Viktor Winschel

Public Deficits and Borrowing Costs: The Missing Half of Market Discipline

EMU driven interest rate convergence has led to a significant reduction of borrowing costs for some European governments in the second half of the nineties. The paper deals with the possible consequences for deficit behaviour. Although the impact of interest rates on deficits is a crucial element of the market discipline hypothesis it has widely been neglected in the literature. In the theoretical part, a standard political economic model of budgetary policy (Hettich-Winer) is adapted. It turns out that borrowing costs, measured as the interest-growth-differential, and the level of public debt should be important determinants for public deficits. The econometric part tests these predictions for a panel of OECD countries. The results indicate that there is indeed a significant impact of borrowing costs on the primary surplus. This impact is characterised by a robust asymmetry: Reactions in times of increasing borrowing costs are more pronounced than in times of relaxing conditions.

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.