Game Theory

Volume 2015, Article ID 570639, 20 pages

http://dx.doi.org/10.1155/2015/570639

## Hypergame Theory: A Model for Conflict, Misperception, and Deception

Department of Electrical and Computer Engineering, Graduate School of Engineering and Management, Air Force Institute of Technology, Wright-Patterson AFB, OH 45433-7765, USA

Received 24 May 2015; Accepted 9 July 2015

Academic Editor: Tonu Puu

Copyright © 2015 Nicholas S. Kovach et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

When dealing with conflicts, game theory and decision theory can be used to model the interactions of the decision-makers. To date, game theory and decision theory have received considerable modeling focus, while hypergame theory has not. A metagame, known as a hypergame, occurs when one player does not know or fully understand all the strategies of a game. Hypergame theory extends the advantages of game theory by allowing a player to outmaneuver an opponent and obtaining a more preferred outcome with a higher utility. The ability to outmaneuver an opponent occurs in the hypergame because the different views (perception or deception) of opponents are captured in the model, through the incorporation of information unknown to other players (misperception or intentional deception). The hypergame model more accurately provides solutions for complex theoretic modeling of conflicts than those modeled by game theory and excels where perception or information differences exist between players. This paper explores the current research in hypergame theory and presents a broad overview of the historical literature on hypergame theory.

#### 1. Introduction

“A conflict is a situation in which there is a ‘condition of opposition’ [1], and parties with opposing goals affect one another [2].” The study of how decision-makers interact during a conflict is known as game theory [3], while the study of how decision-makers make rational decisions is known as decision theory [4].

Game theory has been used to model diverse areas such as economics, natural selection, battles in past wars, and many other types of conflict [5]. The main influence behind the creation of game theory is the resolution of such competitions. Game theory models have many properties associated with them that influence the outcome and how game analysis proceeds but often fail to model the situation when one player has an advantage over the other in a conflict. When one or more players lack a full understanding or have a misunderstanding or incorrect view of the nature of the conflict, hypergame theory can be used to model the conflict.

Decision theory on the other hand is concerned with goal-directed behavior when options exist with different possible outcomes. The main influence behind the creation of decision theory is the rational behavior of the decision-maker [6]. Problems decision theory tries to answer include the following: “shall I bring an umbrella today?” or “I am looking for a house to buy shall I buy this one?” Decision theoretic models often fail to model the notion of fear, where another player may be able to outmaneuver during game play. Instead, models rely heavily on probability distributions to determine the preferred outcome.

Hypergame theory is an extension of game theory that addresses the kind of conflict games where misperception exists. The term hypergame was coined by Bennett in 1977. It seeks to explain how players in a game can have differing views of the conflict [7]. This advance in game theory shows how one player can believe that decisions of the other player are irrational, but the opponent is actually making a rational decision based upon the perceived game model.

Hypergame analysis extends game theory by providing the larger game that is really being played whether or not both players are aware of it. A different game model can represent each player’s view of the conflict, but often the player’s views will overlap where common knowledge exists. Figuring out what strategy a player will use is dependent upon not only his or her observation of the game, but also how that player believes their opponent is viewing the game. This creates many different game models that are examined for the solution to be obtained. The goal of hypergame analysis is to provide insight into real-world situations that are often more complex than a game where the choices of strategy present themselves as obvious.

After its introduction, hypergame theory was used to model past military conflicts, which are prone to having misperceptions and missing information in the process of their unfolding, to show how the outcomes were achieved. Analysis of past conflicts also lends itself to ease of understanding since the fog of war has cleared and the outcome has been determined. Options selected by each side in the conflict are shown to be the rational choice by way of defining the game that each side perceived. In this manner, the hypergame analysis shows why unexpected results were obtained when one or both sides misconstrued the conflict. Hypergame analysis offers advantageous reasoning of strategy selection through situational awareness.

Throughout this paper, the players are often referred to as human entities, engaged in a conflict. The perception or misperception of the players in all cases is the result of sensors, whether mechanical or human senses are combined with brain power. Human players, mechanical players, or artificial intelligence (AI) players are interchangeable in the hypergame models.

Examples in this paper are presented using two players with a limited number of actions/strategies. This allows the complexity of the example to be reduced and the visualization included in the figures to be clear. As more players and actions/strategies increase, the complexity will also increase.

#### 2. Foundations of Hypergame Theory

Game theory, decision theory, and hypergame theory can be used to model conflicts as games. When very little is known about the opponents, game theory is used for adversarial reasoning. Decision theory is a better choice if the opponents are well known, which is often the case in complete information games. If one or more of the opponents are playing different games because they are not fully aware of the nature of the game, hypergames can be used to reason about subgames that are shared between opponents. The following provides a brief overview of decision theory and game theory.

Hypergames extend game theory by allowing for an unbalanced game model that contains different view of the game representing the differences in each player’s information or beliefs. The unbalanced game model allows for a different game model for each player’s view, while having overlap where there is common knowledge. Decision theory has been used in hypergames to model the fear of being outguessed. The fear of being outguessed is common in a game model where the different player’s perceived games are unbalanced.

##### 2.1. Game Theory

Game Theory is a set of analytical tools designed to help understand the phenomena that are observed when decision-makers interact [3]. The assumption is made in game theory that human beings are rational and always seek the best alternative when presented with a set of possible choices. Game theory is highly mathematical and assumes that all human interactions can be understood and navigated by presumptions. Game theoretic models seek to answer two questions about the interaction of the decision-makers [12]:(i)How do individuals behave in strategic situations?(ii)How should these individuals behave?Answers to the two questions do not always coincide [13]. Often the answers to the two questions may be in conflict.

Game theory models have many properties associated with those that influence the outcome and how game analysis proceeds. Cooperative games can exist where there is communication between players, but more often games are seen as noncooperative where the players do not attempt to give up any information to their rivals. Simultaneous games are when players make decisions at essentially the same time and do not know of the opponent’s move in advance (i.e., rock, paper, and scissors). Conversely sequential games are when the opponent’s move is known before a decision is made (i.e., betting in poker or chess). Perfect information versus imperfect information is when all previous moves are known to all players instead of some being hidden. These previous two concepts are often confused with complete information and incomplete information, which are actually intended to be the knowledge of all player’s strategies and payoffs. The payoffs, also known as utilities, have a common property of zero sum or nonzero sum.

The majority of game theory models are identified as either strategic games (normal form), used to represent a simultaneous game, or extensive games, more often used to represent a sequential game even though it can represent simultaneous one as well. A strategic (normal form) game is shown in Figure 1. Strategic games have utilities that are determined by which strategy is selected by each player. When a player’s strategy is selected, all strategies are available to choose from and therefore the game is represented in a grid or matrix format. Extensive games’ outcomes are instead represented as a tree structure where the initial player is at the top with branches leading off for each strategy available, as shown in Figure 2. After the first player chooses an action, the next player has strategies available creating branches for each of its strategies available. All strategies that a player can use may or may not be available at a particular node of the tree dependent upon the previous player’s selected strategy.