In July 2015, representatives from the five Arctic Ocean coastal states (Canada, Denmark, Norway, Russia and the United States) signed the Declaration Concerning the Prevention of Unregulated High Seas Fishing in the Central Arctic Ocean. In the declaration text it is clearly stated that “commercial fishing in the high seas portion of the central Arctic Ocean is unlikely to occur in the near future.” This approach increases the stature of the Precautionary Principle, a strategy that copes with possible risks in cases where scientific information is limited. The declaration is the first official attempt to regulate international waters of the Central Arctic Basin. While commercial fishing in the central Arctic Ocean is unlikely to become common anytime soon, fisheries management in the region includes complex decision making challenges, while it is also complicated by multiple factors, including transboundary fish stocks—those crossing boundaries of Exclusive Economic Zones (EEZs) — and straddling stocks (those typically found in the high seas adjacent to the EEZ) arising from the unsettled maritime boundary lines, thus often calling for the establishment of an effective bilateral or multilateral regime.
The contentious and divisive issue of how to handle Arctic fisheries has mostly been discussed so far in literature from a biodiversity standpoint rather than an economic one. Yet looking at the problem from an economic standpoint could help provide information that could prevent optimal use of resources and thus contribute to preventing irrational behaviors that may lead to the collapse or disruption of the ecosystem. Optimization theory provides critical insights for individual fishers or countries pursuing the most profitable strategy (higher payoffs). At the same time it can also prove useful for broader decision-making processes whereby all interested parties cooperate on the management of Central Arctic fish stocks.
Game theory can potentially contribute in a more complex setting, with two or more actors—states in our case—involved in fishing resource management and with each state being able to choose among a set of available options, with their payoff dependent on other states’ choices.
There are a number of different types of games available in the game theoretical framework. Given the existing risks and uncertainties over Arctic marine resources I would propose a differential game setting as a baseline scenario. A differential game is a mathematical formulation used for either conflict or cooperation where players’ strategies are changing over time.
A differential game seems suitable since there is an underlying assumption that the “Arctic players” involved make decisions at all time points and not necessarily in specific time intervals. Furthermore a repeated static game (players deciding simultaneously with no prior knowledge of other players’ choices), such as the Prisoner’s Dilemma, would probably not work as well here, since the payoff functions of our players would not be time-dependent.
If we are looking for a solution where all involved Arctic states agree to cooperate on the management of marine resources in the Central Arctic, we would probably need to solve it as a standard optimal control problem, through the use of maximum principle or dynamic programming. In other words the outcome of optimizing a joint welfare function should be examined regarding its efficiency, which brings together the different Arctic players in a joint effort to maximize their average individual welfare.
Another theory known as Nash equilibrium could provide useful insights with regard to incentives and motivations, especially in cases, like the one described here, where it is rather daunting to predict how different players will behave in a game. A Nash equilibrium comes down to a set of different strategies for each one of the players included in the game, indicating that neither player has incentive to change their choice (taking others’ choices as given) since their payoffs are not improving anyway.
An open-loop solution that gives Nash equilibrium would result in all players having absolutely no incentive to deviate from their specific strategic path, given the path of other players or in other words having the players at a Nash Equilibrium would make them unwilling to act differently, since they would be worse off if they did.
An Open Loop Nash Equilibrium can be examined where there is exclusive dependence on the time variable; if a player deviates from the equilibrium control, even if briefly, and decides to return to its former behavior, the equilibrium is broken. Conversely, in a feedback (or closed-loop) Nash Equilibrium which is strongly time consistent, the dependence lies on the current state of the system. Differential games can generally help towards answering whether a potential cooperative solution can be achieved through a Nash equilibrium of a non-cooperative game.
Yet another question is whether countries would prefer to cooperate instead of competing for fishing in the Central Arctic. A cooperative scenario would require a Net Present Value (sum of benefits minus sum of costs, both in present values) larger than the non-cooperative scenario, thus covering the opportunity costs arising from the cooperative case. If this condition is not satisfied we will have to accept that there will be a non-cooperative behavior up to the point that cooperation turns lucrative for all players.
Game theoretic approaches with regard to stock management have provided useful insights and directed new lines of inquiry, but the dynamically changing Arctic raises issues that call for coordinated responses, for example through the use of more robust tools such as evolutionary game theory. Given that many species are expected to expand to yet unexploited parts of Arctic waters, one major concern is the consequences of coastal states’ harvesting activities on society’s wellbeing, and the ways in which it will be made possible to leave a positive legacy for future generations.
