Wargaming with a deep knowledge of Hypergame Theory (WHT) is very effective in guiding tabletop exercises using subject matter experts as players. I have found that human knowledge workers (the subject-matter experts) are more capable of being redirected dynamically than simulation software.1 WHT is a powerful way to evaluate a situationally derived decision landscape and prevent surprise. For the United States, which often has a number of favorably valued choices, preventing surprise leads to highly valued outcomes.
This chapter provides a very short introduction to game theory, then discusses what hypergame theory is, and as a step-by-step example applies WHT to the first Gulf War.
Introduction to Game Theory, Its Exciting Ideas, and Its Shortcomings
Game theory is an important quantitative technique used to discern the value of collecting information on people’s choices. Invented in the 1930s and first completely outlined by John Von Neumann in 1944, the idea is profound: Is there a strategy mix that is unpredictable yet delivers the best “repeated play” value of a known game? A known game is one where all the possible choices for both players are known and all of the outcomes of player choices are known as well. By best repeated play value, I mean that over a very large number of observed choices, player performance could not be improved. Both sides of a two-player game can play that well; the intersection of both players’ play is called the Nash Equilibrium Mixed Strategy (NEMS).2 (Gamers will also call these the “minimax” or “maximin” strategies.) And such work generalizes for even more players.
Furthermore, game theory can help determine the “expected value” of the game, which was not as obvious before game theory was invented. An expected value of any game is the “average” payoff—the weighted sum of the payoffs for choices divided by the number of choices made. In the child’s game rock-scissors-paper, for example, the value of the game is zero: we expect to win one-third of the time, draw one-third of the time, and lose one third of the time. Further, in rock-scissors-paper, the NEMS is 1/3 rock, 1/3 scissors, and 1/3 paper; in any given game instance, no one can predict what each player will do, yet this mixed strategy yields the highest mathematical result in repeated play.3
The concept of the value of the game helps strategists decide when to add a new choice to a game or even when to stop playing the game. Strategists often will not play games that have negative value to playing; such games are losing situations that are weighted against them. (Modern casino gamblers appear to reason differently.)4
Game-theoretical reasoning may be even more useful for insurgency or terrorist situations than when it was originally invented. For instance, if the Taliban is collecting historical information about NATO’s actions at a forward operating base in Afghanistan and is trying to decide whether to place a bomb along a frequently used route, then NEMS seems a very valuable tool. The bomber has to guess at the local NATO commander’s strategies, because NATO forces may do something different every day. Armed with the knowledge of how many roads there are and an estimation of the cost of emplacing a bomb, there is a real cat-and-mouse game occurring. In analyzing such situations, planners calculate their own mixed strategy and that of their opponents.
As exciting as these results are, there are practical concerns that the theory has trouble addressing. Situations rarely achieve the kinds of steady states that would reduce them to known games. A bomber is killed, which changes the cost of building bombs; a new kind of armored vehicle is delivered to the operating base—even a change in either side’s perception of acceptable losses should be analyzed. Issues such as these are better addressed by hypergame theory.
Introduction to Hypergame Theory
Hypergame theory was first formulated in Bennett and Dando’s 1979 article on the successful 1940 German campaign against the Allies. They proposed that because of each military’s experiences, goals, and means, the Germans and the Allies visualized the conflict differently from what game theory’s assumption about the consistent alignment of beliefs would suggest.
This simple idea, that even players playing a completely revealed game (such as chess) would see and reason about the contest very differently depending on past experience, resonated with me during my early doctoral studies, which were aimed at applying artificial intelligence techniques to strategy generation. I had observed that chess masters would play much differently against unranked adversaries than when playing other chess masters. The idea blossomed; it actually seemed likely that every nontrivial game was rarely played by both (or more) players in exactly the same way.
