Routing Games with Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived

A new model for coalition formation games

We present two broad categories of games, namely, group matching games and bottleneck routing games on grids. Borrowing ideas from coalition formation games, we introduce a new category of games which we call group matching games. We investigate how these games perform when agents are allowed to make selfish decisions that increase their individual payoffs versus when agents act towards the social benefit of the game as a whole. The Price of Anarchy (PoA) and Price of Stability (PoS) metrics are used to quantify these comparisons. We show that the PoA for a group matching game is at most kα and the PoS is at most k/α where k is the maximum size of a group and α is a switching cost. Furthermore we show that the PoA and PoS of the games do not change significantly even if we increase γ, the number of groups that an agent is allowed to join. We also consider routing games on grid network topologies. The social cost is the worst congestion in any of the network edges (bottleneck congestion). Each player\u27s objective is to find a path that minimizes the bottleneck congestion in its path. We show that the price of anarchy in bottleneck games in grids is proportional to the number of bends β that the paths are allowed to take in the grids\u27 space. We present games where the PoA is O(β). We also give a respective lower bound of Ω(β) which shows that our upper bound is within only a poly-log factor from the best achievable price of anarchy. A significant impact of our analysis is that there exist bottleneck routing games with small number of bends which give a poly-log approximation to the optimal coordinated solution that may use an arbitrary number of bends. To our knowledge, this is the first tight analysis of bottleneck games on grids

Search for a moving target in a competitive environment

We consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.Comment: 14 pages, 0 figure

Load Balancing for Dynamic Clients, Game Theory Approach

We address the problem of load balancing which is considered as a technique to spread work between two or more computers in order to get optimal response time and resource utilization between servers by using Nash equilibrium which is the central concern of game theory. We use a normal form table to express the payoff for every client, every client has estimate time for execution and every server has speed, from these facts, we innovate a dynamic payoff matrix to evaluate a Nash equilibrium point and then determine which server can serve an appropriate client to achieve best load balancing which is called "server matching" (Each client is matched to exactly one server, but a server can be matched to multiple clients or none.). We use Netlogo simulation to implement this matching, besides a useful game theory oolset called GAMBIT (Gambit toolset homepage, 2005) to solve the payoff matrix and compute Nash equilibrium point. This paper was done between the years 2007 – 2009, and to know what was done in this paper we can argue that we contribute in accomplishing the load balancing between servers, using new technique depends on game theory perspective, for that reason we can answer the question why this thesis was done, because it is very vital in achieving this goal. We use in our thesis a simulation methodology to prove the results that we have obtained from the simulation program which is a Netlogo V4.0.2, and we compare the results with traditionally techniques in load balancing. Finally, the results show that we improve the performance for the whole system by 4% in achieving load balancing and overweight the possibilities of using this technique in real system around the world

Metastability of the Logit Dynamics for Asymptotically Well-Behaved Potential Games

Convergence rate and stability of a solution concept are classically measured in terms of “even- tually” and “forever”, respectively. In the wake of recent computational criticisms to this approach, we study whether these time frames can be updated to have states computed “quickly” and stable for “long enough”. Logit dynamics allows irrationality in players’ behavior, and may take time exponential in the number of players n to converge to a stable state (i.e., a certain distribution over pure strategy pro- files). We prove that every potential game, for which the behavior of the logit dynamics is not chaotic as n increases, admits distributions stable for a super-polynomial number of steps in n no matter the players’ irrationality, and the starting profile of the dynamics. The convergence rate to these metastable distributions is polynomial in n when the players are not too rational. Our proofs build upon the new concept of partitioned Markov chains, that might be of indepen- dent interest, and a number of involved technical contributions

10211 Abstracts Collection -- Flexible Network Design

From Monday 24.05.2010---Friday 28.05.2010, the Dagstuhl Seminar 10211 ``Flexible Network Design \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Complexity Theory, Game Theory, and Economics: The Barbados Lectures

This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v