We give an 5·nlog30 5 upper bund on the complexity of the communication game introduced by G. Gilmer, M. Koucký and M. Saks [3] to study the Sensitivity Conjecture [4], improving on their √ 999 1000 √ n bound. We also determine the exact complexity of the game up to n ≤ 9. 1 The O(n) upper bound The GKS communication game, defined by G. Gilmer, M. Koucký and M. Saks [3] is played by two coopera...

This paper defines a rate maximization power allocation game in a frequency selective Gaussian interference channel, af ter assuming a suboptimal but pragmatic multi-user coding scheme. We show that the Nash equilibrium always exists in this game. We consider a distributed power allocation scheme [l, Section IV.], and provide a sufficient condition for the convergence of the distributed algorit...

where B is a real matrix with m rows and n columns, x ranges over the set of row vectors with m components, all non-negative and adding up to one, y ranges over the corresponding set of «-component column vectors, and the pay-off, (x2?, y), indicates the inner product of the two vectors xB and y. One device which may simplify a game computation is that of "dominance" or "majorization" [vNM, p. ...

In this paper, we consider a novel $M$ -ary sequential hypothesis testing problem in which an adversary is present and perturbs the distributions of samples before decision maker observes them. This formulated as adversarial game play...

THOMAS, JAMES M. Automated Scaffolding of Task-Based Learning in Non-Linear Game Environments. (Under the direction of R. Michael Young.) This work described in this dissertation is an attempt to integrate intelligent tutoring capabilities into a framework that can be applied within any exploratory learning game. The goal is to provide dynamic adaptation to the learning needs of an individual s...

In this section, we will first prove that any 2-player zero-sum finite game has a Nash equilibrium of mixed strategies (a special case of Nash’s theorem), and a Nash equilibrium can be found through solving linear programs. We will further show how to prove lower bounds on randomized complexity of Las Vegas algorithms using this result. A 2-player game is a zero-sum game if the sum of the payof...

The infimal convolution of M-convex functions is M-convex. This is a fundamental fact in discrete convex analysis that is often useful in its application to mathematical economics and game theory. M-convexity and its variant called M-convexity are closely related to gross substitutability, and the infimal convolution operation corresponds to an aggregation. This note provides a succinct descrip...

Recall our goal from last class: we wanted to take a game that has nice properties when described as a game of complete information, and then augment it with an extremely weak “mediator”, such that in the new game, we can implement the equilibria of the original (complete information) game as simple ex-post equilibria, which do not require players to know anything about each other’s types. Some...

We present an O(mn2n logZ) deterministic algorithm for solving the mean payo game problem, m and n being respectively the number of arcs and vertices in the game graph and Z being the maximum weight (we assume that the weights are integer numbers). The theoretical basis for the algorithm is the potential theory for mean payo games. This theory allows to restate the problem in terms of solving s...