Understanding how (un)awareness affects decisions: What happens when players don’t know everything?

What is it about?

This research examines how the extent to which players are aware of the game’s elements: actions, players, and payoffs, affects decision-making in strategic interactions, particularly in the well-known Prisoner’s Dilemma. The Prisoner's Dilemma is a basic concept in game theory. In this game, two individuals are caught for a crime but are confined in separate cells and are unable to communicate with one another. Each inmate has two options in the game: confess or remain silent. If both prisoners maintain silence, they receive a moderate sentence, yielding a comparatively favorable outcome. If one inmate remains silent while the other admits guilt, the silent inmate receives a more severe sentence, whereas the confessor is granted a reduced sentence. As a result, the confessing person gains an advantage over the cooperating person. If both prisoners confess, they receive a moderately severe sentence, resulting in a suboptimal outcome. In traditional game theory, players are assumed to be fully aware of all elements of the game. However, real-life situations often involve players who are only partially aware of the rules or options available to them. The awareness is different from the traditional concepts in game theory, like imperfect or incomplete information, which refers to a situation where players are aware of the game elements but lack certain details, such as the exact payoffs or the strategies of other players. In contrast, awareness refers to a player's ability to perceive and understand the game elements, even when complete information is available. Players may have access to all necessary information about the game but may still be completely or partially unaware of it for whatever reason. The study delves into the consequences of imperfect awareness by modeling different scenarios where players might be unaware of the existence of other players, the actions they can take, or the outcomes that could result from their decisions. This is achieved by introducing deviations from the classic Prisoner’s Dilemma, where players' perceptions of the game can differ from the actual game setup (as understood by the game theorist or modeler). The research distinguishes between awareness in a narrow and broad sense, exploring how deviations in awareness can lead to different behaviors, strategies, and, ultimately, outcomes. Awareness, in a narrow sense, refers to the player's ability to detect the game elements, and a player is either unaware (knows nothing) or fully aware (knows all) about that element. For example, if there are three available actions, but a person is aware of only two, they will base their reasoning and choices only on these two options. Awareness, in a broader sense, is also referred to as game awareness, which accounts for persons’ detecting of the game occurrence (what elements are detected), knowing the game elements and game rules (identifying opponents and options, why this happens), and projecting the learned in the near future (what are possible outcomes based on theirs and opponent’s actions, what is the whole meaning of the situation). This allows the player to be aware of some aspects (for example, player existence, but not their type) but also to consider information outside the game's formal rules. That affects their reasoning and strategic decisions by incorporating broader contextual understanding. By exploring these deviations, the study shows that (un)awareness can lead to unexpected results, influencing not only individual decisions but also the overall game structure. The findings have implications for how we model decision-making in uncertain environments, extending beyond traditional game theory to practical fields such as management, security, and even business strategy, where players often operate with incomplete or incorrect information. This research provides a framework and examples to account for the role of awareness in game theory, helping to better predict and explain behaviors in complex, real-world interactions where players might not have full awareness of all available information.

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Photo by VD Photography on Unsplash

Photo by VD Photography on Unsplash

Why is it important?

In the narrow sense of awareness, the research examines how the absence of knowledge about a player changes the game dynamics. For example, if one player is unaware of the other, as in the Prisoner’s Dilemma (PD), the game becomes one-sided. This altered awareness leads the player to perceive a much simpler game, potentially missing out on the strategic interactions that could influence the outcome. In the context of real-world examples, two companies competing in the same market could face similar challenges. If one company is unaware of the competitor’s promotional activities, it could mistakenly believe it has a free hand, which could lead to strategic missteps. Similarly, in cybersecurity, if a manager is unaware of an active hacker threat, they might fail to take defensive actions, leaving their company vulnerable to attacks. Unawareness of actions is another critical scenario where players cannot fully optimize their strategies due to the inability to see all possible choices. This results in suboptimal decision-making because the unaware player assumes the other will act according to a limited set of options. A company that is not aware of disruptive innovations from a competitor might fail to adapt and face market displacement. In the case of cybersecurity, if a manager is unaware of newer, more sophisticated attack vectors, their defensive strategies may become outdated, leading to significant exposure to cyber threats. When it comes to unawareness of outcomes, players may be aware of the game’s actions but lack a full understanding of the payoffs. This partial awareness leads to decision-making that does not maximize utility. In business, this could be seen when a company launches a product without a full appreciation of its potential market impact. Likewise, in cybersecurity, a manager might underestimate the damage caused by a breach, resulting in insufficient defensive measures that exacerbate the problem. If a modeler assumes that only awareness in a narrow sense can occur, they can miss out on how games can be understood more broadly than the initial game setup. However, modeling that does not account for awareness, especially with human subjects, may cease to depict the situation as eligible for real-world application. Skewed awareness, where players are partially aware of elements in the game, introduces even more complexity. The distorted understanding of the game elements leads players to make decisions that result in outcomes different from what a modeler or an omniscient bystander would expect. Each of these scenarios highlights the profound impact that awareness—or lack thereof—has on decision-making in strategic interactions. Whether in business or cybersecurity, awareness influences how strategies are developed, optimized, and executed, often determining the difference between success and failure. However, different approaches to seeking solutions exist. In some cases, the approach to modeling a game with (un)awareness as a corresponding game with incomplete information is used, but its downside is that it disregards the distinction between assigning zero probability and being unaware of a strategy (or an element). Some examples showed that (un)awareness and incomplete information might coexist in a game and differently impact game reasoning and the outcome. So, such situations should be treated as games with unawareness with an appropriate solution concept, such as extended Nash equilibrium. While the findings provoke thought on game theory modeling, the work has only begun. The synthesis of the most prominent deviations due to (un)awareness of game elements in this paper is just a sample of how the game can deviate from the proposed model – in this case – a Prisoner Dilemma. Further extensions and variations, including more subtle differences due to skewed awareness, remain for exploration.