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Game Design Homework Help

Game theory is a multi-disciplinary approach to the study of human behavior, used in such fields as mathematics, economics, and the social sciences. By "games" we actually mean human interactions governed by opposing strategies of the people involved.

As an example, in a patent system, the first research lab to invent a device gets the patent. Game theorists will apply the principles of game theory to find out how many research labs need to be involved to establish a Nash equilibrium, and compare that to the most efficient number of labs. Everything else follows from there.

A good course in non-cooperative game theory will most likely deal with these areas:

  • Games in strategic form and Nash equilibrium
  • Iterated strict dominance, rationalizability, and correlated equilibrium
  • Extensive-form games
  • Applications of multi-stage games with observed actions
  • Repeated games
  • Bayesian games and Bayesian equilibrium
  • Bayesian games and mechanical design
  • Equilibrium refinements
  • Reputation effects
  • Sequential bargaining with incomplete information
  • Payoff-relevant strategies and Markov equilibrium
  • Common knowledge and games

The International Journal of Game Theory is a good place to stay up to date in this field, and game theory tutorials are not hard to find.


A Brief History of Game Theory

The work of Von Neumann and Morgenstern (1944) marked an official start of game theory. Then came the second milestone contribution of John Nash (1951), which basically becomes chapter 1 of any modern game theory textbook. In the 1950s, in the intense atmosphere of war, there were many brilliant breakthroughs in fundamental fields such as computer science, mathematics and physics that set the foundation and landmarks for today's standard. Some said it was a time when “giants roamed the Earth”.

Game theory considers interaction among individuals in a narrow context. A context is narrow when the action of one player can have influence over the course of the whole game, hence each player has to take into account the reasoning of the other in order to make their action. There are two parallel lines in game theory: cooperative game theory and non-cooperative game theory. The cooperative strand studies coalition and contract formation from a normative point of view. It answers questions such as: What should be the society we would like to enter? What kind of contract or coalition could we form? The non-cooperative approach (which becomes more prominent in modern game theory) starts from the individual's perspective. Starting from building blocks of decision theory such as preference and utility function, it investigates positive questions such as: What would really happen after we have all agreed to an agreement? Would we still comply with it? The rationale is that we would comply to an agreement if and only if it aligns with our own interest. In this non-cooperative realm, a Nash equilibrium is defined as a profile of players' actions that maximize the utility of everyone given their correct expectation on everyone else's behavior. There are two parts of this definition. First, the player maximizes his own expected utility based on some belief (or prediction) over the other's behavior. Second, that expectation turns out to be correct. In this way, a Nash equilibrium becomes a situation that is self-enforced (i.e. no one wants to deviate from her chosen action).

This is a broad concept because any self-fulfilling prophecy therefore can be a Nash equilibrium, making the number of Nash equilibria to be more than one. And some people may suggest that some Nash equilibria seem to be better (more rational or more equitable) than others; hence there have been many attempts to refine the Nash equilibrium concept which results in a vast amount of literature on refinements in the 1980s. Even now the problem of equilibrium selection remains open for active contribution. Game theory has had extensive applications in the study of cooperation and competition in society. Different situations can be captured in different hypothetical situation such as the Prisoner's Dilemma for the cooperative decision, the bargaining game for negotiating decision, and the trust game for investment decision. Further information on classical game theory can be found at Standford.edu.


Von Neumann, J.; Morgenstern, O. 1944. Princeton University Press. Theory of games and economic behavior. Princeton, NJ, US.

Nash, Jr. J. F., 1951. Noncooperative games. Annals Math., 54, 289-95.




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Most of the students kept pecking at their laptops. A few took notes the old-fashioned way.

Three decades after bursting into pool halls and living rooms, video games are taking a place in academia. A handful of relatively obscure vocational schools have long taught basic game programming. But in the last few years a small but growing cadre of well-known universities, from the University of Southern California to the University of Central Florida, have started formal programs in game design and the academic study of video games as a slice of contemporary culture.

Traditionalists in both education and the video game industry pooh-pooh the trend, calling it a bald bid by colleges to cash in on a fad. But others believe that video games -- which already rival movie tickets in sales -- are poised to become one of the dominant media of the new century.

Certainly, the burgeoning game industry is famished for new talent. And now, universities are stocked with both students and young faculty members who grew up with joystick in hand. And some educators say that studying games will soon seem no less fanciful than going to film school or examining the cultural impact of television.

According to the International Game Developers Association, fewer than a dozen North American universities offered game-related programs five years ago. Now, that figure is more than 100, with dozens more overseas. At Carnegie Mellon University, a drama professor and a computer science professor have created an entertainment technology program that now enrolls 90 students and will soon open branches in Australia and South Korea.

At the Georgia Institute of Technology, which started new undergraduate and Ph.D. programs in interactive media last year, the director of graduate studies at the university's liberal arts school likens the multiple outcomes possible in video games to the magical realism of writers like Borges.

"The skills and methods of video games are becoming a part of our life and culture in so many ways that it is impossible to ignore," said Bob Kerrey, the former Nebraska senator who is now president of the New School, which includes Parsons.

