Robust game theory

We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our ``robust game' model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call ``robust-optimization equilibrium,' to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an incomplete-information game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robust-optimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results. The research of the author was partially supported by a National Science Foundation Graduate Research Fellowship and by the Singapore-MIT Alliance. The research of the author was partially supported by the Singapore-MIT Alliance.     

ENVIRONMENTAL UNCERTAINTY AND THE TIMING OF ENVIRONMENTAL POLICY

ABSTRACT. This paper shows that the timing of an investment to reduce the emissions of a stock pollutant under environmental uncertainty depends on the specification of uncertainty, on its level, and on the presence of a lower reflecting barrier for the stock pollutant. With quadratic damages, when variability increases with the level of pollution, emissions should be curbed immediately when uncertainty is large enough; when uncertainty is small, however, its impact is ambiguous. A lower reflecting barrier may also significantly influence the investment threshold. These results highlight the importance of better understanding the links between greenhouse gas concentration and weather variability.     

An environmental input-output model with multiple criteria

It is often claimed that there is a trade-off between economic goals and the quality of the environment. For this reason, an environmental input-output optimization model with multiple objectives is formulated. The criteria are the minimization of factor costs to produce the Gross National Product and the minimization of net pollution for a given level of final demand. Using the LeChatelier-Samuelson principle, we analyze the changes in the production of the sectors and in the prices of the goods (described by the dual model) due to the change in the preferences of the decision makers. It can be shown that higher weights for the environmental objectives imply — in tendency —non-decreasing production of the sectors andnon-decreasing abatement activities. The changes of prices are ambiguous. The condition for increasing prices is given. To some degree, the opposite results can be achieved, if maximization of the value of final demand (or of private consumption) and minimization of net pollution under the constraints for primary input are taken as objective functions. In this case, increasing weights for environmental goals will leadin tendency tonon-increasing final demand and tonon-increasing net pollution. Under given conditions, higher environmental quality will be achieved bynon-increasing gross production and abatement activities.     

ECONOMIC IMPACTS OF GLOBAL WARMING: THE CASE OF THE BARENTS SEA FISHERIES

ABSTRACT. . Regional analyses of possible physical and biological effects of global warming in the Barents Sea area have been carried out recently. Based on such studies possible economic impacts of global warming on the Barents Sea fisheries have been quantified, assuming different types of management regimes. The EconSimp2000 model, consisting of the ecosystem model AggMult and the fleet model EconMult have been parameterized based on fleet and catch records from the Norwegian Barents Sea fisheries. The model has been used to study biological and economic impacts of different environmental scenarios representing possible consequences of global warming. The current environmental situation, including normal seasonal and other variations, has been used as a reference scenario. Several biological and economic indicators have been defined in order to evaluate the simulation results of different environmental scenarios and different types of management regimes. The findings support earlier studies where biological and economic impacts of changes in management regime is found to be more pronounced than impacts caused by effects of global warming.     

EVALUATING THE IMPACT OF ENVIRONMENTAL POLICY ON THE TREND BEHAVIOR OF US EMISSIONS OF NITROGEN OXIDES AND VOLATILE ORGANIC COMPOUNDS

The nature of this paper is a practical application of a proper time‐series methodology to evaluate policy impacts when there is uncertainty about the data being difference‐stationary (DS) or trend‐stationary (TS). We use this methodology to examine the trend behavior of two air pollutants, nitrogen oxides (NO_X) and volatile organic compounds (VOC). In particular, we concentrate on answering two questions. First, were there breaks in the trends of NO_X and VOC emissions around the same time environmental policies such as the Clean Air Act Amendments (CAAA) of 1970 were passed? And second, accounting for possible breaks are the US emissions of NO_X and VOC TS or DS? Our empirical results show a clear evidence of a trend shift in NO_X and VOC emissions at the time the CAAA of 1970 were passed, implying that this policy has been effective in reducing air pollution emissions, as well as additional breaks that correspond to other events and environmental policies before and after 1970. The unit root tests indicate that NO_X are DS irrespective of the number of breaks in the trend whereas results for VOC emissions depend on the number of breaks assumed.     

STOPPING RULES AND THE CONTROL OF STOCK POLLUTANTS

A stock pollutant is defined as a residual waste that might accumulate over time. This paper examines some of the important distinctions between degradable and nondegradable stock pollutants and between nondegradable stock pollutants with known versus uncertain environmental cost. The latter case is examined using the more recent literature on stochastic control with Brownian motion. The presence of irreversibility and uncertainty is known to lead to more conservative investment rules and places a value on the preservation of options. In the case of a nondegradable stock pollutant with Brownian environmental cost, options are preserved by stopping accumulation at a lower level than in the corresponding certainty-equivalent problem. The model presented in this paper permits the derivation of closed-form stopping rules. For a simple numerical problem, the optimal nondegradable stock with Brownian environmental cost was 20 to 45 percent lower than the optimal level with known environmental cost. The empirical study of an actual nondegradable stock pollutant will require time series data on private and social cost in order to estimate drift and variance parameters which will influence the actual extent to which the optimal stock is less than the certainty-equivalent stock.     

