Interdependent Scheduling Games

We propose a model of interdependent scheduling games in which each player controls a set of services that they schedule independently. A player is free to schedule his own services at any time; however, each of these services only begins to accrue reward for the player when all predecessor services, which may or may not be controlled by the same player, have been activated. This model, where players have interdependent services, is motivated by the problems faced in planning and coordinating large-scale infrastructures, e.g., restoring electricity and gas to residents after a natural disaster or providing medical care in a crisis when different agencies are responsible for the delivery of staff, equipment, and medicine. We undertake a game-theoretic analysis of this setting and in particular consider the issues of welfare maximization, computing best responses, Nash dynamics, and existence and computation of Nash equilibria.Comment: Accepted to IJCAI 201

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201

Non-clairvoyant Scheduling Games

In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their cost and therefore their behaviors do not necessarily lead the game to an equilibrium. Even in the case there is an equilibrium, its makespan might be much larger than the social optimum, and this inefficiency is measured by the price of anarchy -- the worst ratio between the makespan of an equilibrium and the optimum. Coordination mechanisms aim to reduce the price of anarchy by designing scheduling policies that specify how jobs assigned to a same machine are to be scheduled. Typically these policies define the schedule according to the processing times as announced by the jobs. One could wonder if there are policies that do not require this knowledge, and still provide a good price of anarchy. This would make the processing times be private information and avoid the problem of truthfulness. In this paper we study these so-called non-clairvoyant policies. In particular, we study the RANDOM policy that schedules the jobs in a random order without preemption, and the EQUI policy that schedules the jobs in parallel using time-multiplexing, assigning each job an equal fraction of CPU time

Truthful algorithms for scheduling selfish tasks on parallel machines

AbstractWe consider the problem of designing truthful mechanisms for scheduling selfish tasks (or agents)—whose objective is the minimization of their completion times—on parallel identical machines in order to minimize the makespan. A truthful mechanism can be easily obtained in this context (if we, of course, assume that the tasks cannot shrink their lengths) by scheduling the tasks following the increasing order of their lengths. The quality of a mechanism is measured by its approximation factor (price of anarchy, in a distributed system) w.r.t. the social optimum. The previous mechanism, known as SPT, produces a (2-1/m)-approximate schedule, where m is the number of machines. The central question in this paper is the following: “Are there other truthful mechanisms with better approximation guarantee (price of anarchy) for the considered scheduling problem?” This question has been raised by Christodoulou et al. [Coordination mechanisms, in: Proc. of ICALP 2004, Lecture Notes in Computer Science, Vol. 3142, 345–357.] in the context of coordination mechanisms, but it is also relevant in centrally controlled systems. We present (randomized) truthful mechanisms for both the centralized and the distributed settings that improve the (expected) approximation guarantee (price of anarchy) of the SPT mechanism. Our centralized mechanism holds for any number of machines and arbitrary task lengths, while the coordination mechanism holds only for two machines and task lengths that are powers of a certain constant

Randomized truthful algorithms for scheduling selfish tasks on parallel machines

International audienceWe study the problem of designing truthful algorithms for scheduling a set of tasks, each one owned by a selfish agent, to a set of parallel (identical or unrelated) machines in order to minimize the makespan. We consider the following process: at first the agents declare the length of their tasks, then given these bids, the protocol schedules the tasks on the machines. The aim of the protocol is to minimize the makespan, i.e. the maximum completion time of the tasks, while the objective of each agent is to minimize the completion time of its task and thus an agent may lie if by doing so, his task may finish earlier. In this paper, we show the existence of randomized truthful (non-polynomial-time) algorithms with an expected approximation ratio equal to 3/2 for different scheduling settings (identical machines with and without release dates and unrelated machines) and models of execution (strong or weak). Our result improves the best previously known result Angel et al. (2006) [1] for the problem with identical machines (P∥Cmax) in the strong model of execution and reaches, asymptotically, the lower bound of Christodoulou et al. (2007) [5]. In addition, this result can be transformed to a polynomial-time truthful randomized algorithm with an expected approximation ratio 3/2+ϵ (resp. ) for PmCmax (resp. PCmax)

Randomized truthful algorithms for scheduling selfish tasks on parallel machines

International audienceWe study the problem of designing truthful algorithms for scheduling a set of tasks, each one owned by a selfish agent, to a set of parallel (identical or unrelated) machines in order to minimize the makespan. We consider the following process: at first the agents declare the length of their tasks, then given these bids the protocol schedules the tasks on the machines. The aim of the protocol is to minimize the makespan, i.e. the maximal completion time of the tasks, while the objective of each agent is to minimize the completion time of its task and thus an agent may lie if by doing so, his task may finish earlier. In this paper, we show the existence of randomized truthful (non-polynomial-time) algorithms with expected approximation ratio equal to 3/2 for different scheduling settings (identical machines with and without release dates and unrelated machines) and models of execution (strong or weak). Our result improves the best previously known result [1] for the problem with identical machines (P∣∣Cmax) in the strong model of execution and reaches, asymptotically, the lower bound of [5]. In addition, this result can be transformed to a polynomial-time truthful randomized algorithm with expected approximation ratio 3/2 + epsilon (resp. 11/6 − 1/3m) for Pm∣∣Cmax (resp. P∣∣Cmax)

Value creation in production: Reconsideration from interdisciplinary approaches

This paper presents reconsideration of value creation in production from various aspects of value viewpoints in several disciplines such as production engineering, social sciences, and human sciences. The focal point of investigations is value co-creation by the provision of products and services in and for society. In the past, some methods of social sciences and others proved to be useful in making production more efficient. At present, such methods must help to realise value creation. In fact, production must become more effective in response to human needs in social, economic, and environmental dimensions. Along with the theoretical apparatus, this paper presents some case studies indicating the importance of value creation in production, followed by future perspectives of value co-creation in production