Scheduling Games with Machine-Dependent Priority Lists

We consider a scheduling game in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to which the jobs on the machine are processed. We characterize four classes of instances in which a pure Nash equilibrium (NE) is guaranteed to exist, and show, by means of an example, that none of these characterizations can be relaxed. We then bound the performance of Nash equilibria for each of these classes with respect to the makespan of the schedule and the sum of completion times. We also analyze the computational complexity of several problems arising in this model. For instance, we prove that it is NP-hard to decide whether a NE exists, and that even for instances with identical machines, for which a NE is guaranteed to exist, it is NP-hard to approximate the best NE within a factor of $2-\frac{1}{m}-\epsilon$ for all $\epsilon>0$. In addition, we study a generalized model in which players' strategies are subsets of resources, each having its own priority list over the players. We show that in this general model, even unweighted symmetric games may not have a pure NE, and we bound the price of anarchy with respect to the total players' costs.Comment: 19 pages, 2 figure

Coalition formation and price of anarchy in Cournot oligopolies

Non-cooperative game theory purports that economic agents behave with little regard towards the negative externalities they impose on each other. Such behaviors generally lead to inefficient outcomes where the social welfare is bounded away from its optimal value. However, in practice, self-interested individuals explore the possibility of circumventing such negative externalities by forming coalitions. What sort of coalitions should we expect to arise? How do they affect the social welfare? We study these questions in the setting of Cournot markets, one of the most prevalent models of firm competition. Our model of coalition formation has two dynamic aspects. First, agents choose strategically how to update the current coalition partition. Furthermore, coalitions compete repeatedly between themselves trying to minimize their long-term regret. We prove tight bounds on the social welfare, which are significantly higher than that of the Nash equilibria of the original game. Furthermore, this improvement in performance is robust across different supply-demand curves and depends only on the size of the market

Data-Driven Models of Selfish Routing: Why Price of Anarchy Does Depend on Network Topology

We investigate traffic routing both from the perspective of real world data as well as theory. First, we reveal through data analytics a natural but previously uncaptured regularity of real world routing behavior. Agents only consider, in their strategy sets, paths whose free-flow costs (informally their lengths) are within a small multiplicative (1 + θ) constant of the optimal free-flow cost path connecting their source and destination where θ≥ 0. In the case of Singapore, θ= 1 is a good estimate of agents’ route (pre)selection mechanism. In contrast, in Pigou networks the ratio of the free-flow costs of the routes and thus θ is infinite, so although such worst case networks are mathematically simple they correspond to artificial routing scenarios with little resemblance to real world conditions, opening the possibility of proving much stronger Price of Anarchy guarantees by explicitly studying their dependency on θ. We provide an exhaustive analysis of this question by providing provably tight bounds on PoA(θ) for arbitrary classes of cost functions both in the case of general congestion/routing games as well as in the special case of path-disjoint networks. For example, in the case of the standard Bureau of Public Roads (BPR) cost model, ce(x) = aex4+ be and more generally quartic cost functions, the standard PoA bound for θ= ∞ is 2.1505 [21] and it is tight both for general networks as well as path-disjoint and even parallel-edge networks. In comparison, in the case of θ= 1, the PoA in the case of general networks is only 1.6994, whereas for path-disjoint/parallel-edge networks is even smaller (1.3652), showing that both the route geometries as captured by the parameter θ as well as the network topology have significant effects on PoA (Fig. 1)

A comparison of antibiotic susceptibility testing methods for cotrimoxazole with Burkholderia pseudomallei

Melioidosis is caused by the Gram-negative soil saprophyte, Burkholderia pseudomallei and is endemic in tropical and subtropical regions of southeast Asia and northern Australia. Cotrimoxazole has been traditionally used for the therapy of melioidosis despite results indicating resistance often produced in the disc diffusion test against B. pseudomallei . This inconsistency was addressed by comparing this method with the agar dilution, MicroScan and E-test methods. The results demonstrated that by disc diffusion, 41.3% of 80 B. pseudomallei clinical isolates tested were susceptible to cotrimoxazole, whereas the MicroScan, agar dilution and the E-test demonstrated 92.5, 90 and 97.5% of the isolates to be susceptible, respectively. These results indicate that an MIC based method is required to test the susceptibility of B. pseudomallei against cotrimoxazole.No Full Tex