[2015 Spring, Complex System Seminar] Game theory

Definition of “Game Theory”

  • “… the study of mathematical models of conflict and cooperation between intelligent rational decison-makers.”([1])
  • 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.”([1])
  • 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], [3])

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. ([4])

3. Direct reciprocity

  • Repeated PD game
  • Tit-For-Tat: Select the previous strategy of your partner ([5])
  • win-stay, lose-shift: If your previous strategy was dominant toward the one of your partner, keep it. Otherwise, change it. ([6])

4. Costly signaling([7])

  • 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 ([8])

  • 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 ([9])

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 ([10])

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.”

Reference

[1] Myerson, Roger B. Game theory. Harvard university press, 2013.
[2] http://en.wikipedia.org/wiki/Kin_selection
[3] Hamilton, William D. “The genetical evolution of social behaviour. II.” Journal of theoretical biology 7.1 (1964): 17-52.
[4] Nowak, Martin A., and Karl Sigmund. “Evolution of indirect reciprocity by image scoring.” Nature 393.6685 (1998): 573-577.
[5] Axelrod, Robert, and William D. Hamilton. “The evolution of cooperation.” Science 211.4489 (1981): 1390-1396.
[6] 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.
[7] Gintis, Herbert, Eric Alden Smith, and Samuel Bowles. “Costly signaling and cooperation.” Journal of theoretical biology 213.1 (2001): 103-119.
[8] Fehr, Ernst, and Simon Gächter. “Altruistic punishment in humans.” Nature 415.6868 (2002): 137-140.
[9] Ohtsuki, Hisashi, et al. “A simple rule for the evolution of cooperation on graphs and social networks.” Nature 441.7092 (2006): 502-505.
[10] Rand, David G., et al. “Static network structure can stabilize human cooperation.” Proceedings of the National Academy of Sciences 111.48 (2014): 17093-17098.

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[2015 Spring, Complex System Seminar] Game theory

Today’s Talk (About Game Theory)

Alexander J. Stewart

Today’s Talk (About Game Theory)