4 Presentations

• 
  02:00 PM - 02:25 PM

  Stable coalition structures in differential games

  • Simon Hoof, presenter, Paderborn University

  We study a notion of endogenous coalition formation for symmetric differential games in partition function form. Stable coalition structures are uniquely identified as the subgame perfect equilibrium of an extensive form game. We set up a recursive algorithm that computes a stable coalition structure for an arbitrary number of agents analytically. The results are illustrated within an analytically tractable linear state game of nonrenewable resource extraction. We present the stable coalition structures for up to 200'000 agents. Despite the fact that more agents lead to more coalitions on average, we cannot predict the stable coalition structure if the number of agents increases from n to n+1.

• 
  02:25 PM - 02:50 PM

  Learning applied to water management

  • Tania Jimenez, presenter, Avignon University
  • Mabel Tidball, INRAE

  We consider a groundwater exploitation problem, as in Rubio $\&$ Casino (2003). Water extraction is the only input in the production process of
  the farmers, and the dynamic is given by the evolution of the level of the water table.

  There are two levels of interactions: The farmers decide their own strategy (how much water they will extract from the water table) dynamically taking into account their beliefs
  about the other farmers actions.
  Interactions depend also on the profit function through the
  extraction cost that is a decreasing function on the height of the water table.
  Several papers solve this problem in complete information studying and comparing social optimum,
  feedback and open loop equilibrium, myopic behavior ( Rubio $\&$ Casino (2003), Djiguemde et al. (2018)).
  \\
  In this work we consider the case where farmers do not have information about other farmers' profit functions.
  It is assumed that each farmer relies on simple beliefs about the other
  farmer' behavior (Quérou $\&$ Tidball (2010)). Basically, farmers assume that a variation of their own extraction has a first order linear
  effect on the extractions of others. We use a simple learning procedure where farmers' beliefs
  are updated through observations of resource levels over time.
  \\
  We applied this procedure to complete and compare the possible kind of behaviors observed in the experimental analysis in Djiguemde et al. (2018).

  \vspace{1cm}
  \noindent
  Rubio, S. J., $\&$ Casino, B. (2003). Strategic behavior and efficiency in the common
  property extraction of groundwater. Environmental and Resource Economics, 26(1),
  73-87.
  \\
  Djiguemde, M, Doubois, D., Tidball, M. (2018). Dynamic games applied to common resources: modeling and experimentation. Draft.
  \\
  Quérou $\&$ Tidball (2010). Incomplete information, learning, and natural resource management.
  European Journal of Operational Research, Elsevier, vol. 204(3), pages 630-638.

• 
  02:50 PM - 03:15 PM

  Preservation Value in Socio-Ecological Systems

  • Arnaud Dragicevic, presenter, Laboratory of Forest Economics, Agro ParisTech
  • Jason Shogren, University of Wyoming

  We develop a model that reveals the preservation value of maintaining connectivity within a socio-ecological system (SES). By means of a multiplex network, built from the layers composing the sustainability Venn diagram, we define two measures of preservation value of inter- and intra-layer connections. Most policymakers and researchers have tended to assume that all elements within an SES are unconditionally connected, which implied that dimensions of sustainability functioned unhindered. We must instead explicitly explore how connectivity is operational. Given explicit threats to connectivity, we show under which conditions connectivity is valuable and should be preserved. This implies that policies aimed at sustainability should focus on explicitly addressing connections and disconnections. Using numerical simulations, our results suggest that the preservation value of the SES topological structure is greatest when we secure the connectivity of inter-layer connections.

• 
  03:15 PM - 03:40 PM

  Self enforcing environmental agreements, delayed information and external enforcement in a continuous time Fish Wars model with state dependent constraints

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

  In this paper, we analyse a continuous time version of Fish Wars with the infinite time horizon and state dependent constraints on controls. We calculate the social optimum and a Nash equilibrium which always leads to the depletion of the resource even if the social optimum results in the sustainability. We propose two ways of solving the problems of enforcing optimality: either by a tax-subsidy system or by an environmental agreement even if we assume that it takes time to detect any defection of a player. We also propose a general algorithm of finding financial incentives enforcing the optimal profile in a large class of differential games.

  Keywords: Fish Wars; common fishery; dynamic game; differential game; social optimum; Nash equilibrium; enforcement; Pigouvian taxation; self-enforcing environmental agreements; delayed observation.