Verification with Common Knowledge of Rationality for Graph Games

TL;DR

This paper introduces a new verification approach for graph games based on common knowledge of rationality (CKR), relaxing the traditional Nash equilibrium assumption by incorporating epistemic models to better reflect agents' rational behavior.

Contribution

It proposes a novel verification framework using CKR instead of NE, providing a more realistic model of rationality in multi-agent graph games.

Findings

Analyzes the complexity of verification problems with positional strategies.

Defines a variant of realizability problem based on CKR.

Provides complexity results for the proposed verification approach.

Abstract

Realizability asks whether there exists a program satisfying its specification. In this problem, we assume that each agent has her own objective and behaves rationally to satisfy her objective. Traditionally, the rationality of agents is modeled by a Nash equilibrium (NE), where each agent has no incentive to change her strategy because she cannot satisfy her objective by changing her strategy alone. However, an NE is not always an appropriate notion for the rationality of agents because the condition of an NE is too strong; each agent is assumed to know strategies of the other agents completely. In this paper, we use an epistemic model to define common knowledge of rationality of all agents (CKR). We define the verification problem as a variant of the realizability problem, based on CKR, instead of NE. We then analyze the complexity of the verification problems for the class of positional strategies.