Specifying a Game-Theoretic Extensive Form as an Abstract 5-ary Relation

07/22/2021
by   Peter A. Streufert, et al.
0

This paper specifies an extensive form as a 5-ary relation (i.e. set of quintuples) which satisfies certain abstract axioms. Each quintuple is understood to list a player, a situation (for example an information set), a decision node, an action, and a successor node. Accordingly, the axioms are understood to specify abstract relationships between players, situations, nodes, and actions. Such an extensive form is called a "5-form". Next a "5-form game" is defined to be a 5-form together with utility functions. The paper's main result is to construct a bijection between (a) those 5-form games with information-set situations and (b) 𝐆𝐦 games (Streufert arXiv:2105.11398). In this sense, 5-form games equivalently formulate almost all extensive-form games. Secondary results suggest that a 5-form might be usefully partitioned into subsets.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/23/2020

The Category of Node-and-Choice Extensive-Form Games

This paper develops the category 𝐍𝐂𝐆. Its objects are node-and-choice ga...
research
02/08/2023

Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game

This paper uses value functions to characterize the pure-strategy subgam...
research
05/24/2021

A Category for Extensive-Form Games

This paper introduces Gm, which is a category for extensive-form games. ...
research
04/27/2023

Conditional dominance in games with unawareness

Heifetz, Meier, and Schipper (2013) introduced dynamic game with unaware...
research
05/09/2012

Temporal Action-Graph Games: A New Representation for Dynamic Games

In this paper we introduce temporal action graph games (TAGGs), a novel ...
research
04/27/2019

The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms

The literature specifies extensive-form games in many styles, and eventu...
research
09/14/2021

Towards optimized actions in critical situations of soccer games with deep reinforcement learning

Soccer is a sparse rewarding game: any smart or careless action in criti...

Please sign up or login with your details

Forgot password? Click here to reset