Solving Algorithmic Game Theory : The Price Of Anarchy

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In algorithmic game theory, it is easy to find the Nash equilibrium if one can derive the default strategies of each player from the instructions/parameters of the algorithm. It is also not particularly hard to find the optimal solution to an algorithm either. In algorithmic mechanism design, it would be the goal of the algorithm designer to fashion the algorithm in such a way that causes the Nash equilibrium to be the same as the Pareto optimal (or at least close to optimal) result. This would mean that it would be impossible to make any player better off in the game without hurting another player at the same time (optimal), while it also being impossible for any one player to improve their situation by altering only their strategy (Nash equilibrium). It is the goal to make these two circumstances exist simultaneously.
Next I will discuss my favorite topic regarding algorithmic game theory; the price of anarchy. I have to admit that the reasons this topic is my favorite are rather ridiculous; the name sounds really cool, and I like that the concept is also used in economics. Anyhow, the price of anarchy is a concept that measures how the efficiency of a system is ruined by the participants’ self-centered actions. (Koutsoupias and Papadimitriou, 1999) Essentially, this is the result of an inefficient set of equilibrium outputs. If a system is not designed with the users’ motives in mind, the system is often ruined by participants who are strategically trying to benefit

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