Maximizing Social Welfare Subject to Network Externalities: A Unifying Submodular Optimization Approach

We consider the problem of allocating multiple indivisible items to a set of networked agents to maximize the social welfare subject to network externalities. Here, the social welfare is given by the sum of agents' utilities and externalities capture the effect that one user of an item has on the item's value to others. We first provide a general formulation that captures some of the existing models as a special case. We then show that the social welfare maximization problem benefits some nice diminishing or increasing marginal return properties. That allows us to devise polynomial-time approximation algorithms using the Lovasz extension and multilinear extension of the objective functions. Our principled approach recovers or improves some of the existing algorithms and provides a simple and unifying framework for maximizing social welfare subject to network externalities

Bottleneck congestion and distribution of work start times: The economics of staggered work hours revisited

Since the seminal work of Henderson (1981), a number of studies examined the effect of staggered work hours by analyzing models of work start time choice that consider the trade-off between negative congestion externalities and positive production externalities. However, these studies described traffic congestion using flow congestion models. This study develops a model of work start time choice with bottleneck congestion and discloses the intrinsic properties of the model. To this end, this study extends Henderson’s model to incorporate bottleneck congestion. By utilizing the properties of a potential game, we characterize equilibrium and optimal distributions of work start times. We also show that Pigouvian tax/subsidy policies generally yield multiple equilibria and that the first-best optimum must be a stable equilibrium under Pigouvian policies, whereas the second-best optimum in which policymakers cannot eliminate queuing congestion can be unstable

Efficient Equilibria in Polymatrix Coordination Games

We consider polymatrix coordination games with individual preferences where every player corresponds to a node in a graph who plays with each neighbor a separate bimatrix game with non-negative symmetric payoffs. In this paper, we study $\alpha$-approximate $k$-equilibria of these games, i.e., outcomes where no group of at most $k$ players can deviate such that each member increases his payoff by at least a factor $\alpha$. We prove that for $\alpha \ge 2$ these games have the finite coalitional improvement property (and thus $\alpha$-approximate $k$-equilibria exist), while for $\alpha < 2$ this property does not hold. Further, we derive an almost tight bound of $2\alpha(n-1)/(k-1)$ on the price of anarchy, where $n$ is the number of players; in particular, it scales from unbounded for pure Nash equilibria ($k = 1)$ to $2\alpha$ for strong equilibria ($k = n$). We also settle the complexity of several problems related to the verification and existence of these equilibria. Finally, we investigate natural means to reduce the inefficiency of Nash equilibria. Most promisingly, we show that by fixing the strategies of $k$ players the price of anarchy can be reduced to $n/k$ (and this bound is tight)

Regulating on-street parking

Consider the choices available to a shopper driving to a city and trying to park downtown. One option, typical to many cities, is to follow the signposts to an off-street parking facility, which is often privately operated. Another option is to search for an on-street spot. If this proves unsuccessful, it is always possible to return to the off-street facility. We formalise such a setting and examine optimal on-street parking policy in the presence of an off-street market. Not surprisingly, the amount of socially-wasteful searching behaviour is shown to depend on the prices of both the off- and on-street market. If the off-street market is run competitively, optimal on-street policy reduces to a simple and attractive rule: set the on-street price equal to the resource cost of off-street parking supply. Other pricing rules result in either excessive searching behaviour or excessive off-street investment costs. Time restrictions - a common alternative to on-street fees - are also shown to be inefficient. In practice, however, off-street markets are unlikely to be competitive. We examine the case of a single off-street supplier playing as a Stackelberg follower to the government regulated on-street market. Based on a numerical example (calibrated to London), optimal on-street policy is shown to either involve setting a relatively high on-street price, such that the monopolist is induced to undercut and gain the entire parking demand, or setting a relatively low price, while the monopolist maximises profit on the residual demand curve. Which strategy is optimal is shown to be parameter dependent.parking; transport pricing; publicly provided goods

Regulating on-street parking

Consider a shopper or tourist driving downtown and trying to park. Two strategies are usually available: either park at a private off-street facility or search for a cheaper on-street spot. We formalise such a setting and use the model to study optimal government regulation of the on-street parking market. It is shown that the optimal on-street fee equals the marginal cost of off-street supply at the optimal quantity. If the off-street market is supplied under constant returns to scale, this provides a particular simple operational rule: the price on street should match that off street. We also extend the model to consider maximum length of stay restrictions and non-competitive private supply. A numerical model, calibrated to central London, investigates the magnitude of an optimal fee.Parking, Regulating urban transport, Search.

Climate Uncertainty and the Necessity to Transform Global Energy Supply

This paper analyses the policy relevance of the dominant uncertainties in our current scientific understanding of the terrestrial climate system, and provides further evidence for the need to radically transform - this century - our global infrastructure of energy supply, given the global average temperature increase as a result of anthropogenic carbon dioxide emissions. We investigate the effect on required CO2 emission reduction efforts, both in terms of how much and when, of our uncertain knowledge today of the climate sensitivity to a doubling in them atmospheric CO2 concentration. Also the roles of carbon-free energy and energy savings, and their evolutions over time, are researched, as well as their dependence on some of our characteristic modelling features. We use a top-down model in which there are two competing energy sources, fossil and non-fossil. Technological change is represented endogenously through learning curves, and modest but non-zero demand exists for the relatively expensive carbon-free energy resource.Global warming, CO2 emissions, Climate sensitivity, Fossil to non-fossil transition, Carbon-free power, Energy savings

The complexity of transitions

No abstract

Cooperative dilemmas with binary actions and multiple players

The prisoners’ dilemma, the snowdrift game, and the stag hunt are simple two-player games that are often considered as prototypical examples of cooperative dilemmas across disciplines. However, surprisingly little consensus exists about the precise mathematical meaning of the words “cooperation” and “cooperative dilemma” for these and other binary-action games, in particular when considering interactions among more than two players. Here, we propose new definitions of these terms and explore their consequences on the equilibrium structure of cooperative dilemmas in relation to social optimality. We find that a large class of multi-player prisoners’ dilemmas and snowdrift games behave as their two-player counterparts, namely, they are characterized by a unique equilibrium where cooperation is always underprovided, regardless of the number of players. Multi-player stag hunts allow for the peculiarity of excessive cooperation at equilibrium, unless cooperation is such that it induces positive individual externalities. Our framework and results unify, simplify, and extend previous work on the structure and properties of binary-action multi-player cooperative dilemmas