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Bergen, M., & Munoz, F. D. (2018). Quantifying the effects of uncertain climate and environmental policies on investments and carbon emissions: A case study of Chile. Energy Econ., 75, 261–273.
Abstract: In this article we quantify the effect of uncertainty of climate and environmental policies on transmission and generation investments, as well as on CO2 emissions in Chile. We use a twostage stochastic planning model with recourse or corrective investment options to find optimal portfolios of infrastructure both under perfect information and uncertainty. Under a series of assumptions, this model is equivalent to the equilibrium of a much more complicated bilevel market model, where a transmission planner chooses investments first and generation firms invest afterwards. We find that optimal investment strategies present important differences depending on the policy scenario. By changing our assumption of how agents will react to this uncertainty we compute bounds on the cost that this uncertainty imposes on the system, which we estimate ranges between 3.2% and 5.7% of the minimum expected system cost of $57.6B depending on whether agents will consider or not uncertainty when choosing investments. We also find that, if agents choose investments using a stochastic planning model, uncertain climate policies can result in nearly 18% more CO2 emissions than the equilibrium levels observed under perfect information. Our results highlight the importance of credible and stable longterm regulations for investors in the electric power industry if the goal is to achieve climate and environmental targets in the most costeffective manner and to minimize the risk of asset stranding. (C) 2018 Elsevier B.V. All rights reserved.

Carrasco, J. A., & Yanez, R. (2022). Sequential search and firm prominence. Econ. Theory, 74(1), 209–233.
Abstract: We explore the role of prominence in equilibrium pricing in markets where search is sequential and random. Our model key feature is that more prominent firms are more likely to be sampled first. In contrast to orderedsearch models, we find that more prominent firms inherit larger but less elastic demands, and as such have incentives to post larger prices. However, they might post lower prices but still charge higher markups than less prominent competitors only if they are also sufficiently more efficient. Our results suggest that when search is sequential, the role of prominence depends on whether it modifies the order or just the chances with which firms are sampled.
Keywords: EQUILIBRIUM PRICE DISPERSION; CONSUMER SEARCH; INFORMATION; ECONOMICS; MODEL

ColiniBaldeschi, R., Cominetti, R., & Scarsini, M. (2019). Price of Anarchy for Highly Congested Routing Games in Parallel Networks. Theor. Comput. Syst., 63(1), 90–113.
Abstract: We consider nonatomic routing games with one source and one destination connected by multiple parallel edges. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we prove that under suitable conditions on the costs the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case, and that these counterexamples already occur in simple networks with only 2 parallel links.

Cominetti, R., Quattropani, M., & Scarsini, M. (2022). The BuckPassing Game. Math. Oper. Res., Early Access.
Abstract: We consider two classes of games in which players are the vertices of a directed graph. Initially, nature chooses one player according to some fixed distribution and gives the player a buck. This player passes the buck to one of the player's outneighbors in the graph. The procedure is repeated indefinitely. In one class of games, each player wants to minimize the asymptotic expected frequency of times that the player receives the buck. In the other class of games, the player wants to maximize it. The PageRank game is a particular case of these maximizing games. We consider deterministic and stochastic versions of the game, depending on how players select the neighbor to which to pass the buck. In both cases, we prove the existence of pure equilibria that do not depend on the initial distribution; this is achieved by showing the existence of a generalized ordinal potential. If the graph on which the game is played admits a Hamiltonian cycle, then this is the outcome of priorfive Nash equilibrium in the minimizing game. For the minimizing game, we then use the price of anarchy and stability to measure fairness of these equilibria.

