Challenges for marine decision making in the Arctic

By Melina Kourantidou, MSA 2015 participant, PhD student, Department of Environmental and Business Economics, University of Southern Denmark

In summer 2015 I participated in the Summer Academy on Economic Growth and Governance of Natural Resources  in Lomonosov Moscow State University. I was inspired by the interdisciplinary lectures there as well as by recent developments in Arctic marine governance to propose a game-theoretical model for Arctic fisheries management.

© Fernbach Antal - Fotolia | Dollar Photo Club

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. © Fernbach Antal – Fotolia | Dollar Photo Club

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.

 

A map of the Central Arctic Ocean ©Shephard et al., 2016

A map of the Central Arctic Ocean shows the many countries that border the ocean. © Shephard et al., 2016

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.

Read my full report on the MSA 2015 Web site (PDF)

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.

Better water, better jobs

By Taher Kahil, IIASA Water Program

This year’s theme of the UN World Water Day is “Water and Jobs.” It focuses on how adequate water management can change workers’ lives. Indeed, water management and job creation are tightly linked. Nearly all jobs depend on water, and without reliable and safe access to water, neither small activities nor major global industries can endure. Similarly, labor is necessary to build, maintain, operate, and manage the water system, and to run water-based projects. Furthermore, job creation can be a thirsty business in both developing and developed countries. In many developing countries irrigation projects, requiring significant amounts of water, are considered the main engine for the economy and source of employment. In developed countries, less water is needed but it still requires sufficient quality for manufacturing and service projects creating job opportunities.

© Albert Gonzlez Farran - UNAMID

(cc) Albert Gonzlez Farran – UNAMID

Freshwater bodies such as rivers and aquifers supply the water that people and businesses rely on. But pressures on these bodies have been mounting worldwide during the last century. Population and economic growth have led to greater water use and increased pollution, with many basins around the world undergoing pervasive water shortages and quality degradation. Researchers expect the impacts of climate change to exacerbate these damages. At the same time, the global economy needs to continue growing to be able to adequately sustain the world’s rising population. However, the linkage between water and economic growth has increased global concerns about the impacts of water-related risks such as scarcity, droughts, floods, and pollution on economies’ ability to grow and create jobs. In fact, the World Economic Forum’s 2016 Global Risks Report ranks water as the highest global risk on economies over the next ten years.

When we talk about water and jobs, it is also important to mention that nearly 750 million people lack access to safe water and 2.5 billion live without adequate sanitation across the developing countries. People in these countries are constantly searching for water, which leaves limited time for productive work and skills building that yield better employment.

As we look towards the future, the link between water and employment becomes even more crucial. Water-related risks, which are expected to intensify due to climate change, will likely have adverse impacts on economy and employment, leading to major consequences beyond the water industry. For instance, researchers have linked the extreme drought in Syria between 2007 and 2010 to the uprising that began there in 2011. Several years of drought caused an extensive crop failure and massive losses of livestock, which resulted in 2 to 3 million people driven into unemployment and poverty. This situation contributed to a mass rural exodus into economically depressed cities, deepening existing instability in that country.

How do we avoid more crises like this? The complex and evolving water challenges of the future can only be addressed by investing in sustainable and integrated water management solutions such as those being identified and tested by the Water Futures and Solutions (WFaS) initiative at IIASA . WFaS is a cross-sector, collaborative, global initiative aimed at developing plausible scenarios of future water supply and demand, and identifying robust and no-regret portfolio of solutions for balancing water systems. The initiative brings together researchers and decision makers from governmental and non-governmental organizations as well as from the private industry and from a wide variety of sectors influencing water management. The potential water solutions include improved water policies and governance structures and the adoption of more innovative and environmentally friendly water technologies. Sustainable water resource management does not only address water-related risks, but it can also create green job opportunities for local and disadvantaged communities, for example in efficiency improvement works, in the production of alternative water sources, and in aquatic ecosystem restoration projects.

World Water Day © UN-Water

World Water Day © UN-Water

 

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.

How coordination can boost the resilience of complex supply chains

By Célian Colon, PhD student at the Ecole Polytechnique in France & IIASA Mikhalevich award winner

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

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

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.

The mathematics of love

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 & José Ferrer in Cyrano de Bergerac, 1950. Credit: Public Domain

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."

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.

CaptureMore information: Watch a video of Sergio Rinaldi’s talk at the 2015 Systems Analysis Conference.

Reference
Rinaldi S, Della Rossa F, Dercole F, Gragnani A, Landi P, (2015). Modeling Love Dynamics. World Scientific, Singapore [January 2016]  http://www.worldscientific.com/worldscibooks/10.1142/9656

 

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.

Don’t dope – run the code!

By Andrey Krasovskii, IIASA Ecosystems Services and Management Program

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.

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.

Here is my hypothesis of what Usain Bolt is doing at his laptop. © Weltklasse Zürich - Marcel Giger

Here is my hypothesis of what Usain Bolt is doing at his laptop. © Weltklasse Zürich – Marcel Giger

Reference:
A. A. Krasovskii, “Application of optimal control to a biomechanics model”, Proceedings of the Steklov Institute of Mathematics, 2015, Vol. 291, pp. 118–126. http://dx.doi.org/10.1134/S0081543815080118

 

I would like to thank Sergey Aseev, Katherine Leitzell, as well as my colleagues in the IIASA Ecosystem Services and Management Program (ESM) for their interest and valuable discussions.

 

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.