Game Theory Resources and Texts

Game Theory Resources 

1) Game Theory and Strategy, Phillip Straffin, Part III, The Mathematical Association of America

http://online.kitp.ucsb.edu/online/multicell13/bhanot/pdf/Straffin_Game_Theory_and_Strategy.pdf

Summary

- 2-person games are the easiest to solve in game theory but most real life situations are modeled by -N > 2 person games, which are much more difficult

-There are still equilibria in n-person games but it is difficult to pick one over another as an assymetry exists

-things get further complicated if you allow communicate between players

-coalitions between players can affect the outcome

-a simplification to n-person games can be made if side-payments are allowed.

Motive: If you are interested in n-person games to simulate economic or population situations

Question: What would your strategy be in an n-person game? What conditions should an equilibria have for it to be considered a solution?

Difficulty: 86.9 Flesch-Kincaid Reading Ease

2) Game Theory Explained, Avinash Dixit, PBS

http://www.pbs.org/wgbh/amex/nash/sfeature/sf_dixit.html

Summary:

-introduces definition of Game Theory

-desribes that game theory can be applied to sports, business, economics, politics, law, diplomacy and war

-Game theory got its start with the work of John von Neumann in the 1920s, which culminated in his book with Oskar Morgenstern. 

-introduces Nash Equilibria

-if the relationship between players is repeated over a long period of time

Motive: If you want a brief introductory into the history of Game Theory

Question: In what ways can game theory model real life?

Difficulty: 54.4 Flesch-Kincaid Reading Ease

3) Good Math, Bad Math, Introducing Game Theory, Mark C. Chu-Carroll, 3/19/08

http://scienceblogs.com/goodmath/2008/03/19/introducting-game-theory/

Summary:

-introduces Prisoner's Dilemma

-Game theory is not just about "games" as we think of them

-how 2 players maximizing their individual position can be a poorer choice

-is used in protocol design, models of markets

Motive: Read it if you want a basic introduction using the example situation "Prisoner's Dilemma"

Question: What would your strategy be if you were playing Prisoner's Dilemma?

Difficulty: 68.2 Flesch-Kincaid Reading Ease

4) The Evolution of Cooperation, Robert Axelrod, Basic Books, 1984

Summary:

-discusses the Prisoner's Dilemma tournaments and their winner "Tit for Tat"

-a game theoretic "live and let live" situation in the trenches of WWI. Soldiers would not shoot to kill so in return the other army would not shoot to kill

-cooperate can get started, evolve, and prove stable in situations that would otherwise appear very bleak

-for cooperate to occur the constant scenarios must go on for an indefinite period of time, otherwise slippery slope effect would take over

-the foundation of cooperation is not trust but rather the durability of the relationship

-the evolution simulation for Prisoner's Dilemma showed the retaliation should be done sooner rather than later

-the above is true due to signaling. Like with a pet, the punishment needs to directly proceed the event otherwise the correlation between behavior and punishment will not be made

Motive: If you want a much more in depth look into Game Theory

Question: What are some otherwise chaotic situations that could result in Game Theoretic cooperation?

Difficulty: 4.1 Flesch-Kincaid Reading Ease

Digital Media

5) https://www.youtube.com/watch?v=ITr6z-Jt5KY

Game Theory; Part 7, PatrickJMT, 9/23/12

Summary:

-goes over formulas to solve 2x2 matrix player games

-often times the result will be a mixed strategy

-for a general nxn matrix we will have to convert it to linear programming problems

-some higher nxn matrix games can be reduced down to 2x2 matrices

Motive: If you want to learn exactly how to solve the most simple 2x2 matrix games

Question: How might these formulas be generalized to higher order matrices?

Difficulty
Everything on scale 1-10, easy to hard

Content specific language: 9 (very many math specific words)
Difficult words: 5
Sentence Length and Complexity: 6

6. https://www.youtube.com/watch?v=7DMPk97xhOo

Game Theory Part 2: Nash Equilibrium, Bill Blaine, 5/28/13

Summary

-introduces the Prisonner's Dilemma game and matrix

-defines Nash Equilibria: when both players would lose value by changing their play, thus they stay in the same spot, ie. Equilibria

-finds Nash equilibria for Prisonner's dilemma

-finds that both players will confess in this equilibria

Motive: If you want to learn about basic Nash Equilibria and the solution to Prisoner's Dillema

Question: Why do the final strategies result in lower values than possible?

Difficulty
Everything on scale 1-10, easy to hard

Content specific language: 6 (reachable for non-mathematicians)
Difficult words: 4
Sentence Length and Complexity: 4

Use of texts in total

These texts can be used congruently. You would start with the articles that briefly introduce you to Game Theory and its history. You would then look at the articles dealing with Prisoner's Dilemma. Finally, you would look at the text that takes you into greater detail.