Magnesia-Based Cements: A Journey of 150 Years, and Cements for the Future?

This review examines the detailed chemical insights that have been generated through 150 years of work worldwide on magnesium-based inorganic cements, with a focus on both scientific and patent literature. Magnesium carbonate, phosphate, silicate-hydrate, and oxysalt (both chloride and sulfate) cements are all assessed. Many such cements are ideally suited to specialist applications in precast construction, road repair, and other fields including nuclear waste immobilization. The majority of MgO-based cements are more costly to produce than Portland cement because of the relatively high cost of reactive sources of MgO and do not have a sufficiently high internal pH to passivate mild steel reinforcing bars. This precludes MgO-based cements from providing a large-scale replacement for Portland cement in the production of steel-reinforced concretes for civil engineering applications, despite the potential for CO2 emissions reductions offered by some such systems. Nonetheless, in uses that do not require steel reinforcement, and in locations where the MgO can be sourced at a competitive price, a detailed understanding of these systems enables their specification, design, and selection as advanced engineering materials with a strongly defined chemical basis

Profit Sharing with Thresholds and Non-monotone Player Utilities

We study profit sharing games in which players select projects to participate in and share the reward resulting from that project equally. Unlike most existing work, in which it is assumed that the player utility is monotone in the number of participants working on their project, we consider non-monotone player utilities. Such utilities could result, for example, from “threshold” or “phase transition ” effects, when the total benefit from a project improves slowly until the number of participants reaches some critical mass, then improves rapidly, and then slows again due to diminishing returns. Non-monotone player utilities result in a lot of instability: strong Nash equilibrium may no longer exist, and the quality of Nash equilibria may be far away from the centralized optimum. We show, however, that by adding additional requirements such as players needing permission to leave a project from the players currently on this project, or instead players needing permission to a join a project from players on that project, we ensure that strong Nash equilibrium always exists. Moreover, just the addition of permission to leave already guarantees the existence of strong Nash equilibrium within a factor of 2 of the social optimum. In this paper, we provide results on the existence and quality of several different coalitional solution concepts, focusing especially on permission to leave and join projects, and show that such requirements result in the existence of good stable solutions even for the case when player utilities are non-monotone.

Approximating Optimal Social Choice under Metric Preferences

We examine the quality of social choice mechanisms using a utilitarian view, in which all of the agents have costs for each of the possible alternatives. While these underlying costs determine what the optimal alternative is, they may be unknown to the social choice mechanism; instead the mechanism must decide on a good alternative based only on the ordinal preferences of the agents which are induced by the underlying costs. Due to its limited information, such a social choice mechanism cannot simply select the alternative that minimizes the total social cost (or minimizes some other objective function). Thus, we seek to bound the distortion: the worst-case ratio between the social cost of the alternative selected and the optimal alternative. Distortion measures how good a mechanism is at approximating the alternative with minimum social cost, while using only ordinal preference information. The underlying costs can be arbitrary, implicit, and unknown; our only assumption is that the agent costs form a metric space, which is a natural assumption in many settings. We quantify the distortion of many well-known social choice mechanisms. We show that for both total social cost and median agent cost, many positional scoring rules have large distortion, while on the other hand Copeland and similar mechanisms perform optimally or near-optimally, always obtaining a distortion of at most 5. We also give lower bounds on the distortion that could be obtained by any deterministic social choice mechanism, and extend our results on median agent cost to more general objective functions

Assignment Games with Conflicts: Robust Price of Anarchy and Convergence Results via Semi-Smoothness

We study assignment games in which jobs select machines, and in which certain pairs of jobs may conflict, which is to say they may incur an additional cost when they are both assigned to the same machine, beyond that associated with the increase in load. Questions regarding such interactions apply beyond allocating jobs to machines: when people in a social network choose to align themselves with a group or party, they typically do so based upon not only the inherent quality of that group, but also who amongst their friends (or enemies) chooses that group as well. We show how semi-smoothness, a recently introduced generalization of smoothness, is necessary to find tight bounds on the robust price of anarchy, and thus on the quality of correlated and Nash equilibria, for several natural job-assignment games with interacting jobs. For most cases, our bounds on the robust price of anarchy are either exactly 2 or approach 2. We also prove new convergence results implied by semi-smoothness for our games. Finally we consider coalitional deviations, and prove results about the existence and quality of strong equilibrium