MODELING IMPACTS OF BIOENERGY MARKETS ON NONINDUSTRIAL PRIVATE FOREST MANAGEMENT IN THE SOUTHEASTERN UNITED STATES

Abstract The potential impacts of bioenergy markets on slash pine plantation management on nonindustrial private forestlands in the southeastern United States were analyzed. We developed an integrated Black–Scholes and modified Hartman model to achieve this task. The risk of damage from catastrophic natural disturbances such as wildfires and pest outbreaks associated with the exclusion/incorporation of thinnings and variation in timber salvage rates was also included. Three scenario sets were considered: status quo or no thinning scenario, thinning scenario for pulpwood, and thinning scenario for bioenergy at differing levels of risk and salvage. The results indicated that the incorporation of thinnings either for pulpwood or bioenergy increases the forestland value regardless of the risk when the salvage value of the stand is 0.8. When the two thinning scenarios were compared, the land expectation value for the thinning scenario for bioenergy was greater at any level of risk compared with the thinning scenario for pulpwood, averaging a difference of 11.5% and 11.7% for salvageable portions of 0.8 and 0, respectively.     

Exchange rate uncertainty and trade growth—a comparison of linear and non‐linear (forecasting) models

A huge body of empirical and theoretical literature has emerged on the relationship between foreign exchange (FX) uncertainty and international trade. Empirical findings about the impact of FX uncertainty on trade figures are at best weak and often ambiguous with respect to its direction. Almost all empirical contributions assume and estimate a linear relationship. Possible nonlinearity or state dependence of causal links between FX uncertainty and trade has been mostly ignored yet. In addition, widely used regression models have not been evaluated in terms of ex‐ante forecasting. In this paper we analyse the impact of FX uncertainty on sectoral categories of multilateral exports and imports for 15 industrialized economies. We particularly provide a comparison of linear and non‐linear models with respect to ex‐ante forecasting. In terms of average ranks of absolute forecast errors non‐linear models outperform both, a common linear model and some specification building on the assumption that FX uncertainty and trade growth are uncorrelated. Our results support the view that the relationship of interest might be non‐linear and, moreover, lacks of homogeneity across countries, economic sectors and when contrasting imports vs exports. Copyright © 2005 John Wiley & Sons, Ltd.     

Why local air pollution is more than daily peaks: modelling policies in a city in order to avoid premature deaths

We use a predator–prey representation of an urban system to analyse how policy interventions can prevent the adverse effects of air pollution on people’s health. The number of residents is treated as prey variable, and particulate matter that consists of particles with a diameter of up to 10 micrometres (PM10) as predator variable. This representation allows integration of population trends and the effects of environmental interventions on the average level of PM10 concentration (which establishes a baseline for the potential health burden for residents). For the case of Graz, Austria, we illustrate the insights generated regarding the interdependency of market-based and technological pollution controls, and propose an indicator that assesses the cost of delayed interventions by counting additional premature deaths caused by polluted environments.

     

ON THE ECONOMICS OF BIOLOGICAL INVASION: AN APPLICATION TO RECREATIONAL FISHING

Abstract The paper demonstrates four general mechanisms that may affect economically valuable species when exposed to biological invasion. We distinguish between an ecological level effect and an ecological growth effect. In addition, we present an economic quantity effect working through demand. Finally, we suggest that there is an economic quality effect that reflects the possibility that invasions affect the harvesting agents directly through demand‐side forces. For example, this may occur because the state of the original species or the ecosystem is altered. We depart from the existing literature by revealing ecological and economic forces that explain why different agents may lack incentives to control invasions. The theoretical model is illustrated by the case where escaped farmed salmon (EFS) influence wild Atlantic salmon fisheries.     

