# Higher-Order Decision Theory

@inproceedings{Hedges2017HigherOrderDT, title={Higher-Order Decision Theory}, author={Jules Hedges and Paulo Oliva and Evguenia Shprits and Viktor Winschel and Philipp Zahn}, booktitle={ADT}, year={2017} }

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…

## 11 Citations

Higher-Order Game Theory

- Economics, Computer ScienceArXiv
- 2015

This paper introduces a representation of games where players' goals are modeled based on so-called higher-order functions, and shows that equilibrium conditions based on Nash can be easily adapted to this framework.

Towards compositional game theory

- Economics
- 2016

We introduce a new foundation for game theory based on so-called open games. Unlike existing approaches open games are fully compositional: games are built using algebraic operations from standard…

Sequential games and nondeterministic selection functions

- EconomicsArXiv
- 2018

It is shown, surprisingly, no non-deterministic selection function exists which computes the set of all subgame perfect Nash equilibrium plays, but it is shown that there are selection functions corresponding to sequential versions of the iterated removal of strictly dominated strategies.

Compositional Game Theory

- EconomicsLICS
- 2018

The concept of coutility is introduced, which is the utility generated by an open game and returned to its environment and it is shown 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.

Computational Goals, Values and Decision-Making

- BusinessSci. Eng. Ethics
- 2020

This commentary rejects the idea that a rational agent will never select an action that changes its goal but also argues that an artificial intelligence is unlikely to be purely rational in terms of always acting to maximise a utility function.

Diegetic representation of feedback in open games

- EconomicsArXiv
- 2022

We improve the framework of open games with agency [9, 4] by showing how the players’ counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game itself (hence…

Compositionality and String Diagrams for Game Theory

- Computer ScienceArXiv
- 2016

We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing…

Towards foundations of categorical cybernetics

- Computer Science
- 2021

It is believed that ‘cybernetic’ is an appropriate name for the processes that can be described in this categorical framework for processes which interact bidirectionally with both an environment and a ‘controller’.

On Logic, Choices and Games

- Medicine
- 2019

Suppose that you need to ask a friend to go to a shop and buy something for you, say an umbrella. Your friend might ask, “Sure, no problem, what kind of umbrella do you want”? You might really like…

Bar recursion is not computable via iteration

- Mathematics, Computer ScienceComput.
- 2019

We show that the bar recursion operators of Spector and Kohlenbach, considered as third-order functionals acting on total arguments, are not computable in Goedel's System T plus minimization, which…

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