For example, a player’s understanding of the situation and options might vary in a number of ways:
differences in player knowledge and expertise;
differences in player starting situation assessment;
differences in player ongoing assessment capability (evidence processing);
differences in player understanding of strategy projection (what beats what?);
differences in player information (both at the strategy commitment phase and during the operations);
differences in robustness and resilience of each player’s strategies;
varied player constraints because of time;
differences in player creativity (what tricks can be added, such as feints, hidden reserves, denial and deception operations).
When considering such variation in options and perceptions, an average person’s analytical ability is rapidly outstripped. Few players are capable of considering more than two to five courses of action in a few diverse situations without using tables to organize such data. (Rules of thumb for redressing this limitation are scattered among the literature.) Thus, hypergame theory has to be supported by transactional memory (any artifact created to help humans remember, retrieve, and use information); I chose to extend the usual game-theoretic form.
Hypergame theory combines features of game theory and decision theory into a common table framework to help assess the impact of evidence, opponent knowledge, game knowledge, and contextual knowledge in order to analyze future competitions.
An Example of Descending the Diagonal
To enrich the number of possible strategies considered, I suggest a technique called “descending the diagonal,” which represents expanding a game to consider more possible strategies. Using a larger matrix than whichever table might actually be used to solve a competition helps analysts bound problems about the future. The rationale of the process is to consider a strategy (a row or column in the matrix) as already chosen and then to design an antistrategy (its nemesis). (This is very similar to many game-theoretic ideas from the 1950s.) After the nemesis is devised, we come up with the strategy which beats it, and so on. This is a kind of, “If you do this, then I’ll do this to beat you” analysis.
To make these considerations more concrete and similar to Bennett and Dando’s cited work, let us examine in a step-by-step way the considerations that could have occurred in formulating a battle strategy for the Allies in the first Gulf War. As a quick review: About 500,000 US forces and considerable allies assembled in Saudi Arabia to liberate Kuwait after the Iraqi invasion of 1990. The Iraqis have occupied Kuwait and have pillaged some of it; they have set up a defense and now await an Allied attack (or will watch the Allies give up and egress). The Allied air force has gained air supremacy.
Please note that this scenario favors the Allies; they will recapture Kuwait and damage the Iraqi forces to reduce Iraqi adventurism in the next decades. Ultimately, Allied planners want to unbalance the game to win a great victory, not to just prevail. The Iraqis are the Column Player, and the Allies are the Row Player.
In all of the following tables, the relative assessment number at the intersection of a Row choice and a Column choice summarizes an expert opinion of the range of results.
Because both sides are committing to a battle, only one number is recorded from the Allied (Row) point of view; this is for ease of table creation and decluttering of the visual representation. For the rest of this explanation, and consistent with zero-sum game theory, we will consider Column’s outcome to be the negative of Row’s, so we need not record it. Beware of choosing zero-sum automatically in actual problem solving sessions—adversaries often share some values, or both want to avoid an outcome (such as a nuclear exchange).
The entries in the table represent levels of game victories, where draw (0), marginal victory (1), strategic victory (2), and decisive victory (5) are given relative weights of success. Each side’s semantic definition of the result varies, so a –2 for the Allies is approximately 10,000 personnel killed or seriously wounded and enhanced Iraqi military prestige. A 0 might represent fewer casualties for the Allies and less-retained Iraqi military strength, or a combination thereof. Please note: the “focus” in table 21.1 is where Row is trying to lessen Column’s result.
Table 21.1 Initial situation
Defend
Allied Frontal Attack
Row: -2Column: (–(–2)) = 2
focus
In the Column, “Defend” is a frontal defense, evenly distributed. In the Row, “Frontal Attack” is an unweighted assault across the frontlines. The result of these two strategies is that the Allies will take a significant number of casualties, hence the –2 result. They will accomplish the mission of ejecting the Iraqis from Kuwait.
