advanced game theory guest lecture

GOALS, REASON, AND DANGEROUS

THINGSAn über-ludological approach to game analysis unabashedly rooted in economic game theory

Advanced Game Theory, Sep 24 2007

JONAS HEIDE [email protected]

“It helps […] to think of a game’s structure as akin to an economy, or

an ecosystem; a complex, interacting system that does not dictate

outcomesbut guides behavior through the

need to achieve a single goal: energy, in the case of ecosystems; money, in the case of economics;

victory, in thecase of a game.”

Costikyan, G. (2002). I Have No Words & I Must Design: Toward a Critical Vocabulary for Games. Paper presented at the

Computer Games and Digital Cultures Conference Proceedings, Tampere.

Game theory is…

“…the formal study of decision-making where several players must make choices that

potentially affect the interests of the other players.”

An analytical framework (and general form of notation)

A design tool

An embattled interdisciplinary current

A promise for the unification of the social sciences

The end of the world

AGENDA

BITS OF BACKGROUNDTHE LOGIC OF GAME THEORY

TOOLS AND CONCEPTS

VIDEO GAME APPLICATIONS

“For that which is common to the greatest number has the least care bestowed upon it. Every one thinks chiefly of his own, hardly at all of the common interest”

“If it was a matter of hunting a deer, everyone well realized that he must remainfaithful to his post; but if a hare happened to pass within reach of one of them, wecannot doubt that he would have gone off in pursuit of it without scruple..."

Jean-Jacques Rousseau

Neumann, J. v., & Morgenstern, O. (1944). Theory of Games and Economic Behaviour.

Strong position in economics, mathematics, evolutionary biology, and computer science. Less strong in anthropology, sociology, game studies.

AGENDA


TOOLS AND CONCEPTS


ECONOMICSA person will make those choices which are likely to maximize his or her satisfaction (utility)

A person does not care about other people’s utility

We don’t know people’s preferences a priori (and we should observe behaviour, rather than simply ask)

GAME THEORYIn many situations one’s best choice depends on the choices of others

Your best choice depends on your belief about the other players’ beliefs about your beliefs about…

Highlights information, perception, and strategy

NIGHT DRIVING

Bob Alice

Alice is driving down a poorly lit road and hears the sound of an oncoming driver. On which side should she drive? Crashing = 0 satisfaction pointsPassing safely = 5 satisfaction points

NIGHT DRIVING

AliceLeft Right

Bob

Left

Bob: 5 points

Alice: 5 points

Bob: 0 pointAlice: 0 points

Right

Bob: 0 points

Alice: 0 point

Bob: 5 pointsAlice: 5 points

Assumes that Bob and Alice have the same preferencesPayoffs represent ranking of outcomesGame theory models social situations as if they were games

AGENDA


TOOLS AND CONCEPTS


MODELLING GAMESStrategic form (choices are

made simultaneuously)

Extended form (can model a game over time, can include bluff etc.)

Current Odysseus: 0 pointsFuture Odysseus: 1 point

Current Odysseus remains free

Current Odysseus has himself tied to mast

Future Odysseus ignores sirens

Future Odysseus succumbs to song

Future Odysseus ignores sirens

Future Odysseus succumbs to song (blocked)

Current Odysseus: 1 pointsFuture Odysseus: 0 point

Current Odysseus: 1 pointFuture Odysseus: 0 points

Current Odysseus: 0 pointFuture Odysseus: 1 points

LET’S PLAYTwo playersEach player chooses either ”Nice” or ”Nasty”Points:

Nice/Nasty: Nice gets 0 points, Nasty gets 5 points

Nice/Nice: Both get 3 points

Nasty/Nasty: Both get 1 point

The most famous of all game theory “games”

The object of thousands of studies

Models a “social dilemma”; a situation where one is tempted to do something which would lead to disaster if everyone made the same choice

Alice

Cooperates Defects

Bob

Cooperates

Bob: 3 points

Alice: 3 points

Bob: 0 points

Alice: 5 points

Defects

Bob: 5 points

Alice: 0 points

Bob: 1 point

Alice: 1 point

PRISONER’S DILEMMA

CHICKEN GAMEAlice

Swerves Does not swerve

BobSwerves


Bob: 1 pointAlice: 3 points

Does not swerveBob: 3 pointsAlice: 1 point


First to swerve loses. If no-one swerves, both die.

SUM AND CONFLICTZero-sum games (constant-

sum games): The total outcome is zero (e.g. chess). One players gain is the other player’s loss. Two-player zero-sum games present no incentives for cooperation. With more players, temporary coalitions may form.

