We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sum-rate optimal point on the boundary of the multipleaccess channel capacity region is the unique Nash Equilibrium of the corresponding water-fil...

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games—in which the pure strategy space is (potentially uncountably) infinite—is far more challenging. Nonetheless, many real-world domains action spaces, e.g., where actions refer to an amount time, money, or other resource that naturally modeled as being rea...

We examine experimentally how humans behave when they, unbeknownst to them, play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects’ play was consistent with their Nash equilibrium strategy. But a larger percentage of subjects’ play was more consisten...

Finding Nash equilibrium in a two-player normal form game (2-Nash) is one of the most extensively studied problem within mathematical economics as well as theoretical computer science. Such a game can be represented by two payoff matrices A and B, one for each player. 2Nash is PPAD-complete in general, while in case of zero-sum games (B = −A) the problem reduces to LP and hence is in P. Extendi...

An n-tuple is defined for each n-person monotonic characteristic function game, This n-tuple is an imputation when the sum of the components of it is equal to v( N). On the boundary of the set of all monotonic games" we can obtain a condition for the n-tuple being an imputation. The n-tuple belongs to the core when it is an imputation. If the sum of the components of it exceeds v( N), the kerne...

In this paper we adopt general sum stochas tic games as a framework for multiagent re inforcement learning Our work extends pre vious work by Littman on zero sum stochas tic games to a broader framework We de sign a multiagent Q learning method under this framework and prove that it converges to a Nash equilibrium under speci ed condi tions This algorithm is useful for nding the optimal strateg...

Original scientific paper A zero-sum game approach for H∞ robust control of continuous-time singularly perturbed bilinear quadratic systems with an additive disturbance input is presented. By regarding the stochastic disturbance (or the uncertainty) as "the nature player", the H∞ robust control problem is transformed into a twoperson zero-sum dynamic game model. By utilizing the singular pertur...

This paper examines the convergence of payoffs and strategies in Erev and Roth’s model of reinforcement learning.When all players use this rule it eliminates iteratively dominated strategies and in two-person constant-sum games average payoffs converge to the value of the game. Strategies converge in constant-sum games with unique equilibria if they are pure or if they are mixed and the game is...

We consider a large community of individuals who mix strongly and meet in pairs to bet on a coin toss. We investigate the asset distribution of the players involved in this zero-sum repeated game. Our main result is that the asset distribution converges to the exponential distribution, irrespective of the size of the bet, as long as players can never go bankrupt. Analytical results suggests tha...

Open list proportional representation is an election mechanism used in many elections, including the 2012 Hong Kong Legislative Council Geographical Constituencies election. In this paper, we assume that there are just two parties in the election, and that the number of votes that a list would get is the sum of the numbers of votes that the candidates in the list would get if each of them would...