Parsons has offered game courses to graduate students for five years and this fall began an undergraduate program in game design.

"But if you just look at the surface of people playing games, you are missing the point, which is that games are all about managing and manipulating information," Mr. Kerrey said. "A lot of students that come out of this program may not go to work for Electronic Arts. They may go to Wall Street. Because to me, there is no significant difference -- except for clothing preference -- between people who are making games and people who are manipulating huge database systems to try to figure out where the markets are headed. It's largely the same skill set, the critical thinking. Games are becoming a major part of our lives, and there is actually good news in that."

It is certainly good news to students like Johnny Trinh, 18, a Parsons sophomore from Queens.

"When I came here, I was really surprised that they had so much in-depth set aside for people who want to go into gaming culture," Mr. Trinh said last month during a break in his multimedia programming class as, multitasking, he skimmed the Web message boards for his online gaming team. "When you talk to your parents, they want you to be a doctor or a lawyer, but they are starting to understand that you can have a real job making games, and among the students it is definitely becoming more popular."

Electronic Arts, the No. 1 game maker, based in Redwood City, Calif., has been a leader in encouraging universities to develop game programs. Last year, the company, which is known for franchises including Madden football, contributed millions of dollars to help underwrite a new three-year master of fine arts program in interactive entertainment at U.S.C.

"For 20 years, students came out of school and they had to kind of unlearn what they had learned in computer science, and the stuff they had done in art wasn't appropriate, and we had to do a lot of training internally," said Bing Gordon, the company's chief creative officer. "The big idea now is that in the last three or four years, the students are starting to come out of school immediately able to contribute to real projects, which is what we need.

"Just imagine that a movie studio showed up at a cinema school and said, 'You know, we need three times as many directors and screenwriters as we are able to get now.' That's where we are. In all of traditional media there is a glut of people who want jobs, and that makes for some dog-eat-dog competition. But in our business there still is not as much talent as there is opportunity."

Jason Della Rocca, executive director of the game developers' association, said that no firm figures were available for overall employment in the industry.

But at bellwether Electronic Arts, employment has almost doubled since 2000, to roughly 6,450. Over the same period, the number of employees in Electronic Arts's creative operations -- the people who actually make games -- has almost tripled, to 4,300.

At universities that have embraced video games, the curriculum varies. Georgia Tech has taken a more humanities-centered approach that focuses on the study of games as cultural artifacts, much as a scholar who has no interest in making television programs might study "All in the Family" and "The Jeffersons" to try to parse American race relations in the 1970's.

Institutions like Parsons and U.S.C. try to give students both the technical and academic backgrounds to become working game designers. That involves some traditional lectures, but often means assembling students into teams to make games, starting with pen and paper and gradually incorporating more sophisticated technologies.

"To create a video game project you need the art department and the computer science department and the design department and the literature or film department all contributing team members," Mr. Gordon said. "And then there needs to be a leadership or faculty that can evaluate the work from the individual contributors but also evaluate the whole project."

Most of the game programs are so new that track records hardly exist, but Mr. Gordon said that the master's-level program in entertainment technology at Carnegie Mellon had been the most successful in embracing a multidisciplinary approach and producing work-ready students. That program, which helped pioneer the field when it began in 1999, is led by the odd couple of Donald Marinelli, a drama professor, and Randy Pausch, a computer scientist.

"When students want to come in and complain that they can't work with people from other disciplines, we tell them to come in and tell us both about it," Mr. Pausch said.

Mr. Marinelli added, "When we first got the program started, we worried about if these hardcore geeks would be able to communicate with the artists. But now we find it common to see applications from people who have an undergraduate major in computer science and a minor in visual arts, or a major in music and a minor in computer science. The students have actually been doing this right brain-left brain crossover on their own."

Yet even some in the game industry express doubts about the merit of such programs.

Jack Emmert had already earned his master's degree in ancient Mediterranean history from the University of Chicago and was working on his Ph.D. in Greek and Latin at Ohio State University when he dropped out in 2000 to become creative director at Cryptic Studios, a game company based in Los Gatos, Calif., where he has helped design the successful City of Heroes and City of Villains online games.

"This whole idea of teaching game design is a fabrication," Mr. Emmert said. "I'm a serious academic, and what is the actual skill that they're teaching? If you're not teaching a quantifiable skill, then you are teaching an opinion. Making games is an art form. You need to understand the technical side, but I loathe any attempt to teach game design as an academic discipline."

It is a familiar refrain to Tracy Fullerton, a professor involved with many of the new video game programs at U.S.C. She said it reminded her of complaints from Hollywood old-timers in the late 1960's and early 70's when film schools first started producing directors and screenwriters who had spent more time in classrooms than fetching coffee on Hollywood lots.

"There are definitely some people in the game industry who wonder why academia is taking an interest in them after all this time," Ms. Fullerton said. "It reminds me that there was a moment when film studies really took off and the guys at the studios were like, 'Who are these Spielbergs and Lucases and Coppolas coming out of these film schools with these crazy ideas?' They'll come around."

Articles in this series are examining the professional training of artists across a range of disciplines. The previous article, on voice training for opera singers, with related audio, is at nytimes.com/arts.

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