DeepAI AI Chat
Log In Sign Up

The algebra of predicting agents

03/27/2018
by   Joe Bolt, et al.
1

The category of open games, which provides a strongly compositional foundation of economic game theory, is intermediate between symmetric monoidal and compact closed. More precisely it has counits with no corresponding units, and a partially defined duality. There exist open games with the same types as unit maps, given by agents with the strategic goal of predicting a future value. Such agents appear in earlier work on selection functions. We explore the algebraic properties of these agents via the symmetric monoidal bicategory whose 2-cells are morphisms between open games, and show how the resulting structure approximates a compact closed category with a family of lax commutative bialgebras.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/16/2018

Limits of bimorphic lenses

Bimorphic lenses are a simplification of polymorphic lenses that (like p...
09/15/2020

Compositional Game Theory with Mixed Strategies: Probabilistic Open Games Using a Distributive Law

We extend the open games framework for compositional game theory to enco...
10/08/2019

Bayesian open games

This paper generalises the treatment of compositional game theory as int...
11/19/2017

Morphisms of open games

We define a notion of morphisms between open games, exploiting a surpris...
04/25/2019

The game semantics of game theory

We use a reformulation of compositional game theory to reunite game theo...
12/28/2021

A Compositional Approach to Parity Games

In this paper, we introduce open parity games, which is a compositional ...
05/10/2021

Situated Transition Sytems

We construct a monoidal category of open transition systems that generat...