Adaptation Procedure in Misinformation Games

TL;DR

A new game-theoretic concept, called misinformation games, is introduced that provides the necessary toolkit to study interactions between agents in multi-agent systems, in which the agents are misinformed with regards to the game that they play.

Abstract

We study interactions between agents in multi-agent systems, in which the agents are misinformed with regards to the game that they play, essentially having a subjective and incorrect understanding of the setting, without being aware of it. For that, we introduce a new game-theoretic concept, called misinformation games, that provides the necessary toolkit to study this situation. Subsequently, we enhance this framework by developing a time-discrete procedure (called the Adaptation Procedure) that captures iterative interactions in the above context. During the Adaptation Procedure, the agents update their information and reassess their behaviour in each step. We demonstrate our ideas through an implementation, which is used to study the efficiency and characteristics of the Adaptation Procedure.

Figures (6)

• Figure 1: Example of games without common and correct information.
• Figure 2: Schematic representation of the functionality of Adaptation Procedure from time step $t$ to time step $t+1$, that is ${\mathcal{A}D}^{t+1} \boldsymbol{\left(\right.}mG\boldsymbol{\left.\right)}$.
• Figure 3: Schematic representation of Example \ref{['example:running example-I']}.
• Figure 4: Correspondence between the adaptation graph $\Gamma$ and $\widetilde{\Gamma}$.
• Figure 5: Correspondence between all variations of adaptation graph.

Theorems & Definitions (85)

• Definition 1
• Definition 2
• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Proposition 5
• Proposition 6
• Proposition 7
• Definition 3