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AD-504 (B) · Game Theory with Engineering Applications/Quick Revision Short Notes

Game Theory with Engineering Applications (AD-504 (B)) - Unit 3 Short Notes

How unit 3 is examined

This unit covers systems and their elements, the multivalent model of interactivity, and choice with its molecules, anatomy and space of possibility; none of the three topics was asked in the recent papers, so all are taught briefly but completely.

Introduction to Systems, elements of a System, Framing Systems, open and closed systems

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Definition. <mark>A system is a set of parts, or elements, that interrelate to form a complex whole.</mark> A game is a system because its pieces, rules and players work together to produce play.

Diagram.

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Key points.

  1. A system has four elements: objects, which are the parts; attributes, which are the properties of those objects; internal relationships among the objects; and an environment that surrounds the system.
  2. Objects can be physical (cards, pieces, a board), abstract (a score, a rule) or even the players themselves, and they are the raw material of the system.
  3. Attributes describe the objects, for example the colour, value and position of a piece, and a change in an attribute changes how the system behaves.
  4. Internal relationships are the links between objects and attributes, and they are the most important element because they make the parts work as a whole rather than as a heap.
  5. The environment is the context that surrounds the system; the same system behaves differently in a different environment, as a board game does at home and in a tournament.
  6. Framing a system means choosing where its boundary lies and which viewpoint is taken; the same thing, such as a school or a game of chess, can be framed as several different systems.
  7. A closed system does not exchange matter, energy or information with its environment, so it is self-contained and cut off from outside influence.
  8. An open system does exchange matter, energy or information with its environment, so it is affected by what lies outside it.

Comparison.

Basis Closed system Open system
Exchange with environment None Continuous
Boundary Fixed and sealed Permeable
Outside influence Ignored Shapes the system
Example Formal rules of chess Chess with its players and culture
Predictability High Lower

Example. The formal rules of a board game form a closed system, because the rules alone decide what is legal. The same game as actually played is an open system, because the players' emotions, the crowd and local customs all feed into it.

Answer frame. Open with the definition; draw the element diagram; develop the four elements in order, then framing; close with the open versus closed table and the board game example.

Pitfall: Do not name only three elements; the environment is the one students forget.

Introduction to Interactivity, a multivalent model of interactivity

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Definition. <mark>Interactivity is participation with a system, and the multivalent model states that it has several distinct modes and not one single meaning.</mark> The word "multivalent" means having many values or meanings.

Diagram.

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Key points.

  1. The common idea that interactivity means only clicking a button or pressing a key is too narrow, and the multivalent model corrects it by describing four modes.
  2. Cognitive interactivity is the psychological, emotional and intellectual participation of the player with the system, for example interpreting symbols, solving puzzles and feeling suspense.
  3. Functional interactivity is the utilitarian, structural participation with the object, such as the feel of the controls, the weight of the pieces and how easily the board can be used.
  4. Explicit interactivity is overt participation, meaning the choices and moves that a player makes by acting on the system, such as rolling a die, moving a piece or pressing a button.
  5. Beyond-the-object interactivity is participation in the culture around the game, such as fan communities, forums, shared strategies, rule variants and fan fiction.
  6. The four modes overlap and occur together in real play, so a designer must consider all of them and not just explicit interaction.
  7. Explicit interactivity alone does not guarantee meaningful play, since a player can press buttons without thinking or caring.

Comparison.

Mode What is involved Example in a card game
Cognitive Mind and emotion Reading an opponent's bluff
Functional Physical structure Shuffling and holding cards
Explicit Overt actions and choices Playing a card
Beyond-the-object Culture around the game Online strategy forums

Example. In chess, thinking several moves ahead is cognitive, handling the pieces is functional, moving a piece is explicit, and joining a chess club or studying published openings is beyond-the-object.

Answer frame. Open with the definition and the meaning of multivalent; draw the four-branch tree; develop the four modes in the order cognitive, functional, explicit, beyond-the-object with one example each; close by noting that good design considers all four modes.

Pitfall: Do not equate interactivity with explicit clicking; that is only one of the four modes.

Interaction and choice, choice molecules, anatomy of choice, space of possibility

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Not asked since 2022</span>

Definition. <mark>A choice molecule is the basic unit of interaction: a choice the player faces, the action the player takes, and the outcome that results and is fed back to the player.</mark>

Diagram.

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Key points.

  1. Interaction in a game is a series of choices, and each choice the player makes is the smallest unit through which the player takes part in the system.
  2. The anatomy of choice has three parts: the choices offered to the player, the action the player takes, and the outcome that follows the action.
  3. Feedback of the outcome to the player is essential, because the player must see the result to make the next choice sensibly.
  4. Several choice molecules linked together form a longer chain of play, just as atoms join to form molecules in chemistry.
  5. A choice is meaningful only when its result is discernable, meaning the player can see what happened, and integrated, meaning the result affects the rest of the game.
  6. The space of possibility is the whole set of actions and meanings that can emerge as the game is played, and it is created by the rules and the game design.
  7. A larger and richer space of possibility gives the player more meaningful choices, whereas a tiny space makes play trivial and repetitive.
  8. A designer shapes this space by adding or removing choices and by deciding how strongly each outcome affects later play.

Example. In tic-tac-toe, the choice is which empty square to take, the action is placing an X, and the outcome is a changed board that the opponent sees. The space of possibility is small, which is why the game is quickly solved, whereas chess has a vast space and stays interesting.

Answer frame. Open with the definition of choice molecule; draw the loop diagram; develop the anatomy of choice, then meaningful choice, then space of possibility in order; close with the tic-tac-toe versus chess example.

Pitfall: Do not stop at "choice and action"; the outcome and its feedback complete the molecule.

Last-minute revision

  • A system is a set of interrelated parts that form a complex whole.
  • The four elements of a system are objects, attributes, internal relationships and environment.
  • Framing chooses the boundary and viewpoint from which a thing is seen as a system.
  • A closed system exchanges nothing with its environment; an open system does.
  • Interactivity is participation with a system; the multivalent model gives it four modes.
  • The four modes are cognitive, functional, explicit and beyond-the-object.
  • Explicit interactivity is only overt action such as clicking or moving a piece.
  • A choice molecule is a choice, an action and an outcome with feedback.
  • Meaningful choices are discernable and integrated.
  • The space of possibility is everything that can happen in play.

Memory hooks

  • OAIE: Objects, Attributes, Internal relationships, Environment.
  • CFEB: Cognitive, Functional, Explicit, Beyond-the-object.
  • Choice, Action, Outcome, Feedback: one molecule, then a loop.
  • Closed is sealed like a jar; open is a window with a breeze.
  • Rules draw the walls of the space of possibility.

Coverage checklist

  • Introduction to Systems, elements of a System, Framing Systems, open & closed systems: definition, four elements, framing, open versus closed; no past questions.
  • Introduction to Interactivity, a multivalent model of interactivity: four modes with examples; no past questions.
  • interaction & choice, choice molecules, anatomy of choice, space of possibility: choice molecule, anatomy, space of possibility; no past questions.
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