## Stephan Jagau

I am an experimentalist and economic theorist interested in the foundations of game- and decision theory, as well as in evolutionary theory. My most recent experimental work studies payoff- and risk-dominance in one-shot coordination games using a no-feedback, choice list-like design. My latest theoretical work concerns beliefs and reasoning in infinite games as well as the identification of preferences in strategic settings. I am also co-Pi of an ongoing NSF-grant project implementing selection pressure in online decision-making experiments.

I am an assistant professor at Nottingham University Business School. I am also a member of Maastricht University's EPICENTER. I did my Economics Ph.D. at CREED (University of Amsterdam) and at the Tinbergen Institute, supervised by Theo Offerman and Matthijs van Veelen. I also worked as a postdoctoral scholar at UC Irvine's Department of Economics.

During my research at UC Irvine's ESSL Lab, I started an initiative to virtualize experimentation using Kubernetes and to build an Experimental Social Science Research Network (ESSRN). ESSRN will seamlessly accommodate classical and online experiments on a vast and diverse multi-institutional subject pool, blurring the lines between the traditional lab setup and platforms such as Heroku and mTurk. With support from the National Research Platform, the first iteration of ESSRN has gone live in early 2023.

## Publications

Common Belief in Rationality in Psychological Games: Belief-Dependent Utility

and the Limits of Strategic Reasoning. (with Andrés Perea)

Journal of Mathematical Economics (2022) 100, 102635. Paper

Defaults, normative anchors, and the occurrence of risky and cautious shifts.

(with Theo Offerman) Journal of Risk and Uncertainty (2018) 56(3), 211-236. Paper

A general evolutionary framework for the role of intuition and deliberation

in cooperation. (with Matthijs van Veelen) Nature Human Behaviour (2017) 1(8), 0152.

Paper, Supplementary Information, News & Views (Adam Bear and David Rand)

## Grants and Fellowships

Selection Pressure in Strategic Environments. Link

(co-PI with John Duffy), National Science Foundation #2214979, 07/2022 – 06/2024, $327,637.

Experimental Social Science Research Network. Link

(co-PI with John Duffy & Michael McBride), UCI Seed Funding Program, 04/2022 – 04/2024, $149,929.

Reason within Passions: Towards an Economic Theory of Emotions. Link

Rubicon Postdoctoral Fellowship, Dutch Research Council 019.181SG.023,

November 2018 – December 2020, Euro 134,386.

## Working Papers

To Catch a Stag: Identifying payoff- and risk-dominance effects in coordination games.

Revise & resubmit, Games & Economic Behavior. Full Paper, Slides

Abstract: Five decades after Harsanyi and Selten’s seminal work on equilibrium selection, we remain unable to predict the outcomes of real-life coordination even in simple cases. One reason is that experiments have struggled to quantify the effects of payoff- and risk-dominance and to separate them from context factors like feedback, repetition, and complexity. This experiment is the first to demonstrate that both payoff- and risk-dominance significantly and independently impact coordination decision-making. Three innovations characterize the design: First, payoff- and risk-dominance are disentangled using orthogonal measures of strategic incentives and welfare externalities. Second, a no-feedback, choice-list format minimizes deviations from one-shot incentives. Third, beliefs about others’ behavior are elicited next to decisions. Surprisingly, beliefs do not only drive the effect of risk dominance but also the one of payoff dominance. This is in line with subjects viewing efficient coordination as a "team"-problem.

The Fundamental Theorem of Epistemic Game Theory.

Reject & resubmit, Econometrica. Full 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.

Additive Context-Dependent Preferences. Extended Abstract, Slides

Abstract: “Money equals utility” is a much criticized ‘axiom’ that is central across a vast range of economic experiments and theory. Subjecting this ‘axiom’ to experimental testing requires an empirically tractable theory of context-dependent preferences. This paper presents novel behavioral foundations for additive context-dependent preferences and state-dependent expected utility. Crucially, these behavioral foundations do not require empirically implausible comparisons of alternatives across different states. Moreover, they can handle any state-dependent, multi-alternative decision problem. In particular, no diversity-type assumptions are used. A central application is to direct utility measurement in games, enabling a causal understanding of how e.g. risk attitudes and other-regarding concerns affect strategic choice.

An Additive Equilibrium Theory for Admissibility in Games. (with Christian Bach) Extended Abstract

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.