Looking at the interplay of ecology and economic behavior is one way that scientists can begin to answer these questions. Meticulous research on strategies of defection, cooperation and enforcement can be a cornerstone for establishing and managing effective ways to protect the Arctic marine environment, taking into account the current dearth of research in existing and future biodiversity.
How can we best tackle risks in our complex and interconnected economies? With globalization and information technologies, people and processes are increasingly interdependent. Great ideas and innovations can spread like wildfire. However, so can turbulence and crises. The propagation of risks is a key concern for policymakers and business leaders. Take the example of production disruption: with global supply chains, local disasters or man-made accidents can propagate from one place to another, and generate significant impact. How can this be prevented?
Risk propagation is like a domino effect. Credit: Martin Fisch (cc) via Flickr
As part of my PhD research, I met professionals on the ground and realized that supply risk propagation is a particularly tricky issue, since most parts of the chains are out of their control. Supply chains can be very long, and change with time. It is difficult to keep track of who is working with whom, and who is exposed to which hazard. How then can individual decisions mitigate systemic risks? This question directly connects to the deep nature of systemic problems: everyone is in the same boat, shaping it and interacting with each other, but no one is individually able to steer it. Surprising phenomena can emerge from such interactions, wonderfully illustrated by bird flocking and fish schooling.
As an applied mathematician thrilled by such complexities, I was enthusiastic to work on this question. I built a model where firms produce and interact through supply chain relationships. Pen and paper analyses helped me understand how a few firms could optimally react to disruptions. But to study the behavior of truly complex chains, I needed the calculation power of computers. I programmed networks involving a large number of firms, and I analyzed how localized failures spread throughout these networks, and generate aggregate losses. Given the supply strategy adopted by each firm, how could systemic risk be mitigated?
With my collaborators at IIASA, Åke Brännström, Elena Rovenskaya, and Ulf Dieckmann, we have highlighted the key role of coordination in managing risks. Each individual firm affects how risks propagate along the chain. If they all solely focus on maximizing their own profit, significant amounts of risk remain. But if they cooperate, and take into account the impact of their decisions on the risk profile of their trade partners, risk can be effectively mitigated. Reducing systemic risks can thus be seen as a common good: costs are heterogeneously borne by firms while benefits are shared. Interestingly, even in long supply chains, most systemic risks can be mitigated if firms only cooperate with only one or two partners. By facilitating coordination along critical supply chains, policy-makers can therefore contribute to the reduction of risk propagation.
Colon’s model analyzes how firms produce and interact through supply chain relationships. Credit: Jan Buchholtz (cc) via Flickr
Drawing robust conclusions from such models is a real challenge. On this matter, I benefited from the experience of my IIASA supervisors. Their scientific intuitions greatly helped me focusing on the most fertile ground. It was particularly exciting to borrow techniques from evolutionary ecology and apply them to an economic context. Conceptually, how economic agents co-adapt and influence each other shares many similarities with the co-evolution of individuals in an ecological environment. To address such complex issues, I strongly believe in the plurality of approaches: by illuminating a problem from different angles, we can hope to see it more clearly!
Note: This article gives the views of the author, and not the position of the Nexus blog, nor of the International Institute for Applied Systems Analysis.
By Sergio Rinaldi, IIASA Evolution and Ecology Program and Politecnico di Milano, Italy
Is it possible to predict how love stories develop, progress, and end using mathematical models? I have studied this question over the past 20 years with a group of researchers at IIASA and at the Politecnico di Milano, and as we show in our new book Modeling Love Dynamics (World Scientific, 2016), the answer is yes. The emerging message is that prediction is possible, if we can describe in formulas the way each individual reacts to the love and to the appeal of the partner.
Consider a standard love story, which develops like those described in a classical Hollywood movie such as Titanic. This story can be easily modeled, if one considers reasonably appealing individuals who increase their reaction with the partner’s love – so called secure individuals. Starting from the state of indifference, where the individuals are at their first encounter, their feelings continuously grow and tend toward a positive plateau.
