Section: What about incomplete information? Up Main page

Amusements: Applications of game theory concepts

In each application, discuss what could happen in the corresponding situation, following your analysis of the situation as a game, and using different tools and solutions concepts developed in this introduction.
  
  
Amusement 1: War or Peace
Two countries and separately consider the state of political relations between them. They must choose between a state of war, or a state of peace . The order of their preferences are the following. If both choose war then each will have a gain of 2. If only one declares war then he gets 6 and his neighbor gets 0. If they choose to keep the peace, each gets a gain of 4.
  1. Give the set of players and the set of strategies for each player.
  2. Represent this game in normal form.
  3. Determine the equilibria of this game by mobilizing all the solution concepts that you know.
Amusement 2: A simple game
Consider the following game in normal form:
B
G D
A G
D
What are the Nash equilibria of this game?
Amusement 3: Paper – Scissors – Rock
This is a game between two children Sreyoun and Paul. The two children simultaneously choose an object among the following three objects: paper, scissors and rock. Depending on these choices, either a child wins the game, or there is no winner (the latter case appears if they choose the same object). Rock wins against Scissors, Scissors wins against Paper and Paper wins against Rock. Let be the gain of the child who wins, the gain of the one who loses and the gains in the event of a tie.
  1. Describe the set of players and each player’s strategy set.
  2. Write the simultaneous game in normal form.
  3. Are there strictly dominated strategies?
  4. Are there any Nash equilibria?
  5. Write this simultaneous game in extensive form. What is the nature of information?
  6. Same question if Paul cheats and observes Leyla’s choice before playing.
  7. Same question if Paul only observes Leyla’s choice if she chooses Rock.

References

[Cournot, 1838] Antoine-Augustin Cournot. 1838. Recherches sur les principes mathématiques de la théorie des richesses. Hachette.

[Harsanyi, 1967-68] J. Harsanyi. 1967-68. Games with Incomplete Information Played by Bayesian Players. Management science, 14(), 159—182,320—334,486—502.

[Kreps, 1982] D. Kreps, R. Wilson. 1982. Sequential Equilibria. Econometrica, 50(), 863-894.

[Myerson, 1991] Roger B. Myerson. 1991. Game Theory. Harvard University Press.

[Nash, 1950] John Nash. 1950. Non-cooperative Games. .

[Osborne, 1994] Martin J. Osborne, Ariel Rubinstein. 1994. A Course in Game Theory. MIT Press.

[Savage, 1954] L.J. Savage. 1954. The Foundations of Statistics. Wiley & Sons.

[Selten, 1975] R. Selten. 1975. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. International Journal of Game Theory, 4(), 25-55.

[Sun-Tzu, 1972] Sun-Tzu. 1972. L'Art de la Guerre. Champs Flammarion.

[Vega-Redondo, 2003] Fernando Vega-Redondo. 2003. Economics and the Theory of Games. Cambridge university press.

[Von Neuman, 1944] John Von Neuman, Oscar Morgenstern. 1944. Theory of Games and Economic Behavior. Princeton University Press, Second Ed.

[Yildizoglu, 2011] Murat Yildizoglu. 2011. Introduction à la théorie des jeux. Dunod.

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