Cominetti, R., Scarsini, M., Schroder, M., & StierMoses, N. (2022). Approximation and Convergence of Large Atomic Congestion Games. Math. Oper. Res., Early Access.
Abstract: We consider the question of whether and in what sense, Wardrop equilibria provide a good approximation for Nash equilibria in atomic unsplittable congestion games with a large number of small players. We examine two different definitions of small players. In the first setting, we consider games in which each player's weight is small. We prove that when the number of players goes to infinity and their weights to zero, the random flows in all (mixed) Nash equilibria for the finite games converge in distribution to the set of Wardrop equilibria of the corresponding nonatomic limit game. In the second setting, we consider an increasing number of players with a unit weight that participate in the game with a decreasingly small probability. In this case, the Nash equilibrium flows converge in total variation toward Poisson random variables whose expected values are War drop equilibria of a different nonatomic game with suitably defined costs. The latter can be viewed as symmetric equilibria in a Poisson game in the sense of Myerson, establishing a plausible connection between the Wardrop model for routing games and the stochastic fluctuations observed in real traffic. In both settings, we provide explicit approximation bounds, and we study the convergence of the price of anarchy. Beyond the case of congestion games, we prove a general result on the convergence of large games with random players toward Poisson games.

Cortes, C. E., JaraMoroni, P., Moreno, E., & Pineda, C. (2013). Stochastic transit equilibrium. Transp. Res. Pt. BMethodol., 51, 29–44.
Abstract: We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing invehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic commonlines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic commonlines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a realsize network case as the next step of this research. (C) 2013 Elsevier Ltd. All rights reserved.

Diaz, G., Munoz, F. D., & Moreno, R. (2020). Equilibrium Analysis of a Tax on Carbon Emissions with Passthrough Restrictions and Sidepayment Rules. Energy J., 41(2), 93–122.
Abstract: Chile was the first country in Latin America to impose a tax on carbonemitting electricity generators. However, the current regulation does not allow firms to include emission charges as costs for the dispatch and pricing of electricity in real time. The regulation also includes sidepayment rules to reduce the economic losses of some carbonemitting generating units. In this paper we develop an equilibrium model with endogenous investments in generation capacity to quantify the longrun economic inefficiencies of an emissions policy with such features in a competitive setting. We benchmark this policy against a standard tax on carbon emissions and a capandtrade program. Our results indicate that a carbon tax with such features can, at best, yield some reductions in carbon emissions at a much higher cost than standard emission policies. These findings highlight the critical importance of promoting shortrun efficiency by pricing carbon emissions in the spot market in order to incentivize efficient investments in generating capacity in the long run.
Keywords: Carbon tax; Equilibrium modeling; Market design

Dumett, M. A., & Cominetti, R. (2018). On The Stability Of An Adaptive Learning Dynamics In Traffic Games. J. Dyn. Games, 5(4), 265–282.
Abstract: This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the RouthHurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes and two players we provide a full description of the number and nature of these rest points as well as the global asymptotic behavior of the dynamics. Depending on the parameters of the model, we find that there are either one, two or three equilibria and we show that in all cases the mean field trajectories converge towards a rest point for almost all initial conditions.

Fernandez, M., Munoz, F. D., & Moreno, R. (2020). Analysis of imperfect competition in natural gas supply contracts for electric power generation: A closedloop approach. Energy Econ., 87, 15 pp.
Abstract: The supply of natural gas is generally based on contracts that are signed prior to the use of this fuel for power generation. Scarcity of natural gas in systems where a share of electricity demand is supplied with gas turbines does not necessarily imply demand rationing, because most gas turbines can still operate with diesel when natural gas is not available. However, scarcity conditions can lead to electricity price spikes, with welfare effects for consumers and generation firms. We develop a closedloop equilibrium model to evaluate if generation firms have incentives to contract or import the sociallyoptimal volumes of natural gas to generate electricity. We consider a perfectlycompetitive electricity market, where all firms act as pricetakers in the short term, but assume that only a small number of firms own gas turbines and procure natural gas from, for instance, foreign suppliers in liquefied form. We illustrate an application of our model using a network reduction of the electric power system in Chile, considering two strategic firms that make annual decisions about natural gas imports in discrete quantities. We also assume that strategic firms compete in the electricity market with a set of competitive firms do not make strategic decisions about natural gas imports (i.e., a competitive fringe). Our results indicate that strategic firms could have incentives to sign natural gas contracts for volumes that are much lower than the sociallyoptimal ones, which leads to supernormal profits for these firms in the electricity market. Yet, this effect is rather sensitive to the price of natural gas. A high price of natural gas eliminates the incentives of generation firms to exercise market power through natural gas contracts. (C) 2020 Elsevier B.V. All rights reserved.

