Budget Balancedness and Optimal Income Taxation

We make two main contributions to the theory of optimal income taxation. First, assuming conditions sufficient for existence of a Pareto optimal income tax and public goods mechanism, we show that if agents’ preferences satisfy an extended notion of single crossing called capacity constrained single crossing, then there exists a Pareto optimal income tax and public goods mechanism that is budget balancing. Second, we show that, even without capacity constrained single crossing, existence of a budget balancing, Pareto optimal income tax and public goods mechanism is guaranteed if the set of agent types contains no atoms.Optimal Income Taxation, Public Goods, Budget Balancing, Single Crossing, Nonatomic Economy, Atomless Economy

Endogenous Rationing, Price Dispersion, and Collusion in Capacity Constrained Supergames.

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival’s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with successful collusion, it may be a requirement of successful collusion.Bertrand-Edgeworth ; Supergame ; Collusion ; Capacity

Modeling Electricity Markets as Two-Stage Capacity Constrained Price Competition Games under Uncertainty

The last decade has seen an increasing application of game theoretic tools in the analysis of electricity markets and the strategic behavior of market players. This paper focuses on the model examined by Fabra et al. (2008), where the market is described by a two-stage game with the firms choosing their capacity in the first stage and then competing in prices in the second stage. By allowing the firms to endogenously determine their capacity, through the capacity investment stage of the game, they can greatly affect competition in the subsequent pricing stage. Extending this model to the demand uncertainty case gives a very good candidate for modeling the strategic aspect of the investment decisions in an electricity market. After investigating the required assumptions for applying the model in electricity markets, we present some numerical examples of the model on the resulting equilibrium capacities, prices and profits of the firms. We then proceed with two results on the minimum value of price caps and the minimum required revenue from capacity mechanisms in order to induce adequate investments

Insurer-Provider Networks in the Medical Care Market

Managed care health insurers in the US restrict their enrollees' choice of hospitals to specific networks. This paper investigates the causes and welfare effects of the observed hospital networks. A simple profit maximization model explains roughly 63 per cent of the observed contracts between insurers and hospitals. I estimate a model that includes an additional effect: hospitals that do not need to contract with all insurance plans to secure demand (for example, providers that are capacity constrained under a limited or selective network) may demand high prices that not all insurers are willing to pay. Hospitals can merge to form "systems" which may also affect bargaining between hospitals and insurance plans. The analysis estimates the expected division of profits between insurance plans and different types of hospitals using data on insurers' choices of network. Hospitals in systems are found to capture markups of approximately 19 per cent of revenues, in contrast to non-system, non-capacity constrained providers, whose markups are assumed to be about zero. System members also impose high penalties on plans that exclude their partners. Providers that are expected to be capacity constrained capture markups of about 14 per cent of revenues. I show that these high markups imply an incentive for hospitals to under-invest in capacity despite a median benefit to consumers of over $330,000 per new bed per year.

Sherali-Adams gaps, flow-cover inequalities and generalized configurations for capacity-constrained Facility Location

Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location (CFL) and lower-bounded facility location (LBFL), have proved notorious as far as LP-based approximation is concerned: while there are local-search-based constant-factor approximations, there is no known linear relaxation with constant integrality gap. According to Williamson and Shmoys devising a relaxation-based approximation for \cfl\ is among the top 10 open problems in approximation algorithms. This paper advances significantly the state-of-the-art on the effectiveness of linear programming for capacity-constrained facility location through a host of impossibility results for both CFL and LBFL. We show that the relaxations obtained from the natural LP at $\Omega(n)$ levels of the Sherali-Adams hierarchy have an unbounded gap, partially answering an open question of \cite{LiS13, AnBS13}. Here, $n$ denotes the number of facilities in the instance. Building on the ideas for this result, we prove that the standard CFL relaxation enriched with the generalized flow-cover valid inequalities \cite{AardalPW95} has also an unbounded gap. This disproves a long-standing conjecture of \cite{LeviSS12}. We finally introduce the family of proper relaxations which generalizes to its logical extreme the classic star relaxation and captures general configuration-style LPs. We characterize the behavior of proper relaxations for CFL and LBFL through a sharp threshold phenomenon.Comment: arXiv admin note: substantial text overlap with arXiv:1305.599

Capacity constrained accessibility of high-speed rail

This paper proposes an enhanced measure of accessibility that explicitly considers circumstances in which the capacity of the transport infrastructure is limited. Under these circumstances, passengers may suffer longer waiting times, resulting in the delay or cancellation of trips. Without considering capacity constraints, the standard measure overestimates the accessibility contribution of transport infrastructure. We estimate the expected waiting time and the probability of forgoing trips based on the M/GB/1 type of queuing and discrete-event simulation, and formally incorporate the impacts of capacity constraints into a new measure: capacity constrained accessibility (CCA). To illustrate the differences between CCA and standard measures of accessibility, this paper estimates the accessibility change in the Beijing–Tianjin corridor due to the Beijing–Tianjin intercity high-speed railway (BTIHSR). We simulate and compare the CCA and standard measures in five queuing scenarios with varying demand patterns and service headway assumptions. The results show that (1) under low system loads condition, CCA is compatible with and absorbs the standard measure as a special case; (2) when demand increases and approaches capacity, CCA declines significantly; in two quasi-real scenarios, the standard measure overestimates the accessibility improvement by 14–30 % relative to the CCA; and (3) under the scenario with very high demand and an unreliable timetable, the CCA is almost reduced to the pre-BTIHSR level. Because the new CCA measure effectively incorporates the impact of capacity constraints, it is responsive to different arrival rules, service distributions, and system loads, and therefore provides a more realistic representation of accessibility change than the standard measure

Capacity Constrained Influence Maximization in Social Networks

Influence maximization (IM) aims to identify a small number of influential individuals to maximize the information spread and finds applications in various fields. It was first introduced in the context of viral marketing, where a company pays a few influencers to promote the product. However, apart from the cost factor, the capacity of individuals to consume content poses challenges for implementing IM in real-world scenarios. For example, players on online gaming platforms can only interact with a limited number of friends. In addition, we observe that in these scenarios, (i) the initial adopters of promotion are likely to be the friends of influencers rather than the influencers themselves, and (ii) existing IM solutions produce sub-par results with high computational demands. Motivated by these observations, we propose a new IM variant called capacity constrained influence maximization (CIM), which aims to select a limited number of influential friends for each initial adopter such that the promotion can reach more users. To solve CIM effectively, we design two greedy algorithms, MG-Greedy and RR-Greedy, ensuring the $1/2$-approximation ratio. To improve the efficiency, we devise the scalable implementation named RR-OPIM+ with $(1/2-\epsilon)$-approximation and near-linear running time. We extensively evaluate the performance of 9 approaches on 6 real-world networks, and our solutions outperform all competitors in terms of result quality and running time. Additionally, we deploy RR-OPIM+ to online game scenarios, which improves the baseline considerably.Comment: The technical report of the paper entitled 'Capacity Constrained Influence Maximization in Social Networks' in SIGKDD'2