Algorithmic Game Theory

The current research in algorithms and complexity theory uses game theory as an important tool for modeling and reasoning about innovative computer science applications. The auction comprises two algorithms that include an allocation algorithm, which picks the highest bidder, and a payment algorithm, which uses the bids to charge payments, namely 0 for the losers and the second-highest bid for the winner. An allocation algorithm x is implementable if, for a judiciously chosen payment algorithm, coupling x with π yields a mechanism in which every participant is guaranteed to maximize its payoff by reporting its true preferences. An algorithm for a single-parameter problem is monotone if a greater bid generates a greater allocation. A mixed strategy is a probability distribution over the pure strategies of a player and in mixed-strategy Nash equilibrium (MNE), every player simultaneously chooses a mixed strategy maximizing its expected payoff, given those chosen by the others.