Harrison, R., & Lagunoff, R. (2019). Tipping points and businessasusual in a global commons. J. Econ. Behav. Organ., 163, 386–408.
Abstract: This paper analyzes a dynamic strategic model of resource extraction from a global commons. Countries derive benefits from both direct extraction and aggregate conservation of an open access resource. Each period, a country's output depends both on its resource usage and on the global stock of the resource stored within the ecosystem. Leading examples are ocean fisheries, habitat preservation, forestry, and land carbon biomass. The production coefficients on these inputs vary across countries and evolve stochastically over time. A Businessasusual (BAU) equilibrium characterizes each country's resource usage in the absence of an effective international agreement. Under nonconcave resource dynamics, depletion of the resource in a BAU equilibrium may reach a tipping point below which the stock spirals downward toward a steady state of marginal sustainability. Under the assumptions of the model, the tipping points emerge endogenously. If the number of extractors exceeds some fixed, finite bound, the commons always tips regardless of the initial stock. We find that countries will accelerate their rates of extraction the closer they are to reaching the lowend steady state. By contrast, in the socially efficient plan the commons never tips if the initial stock is large. (C) 2019 Elsevier B.V. All rights reserved.

Munoz, F. D., Wogrin, S., Oren, S. S., & Hobbs, B. F. (2018). Economic Inefficiencies of Costbased Electricity Market Designs. Energy J., 39(3), 51–68.
Abstract: Some restructured power systems rely on audited cost information instead of competitive bids for the dispatch and pricing of electricity in real time, particularly in hydro systems in Latin America. Audited costs are also substituted for bids in U.S. markets when local market power is demonstrated to be present. Regulators that favor a costbased design argue that this is more appropriate for systems with a small number of generation firms because it eliminates the possibilities for generators to behave strategically in the spot market, which is a main concern in bidbased markets. We discuss existing results on market power issues in cost and bidbased designs and present a counterintuitive example, in which forcing spot prices to be equal to marginal costs in a concentrated market can actually yield lower social welfare than under a bidbased market design due to perverse investment incentives. Additionally, we discuss the difficulty of auditing the true opportunity costs of generators in cost based markets and how this can lead to distorted dispatch schedules and prices, ultimately affecting the longterm economic efficiency of a system. An important example is opportunity costs that diverge from direct fuel costs due to energy or start limits, or other generator constraints. Most of these arise because of physical and financial inflexibilities that become more relevant with increasing shares of variable and unpredictable generation from renewables.

Murhula, E., Hashan, M., & Otsuki, A. (2023). Effect of Solid Concentration and Particle Size on the Flotation Kinetics and Entrainment of Quartz and Hematite. Metals, 13(1), 53.
Abstract: Despite the importance of solid concentration in froth flotation, its effect on flotation kinetics and entrainment has rarely been studied. In this study, the flotation kinetics and entrainment in quartz and hematite singlemineral flotation systems as a function of the solid concentration and particle size were investigated using dodecylamine acetate as a collector. Kinetics modeling showed that the Gamma distribution achieved the best agreement with the experimental data, whereas the Classical and Klimpel models poorly fit the data (e.g., RMSE). The flotation rate constants (k) of both quartz and hematite at a higher solid concentration showed a concave shape, with the inflexion point at the middlesize range, whereas this trend altered at lower solid concentrations. Overall, quartz exhibited higher equilibrium recoveries (Rinfinity) than hematite, which indicates its better overall rate constants. The degree of water recovery in both the quartz and hematite systems was higher at higher solid concentrations, but the hematite system exhibited higher water Rinfinity than the quartz system, meaning that the entrainment of gangue could be higher in direct hematite flotation than the reverse one. Therefore, a higher solid concentration is associated with better overall quartz recovery and can reduce hematite loss by entrainment during reverse flotation. An inverse relationship was identified between the solid concentration and particle size in terms of the ratio of water recovery to the concentrate. In the reverse flotation of iron ore, refraining from achieving equilibrium recovery could help limit entrainment, but this was not necessarily the case in direct flotation. No entrainment model or method other than the Warren and Ross model approximated the overall trends of flotation at the finest size range (38 mu m). However, extending the Warren method to polynomial distribution led to an improved fit with the experimental results. In addition to the solid concentration, particle density and size were revealed to be key to developing new entrainment models. Finally, after the fast recovery period (true flotation) was over, the slow recoveries were mainly driven by the slowfloating water fraction.

