In applied game theory the motivation of players is a key element. It is encoded in the payoffs of the game form and often based on utility functions. But there are cases were formal descriptions in the form of a utility function do not exist. In this paper we introduce a representation of games where players’ goals are modeled based on so-called higher-order functions. Our representation provi...

Local fixpoint iteration describes a technique that restricts in function spaces to needed arguments only. It has been studied well for first-order functions abstract interpretation and also model checking. Here we consider the problem least greatest fixpoints of arbitrary type order. We define an algebra simply-typed higher-order with order express evaluation problems as they occur routinely v...

Classical decision theory models behaviour in terms of utility maximisation where utilities represent rational preference relations over outcomes. However, empirical evidence and theoretical considerations suggest that we need to go beyond this framework. We propose to represent goals by higherorder functions or operators that take other functions as arguments where the max and argmax operators...

We give a detailed exposition of the formalism Kinetic Field Theory (KFT) with emphasis on perturbative determination observables. KFT is statistical non-equilibrium classical field theory based path integral formulation mechanics, employing powerful techniques developed in context quantum to describe systems. Unlike previous work KFT, we perform integration over probability distribution initia...

The optimal functional form of convex underestimators for general twice continuously differentiable functions is of major importance in deterministic global optimization. In this paper, we provide new theoretical results that address the classes of optimal functional forms for the convex underestimators. These are derived based on the properties of shift-invariance and sign-invariance.

It is shown that in the estimation of an arbitrary signal corrupted by additive Gaussian noise, the optimum minimum-variance estimator is always a simple linear transformation of the logarithmic gradient of the average likelihood ratio which is obtained in the optimum detection of the same signal. Conversely, the average likelihood ratio can always be expressed in a simple functional form conta...

We give a necessary and sufficient condition for when a set-theoretic function can be written using the recursion operator fold, and a dual condition for the recursion operator unfold. The conditions are simple, practically useful, and generic in the underlying datatype.

We present transformations of linearly ordered sets into ordered abelian groups and ordered fields. We study effective properties of the transformations. In particular, we show that a linear order L has a ∆2 copy if and only if the corresponding ordered group (ordered field) has a computable copy. We apply these codings to study the effective categoricity of linear ordered groups and fields.