The document discusses using game theory to analyze video games. It provides background on game theory, explaining that it is the formal study of decision-making where players' choices affect each other. It outlines some key game theory concepts like the prisoner's dilemma, chicken game, and Nash equilibrium. It then discusses how different types of video games like cooperative, semi-cooperative, and competitive games can be modeled using concepts from game theory.

1. GOALS, REASON, AND DANGEROUS THINGS An über-ludological approach to game analysis unabashedly rooted in economic game theory Advanced Game Theory, Sep 24 2007 JONAS HEIDE SMITH [email_address]

2. “ 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 outcomes but guides behavior through the need to achieve a single goal: energy, in the case of ecosystems; money, in the case of economics; victory, in the case 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.

3. 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

5. AGENDA BITS OF BACKGROUND THE LOGIC OF GAME THEORY TOOLS AND CONCEPTS VIDEO GAME APPLICATIONS

6. 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 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 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 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 “ 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”

7. 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 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 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 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 remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple..." Jean-Jacques Rousseau

8. 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 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 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 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 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.

9. AGENDA BITS OF BACKGROUND THE LOGIC OF GAME THEORY TOOLS AND CONCEPTS VIDEO GAME APPLICATIONS

10. ECONOMICS A 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)

11. GAME THEORY In 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

12. 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 points Passing safely = 5 satisfaction points

13. NIGHT DRIVING Assumes that Bob and Alice have the same preferences Payoffs represent ranking of outcomes Game theory models social situations as if they were games Bob: 5 points Alice: 5 points Bob: 0 points Alice: 0 point Right Bob: 0 point Alice: 0 points Bob: 5 points Alice: 5 points Left Bob Right Left Alice

14. AGENDA BITS OF BACKGROUND THE LOGIC OF GAME THEORY TOOLS AND CONCEPTS VIDEO GAME APPLICATIONS

15. MODELLING GAMES Strategic form (choices are made simultaneuously) Extended form (can model a game over time, can include bluff etc.) Current Odysseus: 0 points Future 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 points Future Odysseus: 0 point Current Odysseus: 1 point Future Odysseus: 0 points Current Odysseus: 0 point Future Odysseus: 1 points

16. LET’S PLAY Two players Each 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

17. 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 PRISONER’S DILEMMA Bob: 1 point Alice: 1 point Bob: 5 points Alice: 0 points Defects Bob: 0 points Alice: 5 points Bob: 3 points Alice: 3 points Cooperates Bob Defects Cooperates Alice

18. CHICKEN GAME First to swerve loses. If no-one swerves, both die. Bob: 0 points Alice: 0 points Bob: 3 points Alice: 1 point Does not swerve Bob: 1 point Alice: 3 points Bob: 2 points Alice: 2 points Swerves Bob Does not swerve Swerves Alice

19. SUM AND CONFLICT Zero-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.

20. INFORMATION Complete information : All players know everything about the game structure Perfect information : The full history of the game is known to all players. The four information types (traditional games) Incomplete and imperfect information E.g. Risk, Mafia, Mah-Jong, Poker Incomplete but perfect information E.g. Battleship, Master Mind, Monopoly … do not know everything about the game state before the game starts Complete but imperfect information (rare) Complete and perfect information E.g. Chess, Checkers, Parcheesi, Croquet … know everything about the game state before the game starts … are not informed about every change of the game state … are informed about every change of the game state The players…

21. STRATEGY A 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

22. EQUILIBRIUM Strategic 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.”

23. AGENDA BITS OF BACKGROUND THE LOGIC OF GAME THEORY TOOLS AND CONCEPTS VIDEO GAME APPLICATIONS

24. “ 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)

25. “… 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)

26. 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.

27. Cooperative game 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 Bob: 1 points Alice: 1 points Bob: 0 points Alice: 0 points Left Bob: 0 points Alice: 0 points Bob: 1 point Alice: 1 point Right Bob Left Right Alice

28. Semi-cooperative game Gauntlet (Atari, 1982) Players have an incentive to cooperate but a temptation to defect Cooperation will be unstable V: 1 points W: 1 points V: 3 points W: 0 points Defect V: 0 points W: 3 points V: 2 points W: 2 point Cooperate Valkyrie Defect Cooperate Wizard

29. Competitive game Spacewar (Russel et al, 1962) Players cannot rely on each other to be peaceful There will be no cooperation Bob: 0,5 points Alice: 0,5 points Bob: 1 points Alice: 0 points Aggressive Bob: 0 points Alice: 1 points Bob: 0,5 point Alice: 0,5 point Peaceful Bob Aggressive Peaceful Alice

30. PLAYER RELATIONSHIP

31. 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)

32. STRATEGIC DOMINANCE

34. 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.

35. 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

36. 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.

37. Thanks for your attention jonassmith.dk [email_address]