Adaptation Procedure in misinformation games

Autonomous Agents and Multi-Agent Systems https://doi.org/10.1007/s10458-025-09704-w (2025) 39:22 Adaptation Procedure in misinformation games Konstantinos Varsos1 · Merkouris Papamichail1,2 · Giorgos Flouris1 · Marina Bitsaki2 Accepted: 27 February 2025 © The Author(s) 2025 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 gametheoretic 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. Keywords Misinformation games · Adaptation procedure · Natural misinformed equilibrium · Stable misinformed equilibrium 1 Introduction The importance of multi-agent systems has been heavily acknowledged by the research community and industry. A multi-agent system is a system composed of multiple interacting autonomous, self-interested, and intelligent agents,1 and their environment. In such settings, agents need to be incentivized to choose a plan of action, and game theory [1] provides a suitable framework for analyzing these interactions. A usual assumption of game theory is that the game specifications (i.e., the rules of interaction, which include the number of players, their strategies and the expected payoff for 1 Note that we use the terms “agent” and “player” interchangeably throughout this paper. B Konstantinos Varsos Merkouris Papamichail Giorgos Flouris Marina Bitsaki 1 Institute of Computer Science, Foundation for Research and Technology - Hellas, N.Plastira 100, Heraklion 70013, Crete, Greece 2 Computer Science Department, University of Greece, Voutes Campus, Heraklion 70013, Crete, Greece 0123456789().: V,-vol 123 22 Page 2 of 47 Autonomous Agents and Multi-Agent Systems (2025) 39:22 each strategic choice) are common knowledge among the players. In other words, players have correct (although not necessarily complete) information regarding the game. However, in realistic situations, a reasoning agent is often faced with erroneous, misleading and unverifiable information regarding the state of the world or the possible outcomes of her actions (see games with misperception [2–4]). This misinformation may affect the interaction’s outcomes. Misinformation in an interaction can occur due to various reasons. For example, the designer may choose to deceive (some of) the agents in order to obtain improved social outcomes or for other reasons (this falls under the general area of mechanism design, see [5]). Or an agent may communicate deceptive information in order to lead the other agents to suboptimal choices and obtain improved outcomes (e.g., fake financial reports misleading investors [6]). Furthermore, when the agents operate in a remote and/or hostile environment, noise and other random effects may distort communication, causing agents to receive a game specification that is different from the intended one (e.g., in the case of autonomous vehicles operating in Mars [7]). Another scenario that could lead to misinformation refers to cases where the environment changes without the agents’ knowledge, causing them to have outdated information regarding the rules of interaction (e.g., an accident causing a major and unexpected disruption in the flow of different roads in a city). Last but not least, endogenous reasons (e.g., limited awareness, bounded computational capacity, cognitive restrictions, biases [8] etc.) may cause agents to misinterpret the situation and assign their own (mistaken) payoffs to different actions. Thereupon, some aspects of the situation, or the modeling and reasoning regarding the situation, leads players to incorporate a possibly incorrect viewpoint of the real aspects. Thus, they may miss crucial specifications, and interact relying on a restricted and incorrect perception of the situation. The key characteristic of the described scenario is that the players do not question the rules of interaction given to them; this differentiates this scenario from standard settings of games with other forms of uncertainty (such as Bayesian games [9, 10], uncertainty theory [11] etc.), in which players are well-aware of the fact that the information given to them is incomplete, uncertain or flawed in various ways, and this knowledge is incorporated in their reasoning (see also Fig. 1). In other words, in misinformation games agents don’t know that they don’t know, as opposed to incomplete or imperfect games where the agents know that they don’t know. The study of settings where any participant has (possibly) wrong knowledge with regards to the real situation, has been recently considered in defining the concept of misinformation games [5, 12]; this work falls under the hood of games with misperception [2–4]. In misinformation games, each player has a subjective view of the abstract game’s specifications, that may not coincide with the specifications of the real interaction, modelling the fact that agents may operate under an erroneous specification. For that, the proposed method agglomerates both the real situation (actual game), and the subjective (misinformed) views of the players. A key characteristic of misinformation games is that the equilibrium (i.e., the set of strategic choices where no player wants to deviate from) is determined by the subjective views of the players, rather than the actual game [12]. This is called the natural misinformed equilibrium in [12]. On the contrary, the actual payoffs received by the players is determined by the actual game, and may be different than the expected ones. Given the discrepancy between the actual and the perceived payoffs, a natural question is how the players will react upon their realisation that the received payoffs are different than expected. However, the approach presented in [5, 12] focuses on one-shot interactions, and thus misses this crucial and interesting part of the problem. To address this limitation, this work enhances misinformation games with an iterative time-discrete methodology, called 123 Autonomous Agents and Multi-Agent Systems (2025) 39:22 Page 3 of 47 22 Fig. 1 Example of games without common and correct information the Adaptation Procedure, which models the evolution of the strategic behaviour of rational players in a misinformation game, as they obtain new information and update their (erroneous) game specifications. The first steps towards this direction were held in [13]; (...truncated)