Definition of “Game Theory”
- “… the study of mathematical models of conflict and cooperation between intelligent rational decison-makers.”()
- originated as sub-fields of microeconomics and applied mathematics
Definition of “Game”
- “In the language of game theory, a game refers to any social situation involving two or more individuals. The individuals involved in a game may be called the players.”()
- Assumption on players
- rational: A player is called as being rational, if he/she makes decisions consistently in pursuit of his own objectives(, which is maximization of his utility frequently).
- intelligent: A player is called as being intelligent, if he/she knows everything that we know about the game and he can make any inferences about the situation that we can make.
Applications of Game Theory
- Industrial organization (and their behaviors): analyzing cooperations(e.g. cartel) and competitions between firms
- Auction theory: in terms of auctioneer and auction participants. e.g. Google auction, Yahoo auction, Soderby`s, ebay and so on.
- Contract theory: Employer vs. Employee / Consumer vs. Producer
- Evolutionary biology
- Political science: international relationship, political parties
- Public policy: Tragedy of commons, welfare policy design
List of Games
Why Do People Cooperate?
1. Kinship selection
- When the sacrificing behavior of an agent can contribute to the spreading of its genes more than the cost for itself, it would choose to do. (, )
2. Indirect reciprocity
- If each player decides whether to help someone or not based on the recipient’s image accumulated through previous altruistic behaviors, altruistic behavior becomes dominant. ()
3. Direct reciprocity
- Repeated PD game
- Tit-For-Tat: Select the previous strategy of your partner ()
- win-stay, lose-shift: If your previous strategy was dominant toward the one of your partner, keep it. Otherwise, change it. ()
4. Costly signaling()
- Group members have a personal characteristic, which we will call quality, that can either be high or low.
- Each individual has occasion to enter into a profitable alliance (e.g. mating or political coalition) with any one of the other group members.
5. Altruistic punishment ()
- If individuals can punish free riders in their group, although the punishment is costly and yields no material gain to the punisher, the cooperation flourishes.
6. Evolution of Social Network ()
– If cooperator pay the required cost, all his neighbors in a network would get benefit.
– In every turn, one randomly chosen player become dead.
– The tendency of new player for that position is decided depending on the sum of accumulated benefits of all neighbors.
7. Static Network ()
– If a social network is static, cooperative strategy becomes more stable.
– “We find that people cooperate at high stable levels, as long as the benefits created by cooperation are larger than the number of neighbors in the network.”
 Myerson, Roger B. Game theory. Harvard university press, 2013.
 Hamilton, William D. “The genetical evolution of social behaviour. II.” Journal of theoretical biology 7.1 (1964): 17-52.
 Nowak, Martin A., and Karl Sigmund. “Evolution of indirect reciprocity by image scoring.” Nature 393.6685 (1998): 573-577.
 Axelrod, Robert, and William D. Hamilton. “The evolution of cooperation.” Science 211.4489 (1981): 1390-1396.
 Nowak, Martin, and Karl Sigmund. “A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner’s Dilemma game.” Nature 364.6432 (1993): 56-58.
 Gintis, Herbert, Eric Alden Smith, and Samuel Bowles. “Costly signaling and cooperation.” Journal of theoretical biology 213.1 (2001): 103-119.
 Fehr, Ernst, and Simon Gächter. “Altruistic punishment in humans.” Nature 415.6868 (2002): 137-140.
 Ohtsuki, Hisashi, et al. “A simple rule for the evolution of cooperation on graphs and social networks.” Nature 441.7092 (2006): 502-505.
 Rand, David G., et al. “Static network structure can stabilize human cooperation.” Proceedings of the National Academy of Sciences 111.48 (2014): 17093-17098.
- Class material for February 26, 2015
After TF-IDF scoring of 100 documents…
- All words in 100 docs are in the corpus.
- Separately, each word in each doc has its own TF-IDF score. That is, each doc is represented as the vector of TF-IDF scores of all words in the corpus.
- e.g.) It was awesome! -> [0, .2345, 0, 0, …, 1.23, 3.4] (if the corpus is ordered as [“you”, “it”, “sucks” , “cold”, …, “was”, “awesome”])
What is this TF-IDF for?
We’ve learned much about TF-IDF method; how to calculate TF score and IDF score, how the conceptual assumption in this method (Bag of Words) and so on. Then, what is this for? How can we use this for what?
- Having a seat with your group members.
- Discuss how to use this score generally or for your project. (10 min)
Is TF-IDF better than just counting hits?
One of the easiest way to find relevant documents about a specific query is finding the documents which contain the query words many times. In what situation, does TF-IDF work better than this?