CMSC 858 F : Algorithmic Game Theory Spring 2014

The problem of finding Nash equilibria is one of the fundamental problems in Algorithmic Game Theory, and has made a nice connection between Game Theory and Computer Science [9]. While Nash [10] introduced the concept of Nash equilibrium and proved every game has a mixed Nash equilibrium, finding a Nash equilibrium in reasonable time seems to be essential. The Nash equilibrium can be used as a basic equilibrium concept, only if it is efficiently computable such that it can be used for predicting the outcome of a real-world game. This highlights the role of computer scientists in this area which aim to design efficient algorithms for finding Nash equilibria of various games (see, e.g., [1, 2, 3, 4, 5, 6, 7]). In this study, we followed this line of research and to understand the polynomial-time algorithms for finding Nash equilibria of a broad range of zero-sum games. In a dueling game, which was initiated by [8] (STOC 2011), two competitors try to design an algorithm for an optimization problem with an element of uncertainty, and the winner is the player who better solves the optimization problem.