously, equilibrium notions that exclude weakly dominated strategies (e.g., perfect equilibrium) strictly refine the combined predictions of corresponding non-equilibrium solution concepts (e.g., admissibility) and Nash equilibrium. This paper uses an epistemic approach to cautious reasoning in games to understand the nature of this “extra refinement”. It emerges that the gap between equilibrium refinements and their non-equilibrium counterparts stems from a questionable requirement that players be fully lexicographically correct about each others’ cautious theories. This is what causes perfect equilibria to strictly refine the set of admissible equilibria. More seriously, the same requirement also causes an iteratively admissible refinement of perfect equilibrium to be impossible for almost all normal form games. This is true even though any game admits a Nash equilibrium in iteratively admissible strategies. As an alternative to full lexicographic correctness, a notion of correct primary theories is developed. Primary correctness additively combines with cautious non-equilibrium solution concepts. This yields foundations for admissible equilibrium and for a novel iteratively admissible equilibrium.