OPEN ACCESS AND EXTINCTION OF THE PASSENGER PIGEON IN NORTH AMERICA

ABSTRACT. An open access model is formulated where X is a renewable resource and E is the level of effort devoted to harvest. Net growth is assumed to exhibit critical depensation and the open access system is described by two nonlinear differential equations where r > 0 is the intrinsic growth rate, K1 is the minimum viable population level, K₂ is the environmental carrying capacity, K₂ > K₁ > 0, q > 0 is the catchability coefficient, ? > 0 is an adjustment coefficient, (p – s) > 0 is the market price net of shipping cost, and c > 0 is the unit cost of effort at the harvest site. It is shown that the E= 0 isocline is a vertical line at X∞=c/[(p‐ s)q] and that the open access system passes through a supercritical Hopf bifurcation as X∞ moves from a level above (K₁+K₂)/2 to a level below (K₁+K₂)/2. For X∞ above (K₁+K₂)/2 the open access equilibrium is locally stable. For X∞ below (K₁+K₂)/2 the open access equilibrium will be locally unstable. At X∞=(K₁+K₂)/2 the system has a stable limit cycle. This analysis is useful in interpreting the economic history of the passenger pigeon. The limited empirical evidence would suggest that X∞=c/[(p – s)q] declined below (K₁+K₂)/2 during the last half of the 19th century as a result of improved rail transport and communications (the telegraph). It is thought that the passenger pigeon was extinct in the wild by 1901. The last passenger pigeon died in captivity at the Cincinnati Zoological Gardens on September 1, 1914. X=rX(X/ K₁– 1)(1 –X/K₂)–qXE and E=α[(p – s)qXE – cE],     

Economic value of greenhouse gases and nitrogen surpluses: Society vs farmers’ valuation

Livestock supply must challenge the growth of final demand in the developing countries. This challenge has to take into account its ecological effects since the dairy and livestock sectors are clearly pointed out as human activities which contribute significantly to environmental deterioration. Therefore, livestock activity models have to include desirable and undesirable outputs simultaneously. Using this perspective, we implement a Data Envelopment Analysis model to evaluate shadow prices of outputs under contradictory objectives between the society and the farmers. We show that farmers are able to reduce pollution significantly if society accepts to balance farmers’ opportunity cost. Finally, we observe that initial levels of the CO₂ tax implemented in European countries are in line with farmers’ valuation while the current level of the CO₂ tax tends to reach the value of pollution targeted by the society.     

A dual-interval vertex analysis method and its application to environmental decision making under uncertainty

In this study, a dual-interval vertex analysis (DIVA) method is developed, through incorporating the vertex method within an interval-parameter programming framework. The developed DIVA method can tackle uncertainties presented as dual intervals that exist in the objective function and the left- and right-hand sides of the modeling constraints. An interactive algorithm and a vertex analysis approach are proposed for solving the DIVA model. Solutions under an associated α-cut level can be generated by solving a series of deterministic submodels. They can help quantify relationships between the objective function value and the membership grade, which is meaningful for supporting in-depth analyses of tradeoffs between environmental and economic objectives as well as those between system optimality and reliability. A management problem in terms of regional air pollution control is studied to illustrate applicability of the proposed approach. The results indicate that useful solutions for planning the air quality management practices have been generated. They can help decision makers to identify desired pollution-abatement strategies with minimized costs and maximized environmental efficiencies.     

Complex structured singular value analysis using fixed-structure dynamic D-scales

Models of systems are always inexact. Hence, to better predict the performance of a system it is necessary to take into account uncertainty in a nominal model of a system. The structured singular value was developed to nonconservatively analyze robust stability and performance for systems with multiple-block uncertainty. In practice, optimization techniques are used to compute an upper bound on the structured singular value. For dynamic uncertainty with bounded magnitude and arbitrary phase (i.e., "complex uncertainty"), the standard approach to computing an upper bound involves finding diagonal scaling matrices D(jω) that minimize σ_max (D(jω)G(jω)D^-1(jω)) over a (theoretically) infinite number of frequencies. The order of the corresponding stable, minimum phase, rational function D(s) (if it exists) is hence arbitrary, which can lead to very high order controllers when D(s) is used for controller synthesis. This paper develops a fixed-structure approach to computing an upper bound for the complex structured singular value. In particular, by relying on results from mixed-norm H₂/H_∞ analysisD(s) is a priori constrained to be a rational matrix function of a chosen order and a new approach to computing an upper bound on the structured singular value is developed. The results are illustrated using two examples which clearly demonstrate the suboptimality of standard curve fitting. The proposed approach can be extended to mixed uncertainty and structured singular value controller synthesis without D — K type iteration.     

