The Pareto Frontier of Inefficiency in Mechanism Design

We study the trade-off between the price of anarchy (PoA) and the price of stability (PoS) in mechanism design in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to these metrics and observe that two fundamental mechanisms, namely the first price (FP) and the second price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms [Formula: see text] that lie exactly on this frontier. In particular, these mechanisms range smoothly with respect to parameter [Formula: see text] across the frontier, between the first price ([Formula: see text]) and second price ([Formula: see text]) mechanisms. En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether nontruthful mechanisms can provide better makespan guarantees in the equilibrium compared with truthful ones. We answer this question in the negative by proving that the price of anarchy of all scheduling mechanisms is at least n, where n is the number of machines.

Additively Separable Hedonic Games with Social Context

In hedonic games, coalitions are created as a result of the strategic interaction of independent players. In particular, in additively separable hedonic games, every player has valuations for all other ones, and the utility for belonging to a coalition is given by the sum of the valuations for all other players belonging to it. So far, non-cooperative hedonic games have been considered in the literature only with respect to totally selfish players. Starting from the fundamental class of additively separable hedonic games, we define and study a new model in which, given a social graph, players also care about the happiness of their friends: we call this class of games social context additively separable hedonic games (SCASHGs). We focus on the fundamental stability notion of Nash equilibrium, and study the existence, convergence and performance of stable outcomes (with respect to the classical notions of price of anarchy and price of stability) in SCASHGs. In particular, we show that SCASHGs are potential games, and therefore Nash equilibria always exist and can be reached after a sequence of Nash moves of the players. Finally, we provide tight or asymptotically tight bounds on the price of anarchy and the price of stability of SCASHGs.

Two-Stage Facility Location Games with Strategic Clients and Facilities

We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to its spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting time for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perfect equilibria exist and we give almost tight constant bounds on the Price of Anarchy and the Price of Stability, which even hold for a broader class of games with arbitrary client behavior. Since facilities and clients influence each other, it is crucial for the facilities to anticipate the selfish clients’ behavior when selecting their location. For this, we provide an efficient algorithm that also implies an efficient check for equilibrium. Finally, we show that computing a socially optimal facility placement is NP-hard and that this result holds for all feasible client weight distributions.

Game-theoretic Analysis of Effort Allocation of Contributors to Public Projects

Public projects can succeed or fail for many reasons such as the feasibility of the original goal and coordination among contributors. One major reason for failure is that insufficient work leaves the project partially completed. For certain types of projects anything short of full completion is a failure (e.g., feature request on software projects in GitHub). Therefore, project success relies heavily on individuals allocating sufficient effort. When there are multiple public projects, each contributor needs to make decisions to best allocate his/her limited effort (e.g., time) to projects while considering the effort allocation decisions of other strategic contributors and his/her parameterized utilities based on values and costs for the projects. In this paper, we introduce a game-theoretic effort allocation model of contributors to public projects for modeling effort allocation of strategic contributors. We study the related Nash equilibrium (NE) computational problems and provide NP-hardness results for the existence of NE and polynomial-time algorithms for finding NE in restricted settings. Finally, we investigate the inefficiency of NE measured by the price of anarchy and price of stability.

Distance Polymatrix Coordination Games

In polymatrix coordination games, each player x is a node of a graph and must select an action in her strategy set. Nodes are playing separate bimatrix games with their neighbors in the graph. Namely, the utility of x is given by the preference she has for her action plus, for each neighbor y, a payoff which strictly depends on the mutual actions played by x and y. We propose the new class of distance polymatrix coordination games, properly generalizing polymatrix coordination games, in which the overall utility of player x further depends on the payoffs arising by mutual actions of players v,z that are the endpoints of edges at any distance h<d from x, for a fixed threshold value d≤n. In particular, the overall utility of player x is the sum of all the above payoffs, where each payoff is proportionally discounted by a factor depending on the distance h of the corresponding edge. Under the above framework, which is a natural generalization that is well-suited for capturing positive community interactions, we study the social inefficiency of equilibria resorting to standard measures of Price of Anarchy and Price of Stability. Namely, we provide suitable upper and lower bounds for the aforementioned quantities, both for bounded-degree and general graphs.

The Synergistic Effects of Alloying on the Performance and Stability of Co3Mo and Co7Mo6 for the Electrocatalytic Hydrogen Evolution Reaction

Metal alloys have become a ubiquitous choice as catalysts for electrochemical hydrogen evolution in alkaline media. However, scarce and expensive Pt remains the key electrocatalyst in acidic electrolytes, making the search for earth-abundant and cheaper alternatives important. Herein, we present a facile and efficient synthetic route towards polycrystalline Co3Mo and Co7Mo6 alloys. The single-phased nature of the alloys is confirmed by X-ray diffraction and electron microscopy. When electrochemically tested, they achieve competitively low overpotentials of 115 mV (Co3Mo) and 160 mV (Co7Mo6) at 10 mA cm−2 in 0.5 M H2SO4, and 120 mV (Co3Mo) and 160 mV (Co7Mo6) at 10 mA cm−2 in 1 M KOH. Both alloys outperform Co and Mo metals, which showed significantly higher overpotentials and lower current densities when tested under identical conditions, confirming the synergistic effect of the alloying. However, the low overpotential in Co3Mo comes at the price of stability. It rapidly becomes inactive when tested under applied potential bias. On the other hand, Co7Mo6 retains the current density over time without evidence of current decay. The findings demonstrate that even in free-standing form and without nanostructuring, polycrystalline bimetallic electrocatalysts could challenge the dominance of Pt in acidic media if ways for improving their stability were found.

Investigation of Co3Mo and Co6Mo7 Binary Alloys as Electrocatalysts for Hydrogen Evolution Reaction in Acidic Media

Metal alloys have become ubiquitous choice as catalysts for electrochemical hydrogen evolution in alkaline media. However, scarce and expensive Pt remains the key electrocatalyst in acidic electrolytes making the search for earth-abundant and cheaper alternatives appealing. Herein, we present a facile and efficient synthetic route towards polycrystalline Co₃Mo and Co₆Mo₇ metal alloys that achieve competitively low overpotentials of 115 mV and 160 mV at 10 mA cm^–2 in 0.5 M H₂SO₄. Both alloys outperform Co and Mo metals which showed significantly higher overpotentials and lower current densities when tested under identical conditions. However, the low overpotential in Co₃Mo comes at the price of stability. It rapidly becomes inactive when tested under applied potential bias. On the other hand, Co₇Mo₆ retains the current density over time without the evidence of current decay. The findings demonstrate that even in free-standing form and without nanostructuring polycrystalline bimetallic electrocatalysts could challenge the dominance of Pt in the acidic media if the ways for improving their stability were found.