Rationality and correctness in n-player games
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Hindsight and Sequential Rationality of Correlated Play
Driven by recent successes in two-player, zero-sum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibrium-based strategies. However, this approach …
counterfactualDecision MakingMisconceptionsSequential Decision MakingAI Plays? δ-Rationality Games with Nash Equilibrium as Special Case
A distortion function, which captures the payoff gap between a player's actual payoff and her true payoff, is introduced and used to analyze games. In our proposed framework, we argue that players' actual payoff function…
Measuring Higher-Order Rationality with Belief Control
Determining an individual's strategic reasoning capability based solely on choice data is a complex task. This complexity arises because sophisticated players might have non-equilibrium beliefs about others, leading to n…
Strategic Behavior under Context Misalignment
We study the behavioral implications of Rationality and Common Strong Belief in Rationality (RCSBR) with contextual assumptions allowing players to entertain misaligned beliefs, i.e., players can hold beliefs concerning …
On Corrigibility and Alignment in Multi Agent Games
Corrigibility of autonomous agents is an under explored part of system design, with previous work focusing on single agent systems. It has been suggested that uncertainty over the human preferences acts to keep the agent…