Perfect Prediction Equilibrium

TL;DR

This paper introduces the Perfect Prediction Equilibrium (PPE), a new solution concept for finite extensive-form games with perfect information, modeling agents with perfect predictive rationality and full transparency.

Contribution

It defines, constructs, and proves the existence, uniqueness, and Pareto optimality of PPE, along with algorithms for its computation, contrasting it with existing equilibrium concepts.

Findings

PPE is stable and Pareto optimal.

Existence and uniqueness of PPE are proven.

Two algorithms for computing PPE are presented.

Abstract

In the framework of finite games in extensive form with perfect information and strict preferences, this paper introduces a new equilibrium concept: the Perfect Prediction Equilibrium (PPE). In the Nash paradigm, rational players consider that the opponent's strategy is fixed while maximizing their payoff. The PPE, on the other hand, models the behavior of agents with an alternate form of rationality that involves a Stackelberg competition with the past. Agents with this form of rationality integrate in their reasoning that they have such accurate logical and predictive skills, that the world is fully transparent: all players share the same knowledge and know as much as an omniscient external observer. In particular, there is common knowledge of the solution of the game including the reached outcome and the thought process leading to it. The PPE is stable given each player's knowledge of its actual outcome and uses no assumptions at unreached nodes. This paper gives the general definition and construction of the PPE as a fixpoint problem, proves its existence, uniqueness and Pareto optimality, and presents two algorithms to compute it. Finally, the PPE is put in perspective with existing literature (Newcomb's Problem, Superrationality, Nash Equilibrium, Subgame Perfect Equilibrium, Backward Induction Paradox, Forward Induction).