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.
We started as Dagstuhl workshops:
and as satellites to the Logics and Social Behaviour series:
A related series of workshops - the category theory we use emerges as the mathematics of complex systems:
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
EMU Enlargement: An Optimal Currency Area Analysis of the West, Middle and Eastern European Countries (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
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)
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
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
(2009) Who should become counsellor in Germany?