Row needs a better approach. The Row player tries to improve results by adding rows. As in all military engagements, Row could maneuver left or right, thereby adding two more rows, as we see in table 21.2. Since the Allies (Row) start south of the Iraqis (Column), heading northward, we will use geospatial labels; thus, “go left” becomes Main (Attack) West, and “go right” becomes Main (Attack) East. Expert opinion assesses that with either of these approaches the Allies will slightly lessen their casualties.
Table 21.2 Adding more rows
Defend
Frontal Attack
–2
Main West
–1
focus
Main East
–1
focus
The “focus” is where Column is trying to worsen Row’s outcomes. Note that the focus is on the worst result for the Column player, in this case –1, which occurs in two rows. Both must be evaluated.
Likewise, the Iraqis can also add columns (see table 21.3). Column could Defend (Weighted) West or Defend (Weighted) East. Defend West was designed to damage a Main West attack and would yield more Allied casualties, so it is assessed as a –3 for the Allies. Likewise Defend East is designed against Main East.
Table 21.3 More columns
The strategy and antistrategy reactions are beginning to appear on the diagonal; this is the concept of “descending the diagonal.” Currently, this analysis favors Column objectives.
Noting the double focus in table 21.2, the Column player will examine those rows that yield better results. Practically, this must be done sequentially. So: (1) When two approaches seem to give the same outcome, start with the one the current player (in this case Column) believes will be the most fruitful; (2) If it isn’t, the planner will shortly discover why the other is more promising.
Table 21.3 shows nine possible combinations of strategies and probable outcomes. A strategy to mitigate outcomes is emerging in the table, but all of the entries in the table must be assessed before completing the analysis. Notice, for instance, that Row’s Main West would achieve success and break through the Iraqi line with fewer casualties when matched against Column’s Defend East (0).
It becomes apparent as the analysis proceeds that the Allies can accomplish the mission by attacking frontally, but will receive unacceptable levels of casualties. In doing this, Row will miss opportunities to fake out Column or to win big. To win big, Row must add another row that effectively deals with these static defenses. Table 21.4 adds another row and creates a dominant row strategy, one with the highest value outcome in every column.
Table 21.4 Dominant row added
Fortunately for Row, there is an effective attack against the current three defenses. Envelop Vertically means to deploy airborne or air mobile troops to hit opponents in the rear. The expected value of the game has gone from negative to positive. The other rows are worse. Column can play either weighted defense (Defend West or East) to gain a drawish result (represented by a 0 result), but they can no longer expect to win.
In table 21.5, Column has added a defense in depth labeled “Defend with Reserves” to get a valuable result against Envelop Vertically. The continuation of analysis (down the diagonal) has stimulated a new strategy for Column. This changes the status of the previously dominant strategy—it is now just another row. This is common: rarely is a strategy dominant at the end of the analysis; there are few strategies that work well regardless of what an opponent does.
Table 21.5 Additional column
In table 21.6, Row considers a wide maneuver to the west of Column’s forces: Envelop West. It is an even better dominant strategy, and it shows why the Allies are likely to win. Indeed, we know after the fact that even in the most pitched battles in the war the Allies quickly broke the enemy. If somehow Row could get Column to configure its defense in the wrong way then Row would do even better.
Table 21.6 Row adds Envelop West
Two Column counterstrategies are possible: Screening and a Republican Guard Counterattack. Again the previously dominant strategy (Envelop West) is reduced by Column’s new strategies.
Note in table 21.7 how the original three rows work pretty well against the last two columns. This is often why our first strategies in our tables are rarely useless. In our minds, we think that if our opponent does something else, then they will be in a worse situation. So as Row generates new strategies, it is important to continue to assess all rows and columns, not just the diagonal focus which is driving new strategy creation.
Table 21.7 All of Iraq’s options
To prevent Column’s Counterattack option, Row needs to signal that they are going to attack frontally (a value of 4 in row 1). In the actual operation as the air campaign kicked off, Allied forces started to move their rearward ground forces closer to the Iraqi front lines, signaling that the Allies were about to attack across the front.
