Game Theory and its Myriad Applications

 

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I'm just sharing one my interests and the subject I enjoyed the most during my studies back in 2010-11.

 Game Theory and its Myriad Applications

A brief background on Game theory at Suny Stonybrook and the game theory summer festivals held there every year by nobel laurets. Game theory is a subject which has a lot of mathematics. A basic introduction to Game theory was made with a brief description of  the history of game theory. It started officially in the 1950s with Von Neumann and Morgenstern.

Game theory can be classified into two groups, co-operative and non-co-operative where non-co-operative is self-enforcing agreement. Game Theory is used in real life situations as well. Why social phenomena’s happen? The use of zero sum game like chess is a finite game and is a proof of the Zermelo’s theorem (1937).

Why do gas stations locate close to each other? Gas stations are highly clustered as competing firms prefer to stay close. It’s a rational decision for the gas stations, even if it’s not the optimal choice for consumers Is price matching good for consumers? Design an auction to maximize revenue- Revenue equivalence theorem shows that different auctions produce the same revenue. Winners curse is an experiment where a glass jar full of coins is auctioned off to students in a class. Using a first price auction where a winner is the highest bid and he pays what he bids.It was found that average bid was lower than the value of the jar AND the winner paid more than value of the jar.

Computer Science applications: biggest application is in mechanism  design to elicit preferences of various bidders. Google user auctions designed by game theorists to sell search advertising.To measure the “efficiency” Vickrey introduced second price auction which ensures that bidders have incentives to reveal their true value. References for sponsored ad auctions. Nash Equilibria is used to design rules in such a way that people report truthfully and maximize revenue.

Political Science Applications: Why do people vote? There are two things in the game: free riding and co-ordination. Shows paradox of voting. AAP: A case of strategic voting gone astray? 15 years ago the Aam Admi Party (AAP) of India was nowhere(uncertainty). Now it is one of the largest party in the Delhi Legislative Assembly after cutting sizably into the vote bank of Congress and BJP.

Swing Voter’s curse: If some voters are informed about politics and others are not then people may abstain when they are uninformed.

Conflict, war and Game theory: it seems irrational for inefficiency of wars. Bueno de Mesqita a political scientist has developed models. Owen another game theorist uses intelligence data to figure out terrorist locations. Ponsati developed software that would allow negotiations between parties to become more efficient.

Labour markets: employers do not know the ability levels of potential employees, higher ability students and lower ability students observable signal to hire.

Co-operative Game Theory: Market Design: started with algorithms to match with various set of whatever. Matching games has no incentive to break. Example to matching games is the Gale-Shapley algorithm used to ensure matches. Matching of interns to hospitals based on their specialisations. Most successful application of matching algorithms is kidney donation but problem is that many related donors do not have same blood type.

Conclusion: A lot of experimental work is going on now which are lab based and field experiments to check if assumptions of rational man hold up in reality. An example: ultimatum game. Field experiments chess players, tennis.