The Application of Non-Cooperative Stackelberg Game Theory in Behavioral Science: Social Optimality with any Number of Players

TL;DR

This paper introduces a new postulate in game theory, proposing that all games can be modeled as Stackelberg games with a rational leader, leading to social optimality among followers under specific conditions.

Contribution

It presents a novel postulate linking all non-cooperative games to Stackelberg frameworks, emphasizing the role of a rational, honest leader in achieving social optimality.

Findings

All games can be mapped to Stackelberg games.

A rational, honest leader ensures social optimality.

Social optimality holds with any finite number of game iterations.

Abstract

Here we present a ground-breaking new postulate for game theory. The first part of this postulate contains the axiomatic observation that all games are created by a designer, whether they are: e.g., (dynamic/static) or (stationary/non-stationary) or (sequential/one-shot) non-cooperative games, and importantly, whether or not they are intended to represent a non-cooperative Stackelberg game, they can be mapped to a Stackelberg game. I.e., the game designer is the leader who is totally rational and honest, and the followers are mapped to the players of the designed game. If now the game designer, or "the leader" in the Stackelberg context, adopts a pure strategy, we postulate the following second part following from axiomatic observation of ultimate game leadership, where empirical insight leads to the second part of this postulate. Importantly, implementing a non-cooperative Stackelberg game, with a very honest and rational leader results in social optimality for all players (followers), assuming pure strategy across all followers and leader, and that the leader is totally rational, honest, and is able to achieve a minimum amount of competency in leading this game, with any finite number of iterations of leading this finite game.