Last, we consider the effects of a deception strategy. If we can raise the likelihood of the enemy choosing the best column for our actual choice then we will have earned a great victory. In table 21.8, one can see how the US Marine Corps feint could influence the Iraqi generals. If they thought they could give the Allies a bloody nose on the beach, without having to expose their forces to air attacks by moving, that lure might become compelling. The Iraqis may also have been influenced by the position of the valuable Iraqi oil fields near the coast or a commonly held notion that forces committed to a wide sweep would get lost in the desert. The feint (Invade Beach) is shown by the –3 in the Defend East column.
Table 21.8 Invade Beach feint
Findings
In real life, we are rarely certain that we have scanned even most of our options. A coping strategy for addressing this realization by planners and actors was discovered by Herb Simon in 1956 when he labeled the use of “tried-and-true” methods of addressing known problems as “satisficing.”5 Military strategists have an entire staff looking for opponent patterns or lazy thinking, while investigating anomalous outliers that might signal the invention of a new option by the opposing player.
What we are really doing is systematically eliciting from a game situation all of the players’ strategies that deliver the big wins and big losses. These might be called the “wild ideas” of brilliant strategists, rather than what we expect. By determining a larger landscape of possibilities, we are actively attempting to prevent surprise by our opponent. Risky, high payoff strategies are generated during initial planning; these extrema lie outside of what we would actually ask warriors to do, but they act as a “type” for reasoning. Then we can dampen such wild ideas’ radical nature and lessen some of their vulnerabilities. We can always attack more slowly, for instance, relying less on our inspiration and completing our projection by acting in a more deliberate manner to ascertain the enemy’s situation more accurately.6
A strategist may waste time by developing new options, but one cannot make the value of the game worse by doing so. Developing a repeatable method, such as descending the diagonal, for finding significant rows or columns is highly desirable. An unknown strategy played as a surprise can destroy the predictive power of a strategy mix from original game theory.
Game theory helps one most when a strategist has run out of new options and players are pretty much restricted to competing in generally known games. Hypergame theory helps best when there is a new game or in a situation where there are significant structural advantages to one side. WHT promotes the concept that both players are creative and resourceful, and may even be deceptive. WHT is a more open approach to the process of examining what might happen in the future based on our possible choices than are scenario-based wargames. While WHT can still benefit from calculating the game-theoretic expected value of a game, that value is highly unlikely to be delivered by a small subset of the WHT well-examined situation/game. Instead an approach of modeling opponents from WHT yields repeatedly better results (Vane 2000).
Last, if we note the salient features of opponents’ plans, we can do whatever we can to delay our decision until their strategy is betrayed by intelligence collection (also called indicators and warnings). At that point, game theory isn’t even needed, because we know the enemy strategy.
In conclusion, hypergame theory is a valuable tool that combines many aspects of decision theory and game theory to address new outcomes, new strategies, differences in player planning capability, and evaluations of deception. In a way similar to Bennett and Dando, using an abstraction of a recent world contest provides a context for exploring how hypergame theory can evaluate the future. Combining wargaming with hypergame theory can develop valuable strategies to educate warriors and support intelligence collection.
About the Author
Russell Vane has been serving in the US wargaming shop assigned to attack IED networks since early 2008. He earned his doctorate from George Mason University in 2001 with the dissertation “Using Hypergames to Select Plans in Competitive Environments.” Thereafter he wrote numerous articles on the futures of artificial intelligence, intelligent augmentation and applying hypergame theory to sensemaking and decision making, including “Planning for Terrorist-Caused Emergencies” for WinterSim 2005. He coinvented a patent for General Dynamics for Cognitive Automation, awarded in 2010. From 1980 until 2000, he applied his master’s degree in computer and information science to delivering numerous defense- and weather-related systems. He coauthored The Arab-Israeli Wars with W. Seth Carus for Avalon Hill Company in 1977. In the late 1970s, he served as an Armored Cavalry officer after earning Airborne and Ranger tabs.
