Game Theory with Engineering applications (CS-803 (B)) Notes

How unit 5 is examined

This unit covers what game rules are, their qualities, their three levels (operational, constitutive, implicit), how they give a game its identity, and case studies on digital games, Tic Tac Toe and a deck of cards; no topic was asked recently, so learn the definitions and the three levels first.

Defining rules

Not asked since 2022

Definition. Rules are the formal structure of a game: they limit what players may do and so define the space in which play happens.

Key points.

Rules limit player action, because they say what a player may and may not do.
Rules are the most formal part of a game, since they are written to be exact and unambiguous.
Rules create meaning: a move matters only because the rules give it an effect.
Rules are shared, so every player is bound by the same set.

A deck of cards

Definition. A deck of cards is a set of 52 cards in four suits of 13 ranks, and it is a game component, not a game.

Key points.

The deck alone has no goal, so it is only a set of objects until rules are applied.
The same deck supports many games such as Poker, Bridge and Rummy, each with different rules.
This shows that rules, not materials, make a game what it is.
Rules of the deck itself (ranks, suits, colours) only give the components; a game adds goals and actions.

Quality of rules

Definition. Good game rules limit player action, are explicit and unambiguous, are shared by all players, are fixed, binding and repeatable.

Key points.

Rules limit player action, so they narrow choices to a defined set.
Rules are explicit and unambiguous, so all players read them the same way.
Rules are shared by all players, so nobody plays under a private rule set.
Rules are fixed: they do not change during play.
Rules are binding and repeatable, so the same game can be played again anywhere.

Rules in context

Definition. Rules are not read in isolation: the way players interpret and apply them depends on the context of play.

Key points.

The same written rule can be applied differently by different groups or cultures.
Context includes players, place, social setting and the medium of the game.
Players may bend rules, for example in a friendly family game, without breaking the game.
A designer must therefore think of how rules will be lived, not only how they are written.

Rules on three levels: Operational

Definition. Operational rules are the guidelines players need to actually play the game, the rules written in the rulebook.

Key points.

They are what players explicitly follow, such as how to deal, move, score and win.
They are the rules a newcomer learns first.
They are stated in the rulebook or the instructions on the box.
They are the level of the rules that is easiest to observe and to change.

Constituative (constitutive rules)

Definition. Constitutive rules are the underlying formal structure of the game: the logic and mathematics beneath the operational rules.

Key points.

They are hidden from the players, who usually never see them stated.
They describe the game as a formal system, for example its state space and outcome logic.
Different operational rules can sit on the same constitutive structure.
Designers analyse them to find balance, dominant strategies and outcomes.

Implicit

Definition. Implicit rules are the unwritten rules of etiquette and good sportsmanship that players follow without stating them.

Key points.

They are seldom written in the rulebook, yet players know them.
Examples are not looking at another player's cards and not gloating over a win.
They vary with culture and with the group of players.
Breaking them does not break the game formally, but it spoils play.

Identity of a game

Definition. The rules give a game its identity: change the rules enough and the game becomes a different game.

Key points.

Rules, not pieces or boards, are what make a game recognisable as itself.
Small changes (house rules) give a variant; large changes give a new game.
The same deck or board can carry different games because the rules differ.
Players agree on the identity of a game because they share its rules.

Specificity of rules

Definition. Specificity is how precisely and completely the rules of a game are stated.

Key points.

Very specific rules leave no doubt and remove disputes, which suits competitive play.
Loose rules allow interpretation and creativity, which suits casual or children's play.
Rules can be too specific, making the game rigid and hard to learn.
Designers set the level of specificity to fit the players and the game.

Rules of digital games

Definition. In a digital game the computer program itself enforces the rules, so they are automatic and mostly hidden from the player.

Key points.

The software applies the rules with no need for players to police them.
The player often learns the rules by playing, not by reading a rulebook.
Automation allows far more complex rules than a human group could manage.
The rules can be changed by updating the code, which cannot happen mid-game in a board game.

Case studies: Tic Tac Toe

Definition. Tic Tac Toe is a two-player game on a 3 by 3 grid in which players alternately mark X and O and the first to get three in a row wins.

Key points.

Operational rules: players alternate turns, mark one empty cell each, and three in a row wins; a full grid with no line is a draw.
Constitutive rules: it is a finite two-player zero-sum game with 255,168 possible complete games, and with perfect play it ends in a draw.
Implicit rules: players do not cheat, take turns fairly, and let X go first by convention.
It shows all three levels of rules in one small game.

Deck of cards case study

Definition. The deck of cards case study shows that one fixed set of components can hold many games, each defined by its own rules.

Key points.

Operational rules differ by game: Poker ranks hands, Bridge bids and takes tricks, Rummy forms sets.
Constitutive rules include chance from shuffling and hidden information in each hand.
Implicit rules include not signalling to a partner and not peeking.
Identity: the deck is the same, but each set of rules makes a different game.

Last-minute revision

Rules limit player action and are the formal structure of a game.
Good rules are explicit, unambiguous, shared, fixed, binding and repeatable.
A deck has 52 cards, 4 suits, 13 ranks, and it is a component, not a game.
Three levels: operational, constitutive, implicit.
Operational rules are the written rules players follow.
Constitutive rules are the hidden formal logic and mathematics underneath.
Implicit rules are unwritten etiquette and sportsmanship.
Rules give a game its identity.
Specificity is how precisely the rules are stated.
Digital games enforce rules automatically in code.
Tic Tac Toe has 255,168 possible games and a draw under perfect play.

Memory hooks

OCI: Operational, Constitutive, Implicit.
Operational = Obvious (written); Constitutive = Concealed (formal logic); Implicit = Unspoken.
Quality of rules: "Ex-SFB-R": explicit, shared, fixed, binding, repeatable.
One deck, many games: rules make the game.
Digital games: the code is the referee.

Coverage checklist

defining rules: definition and key points.
a deck of cards: definition and key points.
quality of rules: the qualities of rules.
rules in context: definition and key points.
Rules on three levels: Operational: operational rules.
Constituative: constitutive rules.
Implicit: implicit rules.
Identity of a Game: identity through rules.
Specificity of Rules: definition and key points.
Rules of Digital games: automation of rules.
Case Studies: Tic Tac Toe: three levels in Tic Tac Toe.
Deck of Cards: three levels and identity in a deck of cards.

Account

Game Theory with Engineering applications (CS-803 (B)) - Unit 5 Short Notes

How unit 5 is examined

Defining rules

A deck of cards

Quality of rules

Rules in context

Rules on three levels: Operational

Constituative (constitutive rules)

Implicit

Identity of a game

Specificity of rules

Rules of digital games

Case studies: Tic Tac Toe

Deck of cards case study

Last-minute revision

Memory hooks

Coverage checklist