The objective of this EArly Concept Grant for Exploratory Research (EAGER) award is to address early-stage obstacles to adoption of large-scale, game-theoretic models of engineering-economic systems in the analysis of energy policy. Game-theoretic models of design-and-pricing have the potential to quantitatively integrate models of consumer behavior, technology performance, engineering design decisions, and market competition with complex regulatory policies targeting both consumer and producer behaviors. This potential cannot be realized, however, without understanding how to formulate and simulate realistic game-theoretic models of large engineering-economic systems. This early-stage research will mathematically formulate game-theoretic regulated design-and-pricing models relevant to engineering organizations and state and federal governments; investigate tractable, reliable, and efficient computational methods for simulating such models; and assess the plausibility of the resulting policy forecasts with medium- and large-scale test problems drawn from the automotive industry. Tools from optimization and complementarity theory will be used to allow analysis of multiple non-smooth regulatory policies such as tiered tax credits, performance standards, and/or credit trading programs that currently exist in our nation's energy policy.
The theory, software, and computational experience resulting from this research will set the stage for full-scale analysis of difficult energy policy questions in large engineering-economics systems with policies targeting both consumer and producer behaviors. Analysis of complex policy issues will be improved with the use of models that can represent policies applied to both heterogeneous consumers and strategic engineering firms. Large-scale game-theoretic models will also resolve impacts of energy policy options on specific firms or groups of consumers, a resolution currently missing from many quantitative analyses underlying energy policy decisions. This EAGER award will lead directly to future research projects addressing specific, complex policy design questions in important engineering-economic systems such as automotive fuel economy policy and energy efficiency of home appliances and electronics. Research results will be disseminated through conference presentations, articles in academic journals, and publically available software.
This award provided supporting funds for expolatory research into numerical methods for "large-scale" equilibrium models of design in regulated markets. Equilibrium models represent interacting firms that choose products to market to consumers; each firm is assumed to have their own objective, nominally profits; the "equilibrium" behavior prescribed is that each firm simultaneously chooses the products they offer and prices for them to maximize their own profits given the decisions of their competitors. "Large-scale" refers to models with hundreds or thousands of product offerings, with several decisions per product. Recent research has shown that such "imperfectly competitive" market behavior can have important consequences for the assessment of regulatory policy; for example, tax credits for alternative fuel vehicles (e.g., hybrids) can incentivize firms to raise the prices of those vehicles. Our interest mainly lies in regulations, like the federal fuel economy standards, that affect both marketing and engineering decisions. Without capturing the strategic economic and engineering feedbacks from such regulations, we cannot assure that our energy efficiency and environmental policy decisions acheive their stated goals. Several examples of this type of equilibrium model have been employed to examine the potential impacts of vehicle fuel economy policy, in particular. However little research has been undertaken to understand the computational reliability and "stability" of simulations based on equilibrium concepts, especially with large-scale, nonlinear, and even non-smooth regulated design problems. This EAGER research explored computational aspects of equilibrium problems, ultimately making several observations: First, it is possible to efficiently simulate equilibrium for "large-scale" markets, like automotive, with hundreds of products and numerous decisions per product. With the right software and methods, we were ultimately able to simulate equilibrium for a full-scale model of the new vehicle market with over 370 vehicles and 4-5 decisions per vehicle. The methods currently used for problems on which our example was based reportedly took days, while our methods and software ultimately took only minutes. Second, "problem formulation matters." One early insight from this research is that some formulations of the equilibrium problem contain "spurious" solutions that can be computed but even though they are not simulations of the relevant equilibrium concept. We derived reformulated computational problems that not only rule out computation of these spurious solutions, but are also faster than current methods. This topic is covered in a paper presented at ASME's 2012 IDETC conference, and is currently in peer review at ASME's Journal of Mechanical Design. Third, two existing methods for computing equilibria can be significantly improved. Many practitioners have used Iterated Optimization (IO), in which we literally simulate the "game" underlying equilibria by optimizing one firm's decisions, holding others fixed, and then iterate through the firms until convergence. This method is easy to conceptualize, implement, and reflects "real-world" intuition about the simulations thus obtained. However IO need not converge at all, and may converge arbitrarily slowly on certain problems. Another technique, used more in academic journals than in practice, is to solve a single mathematical problem that directly encodes simultaneous optimality ("KKT") conditions. This problem is significantly harder to implement and solve, but does have existing theoretical convergence guarantees. For one large-scale example based on the 2006 automotive market, we found that neither method on its own always worked; judicious blending of these two methods not only improved reliability, but significantly improved computational speed. Future work will focus on the theoretical foundations for maximally-efficient hybrid algorithms as well as easy-to-use software libraries. Fourth, regulations can be included without significant simplification. Existing regulations often contain mandates, penalties, and incentives that enter into optimal design and pricing problems as non-smooth or even discontinuous functions. Many existing analyses abstract these issues away, in the process losing fidelity with the real regulated markets. By adapting methods from non-smooth optimization and mathematical programming with complementarity constraints, real policies can be analyzed effectively without simplification. For example, we are currently developing an analysis of piecewise-smooth and bin-based "feebates" - combinations of fees on under-performing vehicles and rebates on over-performing vehicles - in imperfectly competitive markets using this insight. This award supported 1 month of the PI's salary, 1 year of a PhD student's tuition and stipend, hourly undergraduate salary for research assistance, and travel. Research results have been presented at conferences, in journal publications under review and in preparation, and at several presentation at prestigious research institutions. More information, including pdfs of publications and presentations given, can be found at www3.me.iastate.edu/morrow
