A Review of The Price of Malice and the Price of Anarchy

I will review two concepts in this project. These two concept are: the price of anarchy and the price of malice. The price of anarchy is the ratio between, the worst Nash equilibrium possible in a game, and the optimal solution achieved when all agents collaborate. So it is comparing the Nash equilibrium which gives the worst social welfare to the solution that gives the best social welfare. The price of malice is the ratio between, the social welfare achieved when there are malicious agents in the system, and the social welfare when all the agents act selfishly. I will explain these two concepts in relation to a virus inoculation game, with respect to two different conditions. The first condition is the oblivious model where the selfish agents are unaware of the existence of the Byzantine or malicious agents, and the second condition is where they are aware of their existence. I will show the results that have been achieved with respect to these concepts and then I will do a critique of the work done and discuss my opinions.