Non-zero-sum games: The total outcome is not fixed (e.g. the Prisoner’s Dilemma, tournament soccer). The player relationship depends on the specific outcomes.

INFORMATIONComplete information: All players know everything about the game structure

Perfect information: The full history of the game is known to all players.

The players…… are informed about every change of the

game state

… are not informed about every change of

the game state

… know everything about the game state before the

game starts

Complete and perfect informationE.g. Chess, Checkers,

Parcheesi, Croquet

Complete but imperfect information

(rare)

… do not know everything about the game state

before the game starts

Incomplete but perfect information

E.g. Battleship, Master Mind, Monopoly

Incomplete and imperfect information

E.g. Risk, Mafia, Mah-Jong, Poker

The four information types (traditional games)

STRATEGYA strategy is a complete plan of action for any possible game situation (could be written down in advance and executed by someone else)

Easy to specify in the Prisoner’s Dilemma but very difficult in chess

A strictly dominant strategy is one which yields the highest outcome (for a player) regardless of what the other players do

EQUILIBRIUMStrategic equilibrium refers to the “solution” of a game: A state which a game will tend towards

The Prisoner’s Dilemma has one (unique Nash) equilibrium (defect-defect)

No one player can unilaterally change his strategy for a better outcome: ”I can do no better, given that the other player keeps doing what he is doing.”

AGENDA


TOOLS AND CONCEPTS


“The stories in most video games serve the same purpose as calling the über-checker a ‘king.’ It adds interesting shading to the game but the game at its core is unchanged.” (Koster, 2005: p85)

“…the dimensions of Lara Croft’s body… are irrelevant to me as a player, because a different-looking body would not make me play differently… When I play, I don’t even see her body, but see through it and past it.” (Aarseth, 2004: p48)

PLAYER RELATIONSHIP

Competitive games are constant sum games (the total payoff is fixed). In two-player competitive games, no incentives for cooperation exist at all, while for games with more players, such incentives may occur transitorily

Semi-cooperative games are non-zero sum games which reward team-work over mutual non-cooperation but provide temptations for individuals to act selfishly.

Cooperative games are non-zero sum games which reward players for coordinating their strategies; i.e. they reward team-work and provide no temptation for selfish play.

Cooperative game Alice

Right Left

BobRight

Bob: 1 pointAlice: 1 point


LeftBob: 0 pointsAlice: 0 points


Fire Truck (Atari, 1978)

Players’s utility functions are identical (they even have a collective score count).

From the perspective of either, hurting the other player means hurting oneself

Players will cooperate fully

Semi-cooperative game

Wizard

Cooperate Defect

Valkyrie

Cooperate

V: 2 pointsW: 2 point

V: 0 pointsW: 3 points

DefectV: 3 pointsW: 0 points

V: 1 pointsW: 1 points

Gauntlet (Atari, 1982)

Players have an incentive to cooperate but a temptation to defect

Cooperation will be unstable

Competitive game

Alice

Peaceful Aggressive

Bob

Peaceful

Bob: 0,5 point

Alice: 0,5 point


Aggressive


Bob: 0,5 points

Alice: 0,5 points

Spacewar (Russel et al, 1962)

Players cannot rely on each other to be peacefulThere will be no cooperation

PLAYER RELATIONSHIP

STRATEGIC DOMINANCE

“A well-designed game shouldn’t contain an option that is never worth using […] A dominated option is worthless. You wasted your time putting it in your game. A dominant option is worse. It means that all the other options are worthless.” (Rollings & Morris, 2004: p62-63)

STRATEGIC DOMINANCE

All video games have dominated strategies and that is unproblematic

In some games the challenge is choosing between alternatives.

In other games the challenge is discovering one’s options or implementing one’s choice.

The former should not have dominant strategies, but the latter should not be ignored.

From a game theory perspective a video game is an incentive structure inside which players maximize their outcome

Game designers assume that players accept the objective game goals

Game theory is an excellent tool for testing such assumptions

Binmore, K. (1991). Fun and Games: A Text on Game Theory. Lexington-Toronto: D.C. Heath.

Smith, J. H. (2006). The games economists play: implications of economic game theory for the study of computer games. Game Studies: The International Journal of Computer Game Research, 6(1).

Smith, J. H. (2006). Plans and Purposes: How Videogame Goals Shape Player Behaviour. Unpublished PhD dissertation, IT University of Copenhagen, Copenhagen.

Smith, J. H. (Forthcoming). Tragedies of the Ludic Commons. Game Studies.

Thanks for your attention

jonassmith.dk [email protected]

advanced game theory guest lecture

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