GDC2013 - Strange Love: The Relationship Between Game Theory and Game Design

• This talk was given by Frank Lantz.
• Game theory is a mathematical study that applies to many fields including philosophy, military, economy, and strategy. Game designers don't use proper game theory much at all.
• Game theory is the mathematical analysis of situations where multiple parties are making choices. Take for example a costume party where everyone is trying to come up with an awesome unique costume. This decision will depend on other people's decisions and can be modeled mathematically.
• The key terms of game theory are players (the parties involved), strategies (the choices), and payoffs (the results). With all situations, you can make a payoff matrix.
• The origins of game theory come from John von Neumann, who was a great mathematician. He also liked to party and play Poker. He wrote a book called the "Theory of Parlour Games" which started game theory.
• Roulette is a game that can be calculated with possibilities; chess is a game of calculated decision trees. Poker, however, was completely different. Poker was about bluffing and bidding, about making choices based on opponent's choices.
• "Chess is not a game, it's a computational puzzle. Real games, like life, are about bluffing..."
• Game example #1 - Cutting the Cake
• In this game, one player cuts the cake and the other player gets first pick of the piece she'll take.
• For the second player, there is a dominated strategy, the choice that is obvious and best. She'll always pick the bigger piece.
• For the first player, the decision is minimax. He'll go for the choice with the minimal losses (cut the cake as evenly as possible).
• The process of looking through the opponent's eyes is the core of game theory.
• In a zero-sum game, all the choices add up to zero. One wins and the other loses.
• Game example #2 - Matching pennies
• ​In this game, two players choose a side on a penny respectively. If both pennies match, the first player takes the pennies. If both pennies are different, the second player wins and takes them.
• Often the best strategy here is to add some randomness to throw off the opponent.
• What if the game was non-zero sum? Consider "matching pennies with Bill Gates." The same rules apply as before, except if both pennies match on heads, Bill gives you a million dollars. The obvious choice for you is to play heads, but Bill will always play tails. There is a dominant strategy, but it's good to throw in the other choice to throw off your opponent. This is likewise in baseball, where throwing your best pitch will make you become predictable, so it's good to throw in a bad pitch every now and then.
• Game example #3 - Chicken
• In this game, both players drive cars towards a cliff. The first player to swerve is the loser. However, if neither players swerve, then the outcome is very negative for both, resulting in death. This is a non-zero sum game.
• Scientists have found that this payoff matrix applies to animal fights in nature.
• John Maynard Smith's theory of Hawks vs. Doves maps out this behavior. He looked at game theory in relationship to biology and found that animals follow an evolutionary stable strategy. If there are too many doves, then it pays off to be the hawk with the aggressive strength. If there are too many hawks, then they end up fighting each other all the time and it pays off to be a dove. Ultimately, the two species strike an evolutionary balance.
• In the game of Chicken, eliminating choices will force a decision for the other player. If for example, one player removed his steering wheel altogether, he can't swerve because he has no means to, which means the other player is forced to swerve. Sometimes, the irrational beats rationality.
• Game example #4 - Prisoner's Dilemna
• In this game, two criminals are apprehended and placed in different cells. They are asked to betray their partner (defect) or stay silent (cooperate). If both cooperate, they get one year in prison, but if they defect against each other, they'll both get 3 years in prison. If they choose different options, the defector will get off jail scotfree while the other will get 10 years in prison.
• This is a real dilemna because the decision is difficult. There is no dominant strategy.
• The best optimal decision is to defect. It yields the better deals and avoids the nasty 10 year sentence. If the two prisoners are smart game theorists, they will choose this strategy and get 3 year sentences. However, another pair of prisoners can come into this situation, and they're dumb and uninformed. They'll both choose to cooperate, resulting in a much better payoff. The "optimal" solution lead to suboptimal results, but the dumb solution lead to higher payoffs. What?
• The RAND cooperation was a group of military game theorists. Von Neumann and RAND both thought the optimal solution during the Cold War was to pre-emptively bomb Russia first. But it turns out that the irrational decision (not to bomb) saved the world.
• Game theory put us in the brink of nuclear war, but the paradox of irrationality also came from RAND. There's a chance that game theory and Poker, a game that was meant for degenerate gamblers, saved the world.
• Robert Axelrod asks the question, "How do we get to cooperative payoffs?" He created a computer program that simulated the iterated prisoner's dilemna and asked for open submissions for bots to face each other in this simultation. The most successful bot was Anatol Rapoport's Tit for Tot strategy, which always cooperated but will attack if attacked the turn before. This strategy continued to win in future decades even when everyone knew it was the strategy to beat. Tit for Tot is also discovered and observed in biology.
• William Press and Freeman Dyson later categorized Tit for Tot as a subset of zero-deterministic strategies.
• Game example #5 - Ultimatum game
• In this game, one player must divide $100 and offer the deal to another player. The other player can accept the deal or reject it, in which case neither player gets any money.
• Thomas Schelling wrote about game theory. It's not just about conflict and competition, but about coordination, competition, and negotiation.
• What are the applications of game theory to game design?

1. ​​Legacy. Game theory came from real world games like Poker. In addition, many historical game theorists have designed games. John Nash, who developed the Nash's equilibrium, designed a game about networks and relationships.
2. Formal Analysis. Game theory provides a great basis for game balance, yomi, and game economies.
3. Inspiration. Game theory decisions are simple, but not trivial. You can see examples of it in board games, reality game shows, and many social games. Frank Lantz's games (Parking Wars, Spore Islands, Power Plant, The Friend Game) are all also related to decisions players make in regards to each other.
4. Reconciliation. Recently, we've seen games like Journey, Proteus, Dear Esther, The Graveyard, and Heavy Rain. These are games that removes min-maxing and focus heavily on emotional experience.

• ​The key takeaway is that "the rational is not incompatible with the sublime." Explanations do not exhaust a topic. Knowing that a person is made up of atoms doesn't diminish the person in any way.
• Game theory is not just about rationality. Humanities and sciences have separated, but can we bring them both together without diminishing either of them?
• Math, strategy, and rules can co-exist with stories, emotions, and love. Game design is where math and beauty meet.
• ​It's okay if game theory has no practical use. We're not necessarily looking for utility, we're looking for truth.