We consider routing games where the performance of each user is dictated by the worst (bottleneck) element it employs. We are given a network, finitely many (selfish) users, each associated with a positive flow demand, and a load-dependent performance function for each network element. We first prove the existence of a Nash equilibrium, considering two routing scenarios, namely when a user can ...

Studies extending over three decades have concluded that the current orientation of the martian rotation pole is unstable. Specifically, the gravitational figure of the planet, after correction for a hydrostatic form, has been interpreted to indicate that the rotation pole should move easily between the present position and a site on the current equator, 90◦ from the location of the massive Tha...

The present study examined the effect of the geometric parameters of the Rockfill dams on the 2D static analysis of slope stability. In this regard, several numerical models analyzed for eight heights, three slopes of upstream and downstream, three vertical and skewed core thicknesses and four different impounding time stages namely, "End of Construction", "Full Reservoir", "Half Full Reservoir...

We give exponential lower bounds on the Price of Stability (PoS) of weighted congestiongames with polynomial cost functions. In particular, for any positive integer d we constructrather simple games with cost functions of degree at most d which have a PoS of at leastΩ(Φd), where Φd ∼ d/ ln d is the unique positive root of equation xd+1 = (x + 1).This asymptotically closes th...

We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a nonnegative weight per agent). Agents using the same facility share fairly its installation cost, but every agent pays individually a (weighted) connection cost to the chosen location. We study the Price of Stab...

We consider the price of stability for Nash and correlated equilibria of linear congestion games. The price of stability is the optimistic price of anarchy, the ratio of the cost of the best Nash or correlated equilibrium over the social optimum. We show that for the sum social cost, which corresponds to the average cost of the players, every linear congestion game has Nash and correlated price...

Mediators are third parties to whom the players in a game can delegate the task of choosing a strategy; a mediator forms a mediated equilibrium if delegating is a best response for all players. Mediated equilibria have more power to achieve outcomes with high social welfare than Nash or correlated equilibria, but less power than a fully centralized authority. Here we begin the study of the powe...

We revisit Roughgarden and Tardos’s price of anarchy in network routing, in a new model in which routing decisions are made by the edges as opposed to the flows. We propose two models: the latency model in which edges seek to minimize the average latency of the flow through them on the basis of knowledge of latency conditions in the whole network, and the pricing model in which edges advertise ...