Philipp Zahn

Selection Equilibria of Higher-Order Games

In applied game theory the modelling of each player’s intentions and motivations is a key aspect. In classical game theory these are encoded in the payoff functions. In previous work [2, 4] a novel way of modelling games was introduced where players and their goals are more naturally described by a special class of higher-order functions called quantifiers. We refer to these as higher-order games. Such games can be directly and naturally implemented in strongly typed functional programming languages such as Haskell [3]. In this paper we introduce a new solution concept for such higher-order games, which we call selection equilibrium. The original notion proposed in [4] is now called quantifier equilibrium. We show that for a special class of games these two notions coincide, but that in general, the notion of selection equilibrium seems to be the right notion to consider, as illustrated through variants of coordination games where agents are modelled via fixed-point operators. This paper is accompanied by a Haskell implementation of all the definitions and examples.

Higher-Order Decision Theory

This paper investigates a surprising relationship between decision theory and proof theory. Using constructions originating in proof theory based on higher-order functions, so called quantifiers and selection functions, we show that these functionals model choice behavior of individual agents. Our framework is expressive, it captures classical theories such as utility functions and preference relations but it can also be used to faithfully model abstract goals such as coordination. It is directly implementable in functional programming languages. Lastly, modeling an agent with selection functions and quantifiers is modular and thereby allows to seamlessly combine agents bridging decision theory and game theory.

Compositional Game Theory

We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which standard economic tools are not practical. An open game represents a game played relative to an arbitrary environment and to this end we introduce the concept of coutility, which is the utility generated by an open game and returned to its environment. Open games are the morphisms of a symmetric monoidal category and can therefore be composed by categorical composition into sequential move games and by monoidal products into simultaneous move games. Open games can be represented by string diagrams which provide an intuitive but formal visualisation of the information flows. We show that a variety of games can be faithfully represented as open games in the sense of having the same Nash equilibria and off-equilibrium best responses.

The Macroeconomy and Individuals’ Support for Democracy

How important are national macroeconomic indicators for people’s satisfaction with democracy? This paper empirically explores the link from macroeconomic variables to support for established democratic systems. We combine country-level data on growth, inflation, and unemployment from the OECD with survey data from the Eurobarometer for nineWestern European countries for the period 1976-2001. We regress individual satisfaction with democracy on macroeconomic variables and individual controls. Our regressions include country-specific time trends as well as fixed effects for countries and surveyyears. Pooling observations from nine countries, we find that growth (inflation and unemployment) is positively (negatively) correlated with satisfaction with democracy. The effect goes beyond what can be explained by individual characteristics and is non-negligible if interpreted in light of the recent economic crisis. Our findings are robust to alternative specifications using logit and ordered logit models.

Beschäftigung und Arbeitslosigkeit älterer Arbeitnehmer / Employment and Unemployment of the Elderly

Summary In 1997, the German government enacted a reform of the unemployment insurance system which lead to a reduction of the maximum entitlement length for unemployment benefits of the older unemployed in the subsequent years. This paper analyses the effects of this reform on the risk of unemployment and on unemployment duration of the older unemployed aged 54-56. This group is of particular interest because it lost a smooth early retirement path via the unemployment benefits scheme. In our empirical analysis we use German administrative individual data drawn form the registers of the federal employment agency and of the public pension funds. After the reform we expect a lower risk of unemployment and shorter unemployment durations for the considered age group. This is confirmed by our empirical analysis. We show that the reform effectively reduced the amount of early retirement at the expense of the unemployment insurance. In particular larger companies and their employees use extended entitlement periods for unemployment benefits for early retirement purposes.

Contextuality and the Weak Axiom in the Theory of Choice

Recent work on the logical structure of non-locality has constructed scenarios where observations of multi-partite systems cannot be adequately described by compositions of non-signaling subsystems. In this paper we apply these frameworks to economics. First we construct a empirical model of choice, where choices are understood as observable outcomes in a certain sense. An analysis of contextuality within this framework allows us to characterize which scenarios allow for the possible construction of an adequate global choice rule. In essence, we mathematically characterize when it makes sense to consider the choices of a group as composed of individual choices. We then map out the logical space of some relevant empirical principles, relating properties of these contextual choice scenarios to no-signalling theories and to the weak axiom of revealed preference.