Algorithmic Game Theory

An introduction to algorithmic game theory: what changes when the input is not passive data but strategic agents who will misreport or deviate the moment it helps them, so correctness gives way to designing for incentives. A game is players, strategies, and payoffs; a dominant strategy is best no matter what others do, and the Prisoner's Dilemma shows that dominant-strategy play (mutual defection) can be worse for everyone than the cooperation they cannot reach. Nash equilibrium generalizes this to a no-regret stable profile that always exists in mixed strategies (Nash's theorem), though stability is not optimality. The algorithmic turn is mechanism design, reverse game theory: choosing the rules so that selfish play produces the outcome you want, as auctions, matching markets, and pricing schemes do.