Mala Powers and José Ferrer in Cyrano de Bergerac, 1950. – Public Domain
Love stories become more intriguing when one individual is not particularly appealing, if not repelling, as in the fairy tale “Beauty and The Beast.” Indeed, in these cases, there exists also a second romantic regime, which is negative and can therefore entrain, in the long run, marital dissolution. In order to avoid that trap, people who are not very charming, or believe to be so, do all they can to look more attractive to the partner. At the first date, she wears her nicest dress and he shows up with his best fitting T-shirt. However, after a while, the bluffing can be interrupted, because the couple has entered the safe basin of attraction of the positive regime. Needless to say, the model also supports much more sophisticated behavioral strategies, like that described by Edmond Rostand in his “Cyrano de Bergerac,” the masterpiece of the French love literature.
Not all individuals are secure. Indeed, some people react less and less strongly when the love of the partner overcomes a certain threshold. These individuals, often very keen to flirtation, are incapable of becoming one with their partner. The model shows that couples composed of insecure individuals tend, with almost no exception, toward an unbalanced romantic regime in which the most insecure is only marginally involved and is therefore prone to break up the relationship at the first opportunity. This is why after just 20 minutes of the very long “Gone with the Wind,” when one realizes that Scarlett and Rhett are both insecure, the model can already predict the end of the film, where he quits her with the lapidary “Frankly, my dear, I don’t give a damn.” The same conclusion is expected if only one of the two individuals is insecure. This explains the numerous failures in the romantic life of some individuals, like the beautiful star Liz Taylor, who is described as very insecure in all her biographies, and went, indeed, through eight marriages.
Clark Gable and Vivien Leigh in Gone with the Wind, 1939 – MGM Pictures | Public Domain
Mathematical models can also be used to interpret more complex romantic behaviors. Particularly important is the case of individuals who overestimate the appeal of the partners when they are more in love with them (like parents who have a biased view of the beauty of their own kids). Interestingly, if insecurity is also present, biased couples can have romantic regimes characterized by recurrent ups and downs. In other words, the theory says that bias and insecurity is an explosive mix that triggers turbulence in the life of a couple.
In the second part of the book we focus on the effects of the social environment and to the consequences of extra-emotional compartments. In this context, our analysis of the 20-years long relationship between Laura and the famous Italian poet Francis Petrarch shows that poetic inspiration is an important destabilizing factor, responsible for transforming a quiet relationship into a turbulent one.
Finally, we studied triangular relationships, with emphasis on the effects of conflict and jealousy. In all these cases the dynamics of the feelings can be very wild, up to the point of being chaotic and, hence, unpredictable. When this occurs, the life of the couple becomes unsustainable, because painful periods of crisis can virtually start at any moment: a heavy permanent stress. The model can thus explain why the relationship is often interrupted, sometimes even tragically, as in the famous film by François Truffaut “Jules et Jim”, where Kathe’s suicide is perceived as a real relief.
During his workout in the IIASA gym, my colleague Pekka Lauri often runs on a treadmill. He adjusts the velocity of running using the control panel, and it indicates the distance and approximate calories burnt. While Pekka may not be thinking about mathematical models during his workout break, running and other athletic performance can be modeled using some of the same techniques that we use for other questions at IIASA.
Outside of my academic work at IIASA, I am highly interested in sports, and athletics in particular. My wife, Katy Kuntsevich, has won Austrian championships in high jump several times, and my brother, Nikolay, was on his university team as a 400 meter runner.
Visiting my hometown Ekaterinburg, Russia, back in 2014, I got into a dispute with my father, who is a university professor in theoretical mechanics. Namely, my argument was that the sprinters’ acceleration at the finish line of the 100 meter race should be negative. Later on, during the Christmas holidays, I decided to mathematically support my statement.
Left: Prof. Krasovskii with a page from his Lectures in Theoretical Mechanics (Chapter 2, Kinematics, in Russian) featuring Valeriy Borzov on finish. This page was a reason for my study. Top right: Portrait of Isaac Newton.
When athletes run a race, their horizontal velocity can be estimated by modern technologies such as high resolution cameras and lasers. Knowing the horizontal instantaneous velocity, one can calculate acceleration. According to Newton’s law, one can introduce the forces applied to the body center mass of the athlete. Outside a gym treadmill it gets a bit more complicated, with air resistance and headwind or tail-wind. Against these aerodynamic forces the runner applies horizontal force, which drags him forward. In reality it is an “aggregate” of impulsive normal forces generated by feet and the stroke frequency.
