Plurality through N-Person Games

There are observations from both Ludwig Wittgenstein and John Forbes Nash Jr., converging on the inherently temporal nature of the human condition: Wittgenstein remarking eternal life doesn’t represent infinite duration; Nash remarking the future is presumably long, unless some miracle occurs to bring it forward.

N-Person Games

In 1950, John Nash contributed a one-page PNAS article that defined and characterized a notion of equilibrium for n- person games.

This work came from the study of von Neumann’s and Morgenstern’s Theory of Games and Economic Behavior, where the definition of equilibrium for “noncooperative” games was largely confined to the special case of “two-person zero-sum” games, in which one person’s gain is another’s loss, so the payoffs always sum to zero.

Nash proposed a notion of equilibrium which applied to a wider class of games without restrictions on the payoff structure or number of players, where each named person can anticipate the actions of others.

Standardisation of Language

Published in 1922, Ludwig Wittgenstein’s Tractatus had the broad goal of identifying the relationship between reality and language, to which the idea of names (expressed n) reoccur interactively and interconnectedly:

4.22 The elementary proposition consists of names. It is a connexion, a concatenation, of names.

Tractatus is not so concerned with reaching a predictive understanding of human affairs as John Nash’s early game theory, but does acknowledge a state of play:

2.03 In the atomic fact objects hang one in another, like the members of a chain.

2.031 In the atomic fact the objects are combined in a definite way.

2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact.

Plurality in Contracts

John Nash’s early work in game theory and bargaining later resumed — after a hiatus with mental illness — into work on the Ideal Money, which became the Asymptotically Ideal Money, where Nash realised the first ideas on the application of such a standardised money would be to the “possible precision, as an indicator of quality, of the contracts for performances of future contractual obligations.”

Similar to how Wittgenstein remarked in Tractatus that sometimes language can only state the senselessness of a proposition, Nash acknowledged in his Agencies Method of wishing to eliminate problems arising in the consideration of coalitions and coalition formation (which can be implemented by contracts) from “verbal complications”.

The multi-dimensional nature of plurality and contracts in themselves are reflected in Nash’s comments on culture and the impossibility of inclusiveness, while at the same time referring to a voluntary but irrevocable election procedure, so that Wittgenstein’s statement that things hang in one another (like a chain), means that such a chain need not last into all eternity and be witnessed as such, but only be so good as to regularly readjust.

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Ideas in games, language, and trust.

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Jon Gulson

Jon Gulson

Ideas in games, language, and trust.

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