Research

During my dissertation on money theory and exchange rate systems I have found myself trapped in reflexive, self-referential vicious circles. The Lucas critique, self-fulfilling prophecies, institutional formations and their dynamics, interaction of the context and the content as in the interaction of the modeller and the modelled system, money value and econometric models need to take reflexive phenomena into account much beyond what is possible with the traditional tools of economics. After the PhD I have found an approach to model reflexivity and not to avoid it just as computer science did in the 1990ies.

I am now using the methods adapted from computer science to deal with reflexivity and its cousin compositionality. It arises in the formal semantics researched in theoretical computer science where computable functions can take or output other functions as it happens in Turing machine or lambda calculus. Using these methods we are now able to model complex systems and behavioural economics with goals that generalise utility maximiser for example into general control structures.

Reflexivity is the cousin of compositionality, also called non reductionism or synthesis. Our games are fully compositional in that we can freely compose arbitrarily complex and irregular games, sequentially or in parallel and with any kind of generalised reflexive goals. We use string diagrams as our visual programming language adapted from quantum computing.

Our games are all computable since their ingredients are formally algorithms. Effectively we are developing a programming language for social systems and its accompanying compiler and interpreter.

I am now ready to attack money theory that I was taught to not exist by Martin Hellwig. We now have the mathematics for it.

Conferences

We started as Dagstuhl workshops:

Categorical Methods at the Crossroads (2014)

Coalgebraic Semantics of Reflexive Economics (2015)

and as satellites to the Logics and Social Behaviour series:

Logics for Social Behaviour (Leiden, 2014)

Trends in Logic XV: Logics for Social Behaviour (2015)

Logic for social behaviour 3 (2016)

Open Games Workshop (2017) Glasgow

Open Games Workshop (2018) Oxford

A related series of workshops - the category theory we use emerges as the mathematics of complex systems:

Applied Category Theory at NIST (2018)

Applied Category Theory (Conference and Journal) (2018)

Published

Compositional Game Theory, LiCS 2018, (preprint) with Neil Ghani, Jules Hedges and Philipp Zahn

Uncertainty Quantification and Global Sensitivity Analysis for Economic Models, forthcoming in Quantitative Economics 2018, (working paper) with Bruno Sudret, Stefano Marelli, Daniel Harenberg

Higher-Order Decision Theory, ADT 2017, with Evguenia Winschel, Philipp Zahn, Jules Hedges, Paulo Oliva, Lecture Notes in Artificial Intelligence

Selection Equilibria in Higher Order Games, PADL 2016, with Evguenia Winschel, Philipp Zahn, Jules Hedges, Paulo Oliva, Lecture Notes in Computer Science

Coalgebraic Analysis of Subgame-perfect Equilibria in Infinite Games without Discounting Mathematical Structures in Computer Science, with Samson Abramsky (2015)

Solving, Estimating and Selecting Nonlinear Dynamic Models without the Curse of Dimensionality (2010) Econometrica 78(2), pages 803-821, with Markus Kraetzig

Likelihood Approximation by Numerical Integration on Sparse Grids (2008) Journal of Econometrics, 144, pages 62-80, with Florian Heiss

Public Deficits and Borrowing Costs: The Missing Half of the Market Discipline (2001) Journal of Public Finance and Public Choice 20 (2-3), pages 169-190, with Friedrich Heinemann

Other

The Empirical Analysis of Exchange Rate Regimes and Nonlinear Structural Econometrics (2005) PhD Thesis

EMU Enlargement: An Optimal Currency Area Analysis of the West, Middle and Eastern European Countries (2005) part of my PhD thesis

Does the Nominal Exchange Rate Facilitate the Real Exchange Rate Adjustment in Floating Exchange Rate Regimes: A SVAR Decomposition of German Exchange Rates: 1973-1998 (2005) part of my PhD thesis

Risc management with shortfall measures: the Program Mamba: Metzler Asset Management Benchmark Analyser (1996) ZEW-Documentation 96-09, with Olaf Korn, Andrea Szczesny, Michael Schroeder

Book on political economics: public choice, material

Working Papers

Higher-Order Game Theory arXiv working paper with Evguenia Winschel, University of Mannheim, Philipp Zahn, University of St. Gallen, Jules Hedges, Oxford University, Paulo Oliva, Queen Mary University London

Compositionality and String Diagrams for Game Theory arXiv working paper with Evguenia Winschel, University of Mannheim, Philipp Zahn, University of St. Gallen, Jules Hedges, Oxford University, Paulo Oliva, Queen Mary University London

A Compositional Coalgebraic Semantics of Strategic Games, arXiv working paper, with Achim Blumensath (2013)

Current Interests

I am always studying mathematical background material: graphical linear algebra, linear algebra done right, interacting Hopf algebras, classical physics, quantum mechanics, pictorial quantum physics, analytic differential geometry, geometry and topology, synthetic differential geometry

Awards

Publication Prize, Fontana Foundation, 2009

Publication Prize, Fontana Foundation, 2008

Best Paper, Institute of Computational Economics, University of Chicago, 2006

Lindau Meeting of Nobel Prize Winners, Participation Award, 2006

Press

(2009) Who should become counsellor in Germany?

I am now working at how to transform the "I" into a "we".

(2010) Article about my work in the Wirtschaftswoche.

(2013) I recently became an aseconaut.

The lab is now located at the University of Hawaii in Manoa.

(2013) Interview about my work in the journal Special Issue Studia Humana