The dynamics of an athlete have been described by an ordinary differential equation studied in papers on sprint modeling, first published by physicist J. Keller. This equation has been considered in numerous papers, which have shown that the equation fits the real data for short-distance running (100 and 200 meters). The indicated studies are devoted to the calibration of parameters, to the wind impact analysis, and to the choice of force functions such that the solution satisfies the actual motions, e.g. the running records of Usain Bolt.
The problem of running dynamics reminded me of a type of model that we sometimes use at IIASA, called an optimal control model. Optimal control models are used to calculate the best or most efficient way of doing something, for example, driving from one place to another. If I want to drive from Vienna to Laxenburg, I start my car’s engine at my house (point A). I look at the time, and plan to arrive to IIASA (point B) in 30 minutes. In optimal control terms, the car is a control object, and the driver controls it by pushing the gas/brake pedals and steering the wheel. In the driving process the car meets certain constraints (e.g. the engine power, available roads, and speed limits) and disturbances (e.g. traffic jams, lights, and weather conditions). Obviously, there are many ways of controlling the car in order to reach IIASA in 30 minutes. What if among those admissible controls, I wanted to find an optimal control minimizing car’s energy expenditures during the 30-minute trip from A to B? Here energy is an intensity (cost) of control actions, i.e. fuel (petrol/electricity), or corresponding greenhouse gas emissions. Well, in this case one needs to solve the classical minimum energy control problem. The solution to this problem gives an optimal plan that the car driver (or autopilot) needs to implement. Note, that the corresponding time-optimal control problem consists in finding the fastest driving time to IIASA under given fuel reserve. Optimal control theory (OCT) is an efficient tool for solving such dynamic optimization problems.
My research question was: “Can one control his/her running similar to driving a car?” The answer is: “Yes!”
I applied an optimal control model to Usain Bolt’s performance data at the Beijing Olympic Games in 2008, when he ran the 100 meter sprint in 9.69 seconds. According to the model, under the same conditions he could have distributed his energy optimally and run the distance in 9.56 s. It is worth mentioning that this time is close to his current world record, 9.58 s, achieved at the 2009 World Championships in Berlin. In the paper I also provide modeling results for optimal (energy-efficient) running over 100 m: calculation of the minimum energy and trajectories of acceleration, velocity, and distance from start.
In the conclusion, I argue that applying advanced science in the athletic training programs is far better than doping–better in terms of a healthy body, mind and soul.
As an environmental economist working on economic valuation and optimisation of water use, the academy was very interesting for me. Water management is a dynamic process and requires bringing perspectives and expertise from different disciplines together. Application of systems analysis enables us to combine aspects from various domains, come up with models that identify nonlinearities, project regime shifts, and tipping points in the management of water as well as other natural resources. Such projects require interdisciplinary collaboration and communicable results to inform policy. Scientists need to translate their results to a language accessible to the policymakers, in order for society to pick up on and capitalize on the research efforts. The MSA 2015 provided me with necessary training to go deeper into different modelling methodologies, and learn the concepts and principles of science for policy first-hand from IIASA scientists.
The reading list sent before the course gave me the impression that I would probably be the only environmental economist amongst a crowd of mathematical modellers. However, arriving in Moscow, I found that the MSA 2015 participants came from a broad range of backgrounds and countries at different stages of their careers in academia or policy. We all came to learn and discuss the natural resource constraints to infinite economic growth on finite planet.
During lectures, the theoretical foundations of different mathematical approaches such as dynamical systems theory, optimal control theory and game theory were presented by leading scientists, such as Michael Ghil. Fundamentals of addressing challenges of natural resource management and comparing contemporary models of economic growth were also covered as central themes.
The course acknowledged the issues related with ecosystems services, public goods, inter-generational and international fairness, and public and common pool resource dynamics in the face of economic growth and resource constraints. The training underlined feedbacks between institutional dynamics and resource dynamics in complex social-ecological system and need for interdisciplinary and policy-relevant research, an important take-home message for next generation scientists.
Photos by M. Nazli Koseoglu
What makes the MSA so special? Apart from lectures, we had tutorials, a group project, poster and project presentation sessions, as well as interesting talks on IIASA activities by Margaret Goud-Collins and Elena Rovenskaya, and an inspiring session on the importance of finding the right mentor for a successful career by Prof Nøstbakken. The MSA 2015 program had a good balance of theory and practice, which encouraged participants to be proactive and engaged.