Pineda, C., Cortes, C. E., JaraMoroni, P., & Moreno, E. (2016). Integrated traffictransit stochastic equilibrium model with parkandride facilitiesd. Transp. Res. Pt. CEmerg. Technol., 71, 86–107.
Abstract: We propose an Integrated Stochastic Equilibrium model that considers both private automobile traffic and transit networks to incorporate the interactions between these two modes in terms of travel time and generalized costs. In addition, in the general version of the model, travelers are allowed to switch from personal vehicles to mass transit at specific locations in a parkandride scheme. The assignment for traffic equilibrium is based on the Markovian Traffic Equilibrium model of Baillon and Cominetti (2008), whereas the equilibrium of the transit network is represented by the Stochastic Transit Equilibrium model of Cortes et al. (2013). Stochastic travel decisions are made at the node level, thereby avoiding the enumeration of routes or strategies and incorporating various perception and uncertainty issues. We propose a MethodofSuccessiveAverages algorithm to calculate an Integrated Stochastic Equilibrium and conduct numerical experiments to highlight the effect of stochasticity on equilibrium flows and travel times. Our experiments show that higher stochasticity implies greater dispersion of equilibrium flows and longer expected travel times. Results on a real network with mode combination and park and ride facilities provide insights regarding the use of park and ride in terms of number and location, potential modal share of the combined mode option under different circumstances, and travel time impact due to the implementation of such park and ride facilities in a real setting. (C) 2016 Elsevier Ltd. All rights reserved.

Villena, M. J., & Reus, L. (2016). On the strategic behavior of large investors: A meanvariance portfolio approach. Eur. J. Oper. Res., 254(2), 679–688.
Abstract: One key assumption of Markowitz's model is that all traders act as price takers. In this paper, we extend this meanvariance approach in a setting where large investors can move prices. Instead of having an individual optimization problem, we find the investors' Nash equilibrium and redefine the efficient frontier in this new framework. We also develop a simplified application of the general model, with two assets and two investors to shed light on the potential strategic behavior of large and atomic investors. Our findings validate the claim that large investors enhance their portfolio performance in relation to perfect market conditions. Besides, we show under which conditions atomic investors can benefit in relation to the standard setting, even if they have not total influence on their eventual performance. The 'two investorstwo assets' setting allows us to quantify performance and do sensitivity analysis regarding investors' market power, risk tolerance and price elasticity of demand. Finally, for a group of well known ETFs, we empirically show how price variations change depending on the volume traded. We also explain how to set up and use our model with real market data. (C) 2016 Elsevier B.V. All rights reserved.

Yushimito, W. F., Ban, X. G., & HolguinVeras, J. (2014). A TwoStage Optimization Model for Staggered Work Hours. J. Intell. Transport. Syst., 18(4), 410–425.
Abstract: Traditional or standard work schedules refer to the requirement that workers must be at work the same days and during the same hours each day. This requirement constrains workrelated trip arrivals, and generates morning and afternoon peak hours due to the concentration of work days and/or work hours. Alternative work schedules seek to reschedule work activities away from this traditional requirement. The aim is to flatten the peak hours by spreading the demand (i.e., assigning it to the shoulders of the peak hour), lowering the peak demand. This not only would reduce societal costs but also can help to minimize the physical requirements. In this article, a twostage optimization model is presented to quantify the effects of staggered work hours under incentive policies. In the first stage, a variation of the generalized quadratic assignment problem is used to represent the firm's assignment of workers to different work starting times. This is the input of a nonlinear complementarity problem that captures the behavior of the users of the transportation network who are seeking to overcome the constraints imposed by working schedules (arrival times). Two examples are provided to show how the model can be used to (a) quantify the effects and response of the firm to external incentives and (b) evaluate what type of arrangements in starting times are to be made in order to achieve a social optimum.
