Rationality and correctness in n-player games

TL;DR

This paper explores conditions for Nash equilibrium in n-player games, introducing MARC, which aligns with mutual knowledge of rationality, and analyzing its applicability in two-player and multi-player contexts.

Contribution

It introduces the MARC concept, connecting rationality and correctness assumptions, and analyzes its validity across different game types.

Findings

MARC holds in all two-player zero-sum games.

MARC does not generally hold in n-player games.

Provides theoretical insights into rationality assumptions in game theory.

Abstract

There are two well-known sufficient conditions for Nash equilibrium in two-player games: mutual knowledge of rationality (MKR) and mutual knowledge of conjectures. MKR assumes that the concept of rationality is mutually known. In contrast, mutual knowledge of conjectures assumes that a given profile of conjectures is mutually known, which has long been recognized as a strong assumption. In this note, we introduce a notion of "mutual assumption of rationality and correctness" (MARC), which conceptually aligns more closely with the MKR assumption. We present two main results. Our first result establishes that MARC holds in every two-person zero-sum game. In our second theorem, we show that MARC does not in general hold in n-player games.