I particularly liked the poster session. We presented our ongoing projects and received feedback from the lecturers and other participants. It was great to get comments and perspectives that I never thought of, and tips from senior researchers. In the late days of the academy we were assigned to prepare a group project on Artic systems which allowed us to put what we had learned at the lectures into practice and apply important topics outside our exact fields of study; in my case, these topics were petroleum economics and artic futures. I found the multi-disciplinary group work to be a great exercise for the development of my current study.
Attending the MSA 2015 provided useful training, both theoretical and practical, for understanding systems analysis approaches better. The host institution and organizing committee at Lomonosov Moscow State Univesrity provided impeccable hospitality, and the setting, in a landmark building in a landmark city, was a great perk. I received very constructive feedback, and made good connections around the world. I would recommend all early-career researchers in relevant fields to take this great opportunity next summer!
The seminal book The Limits to Growth by Donella Meadows and colleagues was a first attempt to make a world model that integrated environment, economics, population, and industrial pollution. Without drastic changes to curb human population growth, consumption of non-renewable resources and industrial effluence, the model scenario projected a collapse of the world social-industrial system, because physically it is not possible to keep growing on a finite planet. This important message spurred many people in the environmental sciences, but was largely ignored, or worse ridiculed, by the dominant economic and political leaders. Perhaps their work was too pessimistic (although some could say realistic) and called for change for which society was not yet ready.
My co-authors and I feel their message was interpreted incorrectly. The restrictions imposed by The Limits to Growth do not entail stagnation and strife but rather give us an opportunity for new priorities, greater equity, and greater well-being. Living within the limits can offer agreeable, pleasant, even thriving and wonderful living conditions.
People today are confronted with a number of very serious problems: poverty, increased inequalities among countries and people, refugees, regional conflicts and civil wars, global climate change, accelerating exploitation of the global non-renewable and renewable resources, rapid land use change and urbanization, and increased emissions of harmful chemicals into the environment. History has shown us that we cannot solve these problems using traditional methods based on short-sighted economic growth.
Additionally, we know from natural laws that continuous growth in a finite environment is not possible. How can we ensure sustainable development for society on Earth? It would be possible by imitating the system that understands how to sustain long-term development: to learn from nature and follow nature’s way. Nature shifts from quantitative biomass growth when the resources become limiting to qualitative development by increasing resource use efficiency, in terms of both improved network connectivity and information on process regulation and feedbacks. The two main ecosystem functions, flow of energy and transfer of nutrients, are accomplished by renewable energy and complete recycling of the needed elements. Nature also originated and perfected the use the 3Rs: Reduce, Reuse, and Recycle.
Our book employs a global model to experiment with applying these properties of nature in society. Using global statistics, the model considers how the development will change if:
A revenue-neutral, resource-based Pigovian tax is increased significantly and along with commensurate tax reduction to enhance recycling and application of renewable energy
We increase investment in education, innovation, and research significantly to raise the level of understanding by the population and to develop new progressive ideas to address our global problems.
We increase pollution abatement considerably to reduce its negative impacts on our health, nature, and production.
We increase aid from the developed to the developing countries to 0.8% of GNP, which would enhance the cooperation among countries, reduce poverty and population growth and thereby also the number of refugees. In this context, it is important that the aid is given as support to education, health care, and family planning and not at all as military aid.
The model calculations show that it is possible to obtain a win-win situation, where both industrialized and developing nations can achieve a better standard of living – the developing countries mostly quantitatively and the developed countries mostly qualitatively. The calculations are compared with scenarios based on “business as usual” practices. The business as usual scenario shows a major collapse around the year 2060, which is in accordance to the Limits to Growth results from 1972 and the follow-up-publications from the Club of Rome.
Furthermore, the book demonstrates calculations of ecological footprints and sustainability by assessing our consumption and loss of work energy due to our use of resources and destruction of nature. These calculations lead to the following conclusions:
Maintain natural areas and the ecosystem services they provide.
Improve agricultural production by increasing efficiencies and technologies.
Shift our thoughts and actions from quantitative growth to qualitative development, for instance by using the three R’s.
Shift to renewable energy.
Leave today’s policy focused entirely on short-sighted economic considerations and start to discuss how we can improve environmental management, increase the level of education and research, and achieve greater equality in society.
Develop and promote alternative measures of welfare and well-being.
Reduce, rather than reward, financial speculations, exorbitant profits, and stock market gambling.