COST-BENEFIT ANALYSIS APPLIED TO WILDERNESS PRESERVATION—OPTION VALUE UNCERTAINTY AND DITONICITY

It has been recognized for some time that when cost-benefit analysis is applied to irreversible environmental decisions, such as that of developing or preserving wilderness land, there can be an option value associated with the preservation decision, which arises when there is future uncertainty with respect to the benefits of development or preservation. In this paper the provenance of option value is examined and it is shown that an important cause is a special kind of uncertainty, viz. the possibility of reversals in direction of the relative valuations of wilderness land and developed land, a property we refer to as ditonicity. It is shown that the more ditonic the relative valuation process the greater the deviance between the certainty-equivalence development policy and the stochastically optimal one, and thus by implication the greater the option value. In the two cases with zero ditonicity, when relative wilderness valuations always increase or always decrease (even though in a stochastic fashion), there is zero option value. The model used assumes that service flows from wilderness and developed land are size-dependent, with future relative values known only in terms of a stochastic process, which can take jumps up or down of the same proportional size, at random times. Development can be partial or total and can occur in impulses at any time over an infinite time horizon.     

MODELING THE SPATIAL DISTRIBUTION OF THE ECONOMIC COSTS AND BENEFITS OF ILLEGAL GAME MEAT HUNTING IN THE SERENGETI

ABSTRACT. Illegal game meat hunting in the Serengeti National Park, Tanzania, and adjacent game reserves provides an important source of protein and cash income to local communities. We construct a profitability model that describes the spatial distribution of the economic costs and benefits of illegal hunting in the Serengeti during the late 1980s and early 1990s. Costs included capital investment in hunting weapons, W_R, and the opportunity cost of hunting, W_O, both held to be constants; and two spatially variable components, the logistic effort of traveling to hunting areas, W_L, and the penalties incurred if arrested, W_P. Benefit was the expected income from the sale of meat from resident wildlife species. The model suggests: (1) W_R is the most important cost. (2) W_L is the second most important cost and likely to determine the spatial distribution of hunting activity if hunters seekto minimize costs. (3) W_O and W_P are of minor importance, the former because alternative sources of income provide low pay, the latter because the overall chance of being arrested is low. (4) W_P exceeds W_L only in areas close to the boundary of protected areas. (5) Although resident wildlife contributes only a minor share of illegal offtake compared to the migratory herds, hunting resident wildlife is profitable in 68% of the area. This suggests that hunting of resident and migratory wildlife is highly profitable and may explain why the utilization of the target populations has become increasingly unsustainable.     

A MODEL OF THE ENZOOTIOLOGY OF LYME DISEASE IN THE ATLANTIC NORTHEAST OF THE UNITED STATES

A mathematical model is presented for the dynamics of the rate of infection of the Lyme disease vector tick Ixodes dammini (Acari: Ixodidae) by the spirochete Borrelia burgdorferi, in the Atlantic Northeast of the United States. According to this model, moderate reductions in the abundance of white-tailed deer Odocoileus virginianus may either decrease or increase the spirochete infection rate in ticks, provided the deer are not reservoir hosts for Lyme disease. Expressions for the basic reproductive rate of the disease are computed analytically for special cases, and it is shown that as the basic reproductive rate increases, a proportional reduction in the tick population produces a smaller proportional reduction in the infection rate, so that vector control is less effective far above the threshold. The model also shows that control of the mouse reservoir hosts Peromyscus leucopus could reduce the infection rate if the survivorship of juvenile stages of ticks were reduced as a consequence. If the survivorship of juvenile stages does not decline as the rodent population is reduced, then rodent reduction can increase the spirochete infection rate in the ticks.     

一个供应链系统可靠性模型时间依赖解的渐近行为

本文研究一个供应链系统可靠性模型的时间依赖解.利用C0-半群理论研究该模型相应算子的谱的特征,获得了该系统模型时间依赖解的渐近行为,推广了文献[8]中的结果.     

ANALYSIS OF THE STICK-SLIP PROBLEM FOR NON-NEWTONIAN FLOWS

In this paper we consider the stick-slip problem for non-Newtonian flows: the fluid emerges from a 2-dimensional bounded strip {(x, y); ?N < x < 0, |y| < 1} into the space {0 < x < N} and its free boundary is linearized to {x > 0; |y| = 1}. The fluids we consider are a class of Oldroyd models, excluding some special models such as the upper convected Maxwell model. We are not studying the full non-Newtonian flow, but rather the simpler problem where, in some terms of the constitutive equations of the model, the underlying velocity is assumed given, and Newtonian-like.     

SURVIVAL OF THE FITTEST IN A QUASILINEAR SIZE‐STRUCTURED POPULATION MODEL

ABSTRACT. We present a size‐structured model which describes the dynamics of n ecotypes competing for common resources. We prove that if reproduction is closed, i.e., offspring of one ecotype belongs to the same ecotype, then competitive exclusion between these ecotypes will occur. We give conditions on the model parameters which determine the fittest ecotype that wins the competition. Furthermore, we show that if reproduction is open then coexistence between the n ecotypes is possible.