## Tuesday, April 6, 2010

### Hypergame Analysis, Part 1

In situations of competition and conflict, no single player can dictate the outcome. What occurs depends on the strategy each player pursues. In turn, the strategy each player pursues depends on the strategy each player believes his or her opponent will pursue, and so on. Analysts often use game theory to model such situations.

In 1977, Peter Bennett introduced hypergame analysis, an elegant and useful extension to game theory. Unlike standard game theoretic models, Bennett’s concept permits players to perceive different games. This feature better approximates real-world conditions and, in particular, allows analysts to model situations involving manipulation, stratagem, and deception more directly.

In hypergame terms, a situation in which both players correctly perceive the same game is designated a level-zero hypergame. A situation in which both players believe they are playing the same game while at least one player misperceives the game is designated a level-one hypergame. A situation in which at least one player perceives the other player’s (assumed) misperceptions is designated a level-two hypergame.

Example:
A scammer offers a great deal to a mark on the street: “My friend’s business has failed,” says the scammer, “and I’ve got a van full of DVD players I need to sell quickly at a great price.” The mark hesitates. Maybe they’re stolen, he thinks. He decides to take a look anyway. The scammer opens the back of a van containing stacks of boxes. He opens one to reveal an off-brand but slick-looking portable DVD player. “This is yours for \$20,” he tells the mark, who weighs the opportunity. The stuff’s obviously boxed, the mark tells himself; maybe it’s not stolen after all. He ignores his initial misgivings, hands over a twenty, and walks away with a mint-in-the box DVD player, or so he believes. When he gets to his car, he eagerly opens the box and discovers a brick. He drives back to the scene of the crime, but the scammer is gone. This situation is easily described using the hypergame framework. The mark assumes the two are playing the same game. In this game, the scammer’s options are {(sell a stolen player) (sell a legitimate player)} while the mark’s options are {(buy a player) (walk away)}. The mark’s challenge, then, is to decide whether the players are stolen. If the mark doesn’t care either way, then the choice is easy: buy a player. The scammer is playing a different game. For the sake of this example, let’s assume the scammer keeps a couple of real DVD players handy in case he suspects the mark might blow the con. In the scammer’s game, then, the mark’s options are {(buy a player) (walk away) (blow the con)} and the con’s options are {(sell a broken player) (sell a working player)}. If all goes well for the scammer, the mark never suspects (1) the scammer is playing a different game and (2) the scammer is playing a higher-order game–that is, the scammer is not only playing a different game but is aware of the mark’s misperceptions. This yields an advantage to the scammer. As long as the mark doesn’t suspect that most of the boxes contain bricks, he believes his choice is simply an ethical one: should I buy possibly stolen merchandise ? The concept of higher perspectives is sometimes referred to as expectation.5 Expectation is arguably as critical to the hypergame approach as is the more basic concept of different games.

Weaknesses: Hypergames of level three and higher are possible but challenging because they require increasingly convoluted mental recursions (I think he thinks I think he thinks, and so on). Hypergame analysis as described in the existing literature can be fairly complex. It is not something an interested analyst or red teamer will typically pick up in a day. When it is used, it is usually delegated to a specialist, who must then translate the outcome back into terms a decision maker can absorb.

Strengths: As the example illustrates, the player who correctly perceives a level-two hypergame enjoys a clear decision advantage over a player who believes the two sides are playing the same game. This situation does not necessarily arise by chance, and a clever player will aim to create and exploit such conditions. As a result, the benefit of hypergame modeling to a red teamer or decision maker rests not strictly in describing a situation but also in modeling a situation explicitly in order to gain a position of advantage.
Awareness of the hypergame construct encourages a player to avoid granting his or her opponent a position of advantage.

Conclusions: In any game-like contest, a player should always remember to ask “what do I perceive, and what does my opponent perceive?” To be avoided, for example, are states in which you, a player, believe you and your opponent are playing the same game when your opponent is actually playing a level-two hypergame. To be sought are states in which these roles are reversed.