4 Presentations

• 
  02:00 PM - 02:25 PM

  Concentric Framework for Sustainability Assessment

  • Arnaud Dragicevic, presenter, Laboratory of Forest Economics, Agro ParisTech

  By means of a hypergraph, we study the resilience and the connectivity of a socio-ecological system (SES), which takes the form of a concentric diagram reflecting strong sustainability. The structure is subjected to dynamics of spread of a global reform. The model outcomes reveal that, in the concentric representation of sustainability, the environmental layer is endowed with the maximum magnitude of efficiency of the knock-on effect. The existence of risk of reform abrogation prevents the equilibrium density of reformed nodes from reaching stationarity. The numerical simulation results confirm that the environmental layer is the most efficient when comes to launching a reform through a small number of nodes. They also show that connectivity between all types of elements is most fairly valued from the environmental perspective.

• 
  02:25 PM - 02:50 PM

  Finders, keepers?

  • Niko Jaakkola, presenter, ifo Institut
  • Daniel Spiro, Uppsala University
  • Arthur van Benthem, The Wharton School, University of Pennsylvania

  Natural resource taxation and investment very often exhibit cyclical behavior, driving political turmoil and shifts in power. By way of a rational-expectations model under limited commitment, we show that cycles arise endogenously from the interaction between firms' investment decisions and government taxation. We emphasize the role of large resource revenues, which induce a high tax, lowering exploration investment and thereby future findings. This leads the government to reduce tax rates, inducing high investment and high future taxes, and so on. We investigate which factors reinforce cycles and present ways of avoiding them. Tax oscillations are more pronounced for resources which take longer to develop and in new resource-exporting countries. Cycling may occur even under a government that cares about the future, but a sufficiently patient government is also able to avoid cycles altogether. Tax differentiation on mine vintage avoids cycles as well and, surprisingly, increases government revenues. Our findings are consistent with stylized facts: we document evidence of cyclical behavior in a large number of countries with both strong and weak institutions, and provide detailed case studies of two Latin American countries.

• 
  02:50 PM - 03:15 PM

  Linear quadratic game of exploitation of common renewable resources with inherent constraints

  • Rajani Singh, University of Warsaw
  • Agnieszka Wiszniewska-Matyszkiel, presenter, Institute of Applied Mathematics and Mechanics, Warsaw University

  In this paper we present an analysis of a discrete time dynamic game of extraction of common renewable resource---fishery---by many players with infinite time horizon and possibility of depletion. The game is defined such that increasing number of players does not mean introduction of additional users of the resource, but decomposition of the decision making structure of the same mass of users (into regions, countries, firms). The game is linear-quadratic with constraints which are inherent to the problem: player cannot extract negative amount or more than available. Such an obvious modification of the standard framework of linear quadratic game substantially changes both Nash equilibrium and social optimum. We look for Nash equilibria and social optima in feedback form (strategies dependent on the state of the resource).

  After modification, we can calculate social optima for arbitrary number of players and prove that they are identical, while Nash equilibrium can be computed only for continuum of players, and we obtain piecewise linear equilibrium with surprisingly compound value function resulting from exhaustion: nonsmooth, piecewise linear-quadratic with infinitely many intervals. For finitely many players a negative result can be proved, that the equilibrium is not even piecewise linear while the value function piecewise linear-quadratic with less than three intervals.

  In obtained results, we always have sustainability at social optima and exhaustion in finite time for reasonable interval of initial states for Nash equilibria.

  When applicational aspect is considered, we also calculate a tax rate enforcing social optimum (and, therefore, sustainability) in the game with continuum of players.

  Besides, during the process of computation of social optimum, we discovered that this simple dynamic optimization problem constitutes a counterexample to correctness of skipping or relaxation of checking terminal condition---a simplification often used in applications.

• 
  03:15 PM - 03:40 PM

  Dynamic multicriteria games with finite horizon

  • Anna Rettieva, presenter, Institute of Applied Mathematical Research Karelian Research Center of RAS

  Mathematical models involving more than one objective seem more adherent to real problems. Players can have more than one goal which are often not comparable. These situations are typical for game-theoretic models in economics and ecology.
  The new approaches to construct a cooperative behavior in dynamic multicriteria games with finite planning horizon are presented. We consider a dynamic, discrete-time game model where the players use a common resource and have different criteria to optimize. First, we construct the guaranteed payoffs and multicriteria Nash equilibrium. Second, we find the cooperative equilibrium as a solution of a Nash bargaining scheme with the multicriteria Nash payoffs playing the role of the status quo points. Third, we construct payers’ strategies and payoffs in the case of a coalition formation in two ways: when free riders have/haven’t information about the fact that the coalition was formed. The results of numerical modelling show that the presented approach for cooperation determination is beneficial for the players and improves the ecological situation.