4 Presentations

• 
  02:00 PM - 02:30 PM

  A discrete time LQ Stackelberg game modelling fishing in presence of a poacher

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

  We analyse the simplest linear quadratic Stackelberg dynamic game of extraction of a fishery by two players: a far-sighted Owner of the lake and a myopic Poacher. Obviously, the interpretation of the game implies that there are linear state-dependent constraints on players' decisions. Besides of being far-sighted, the Owner is the Stackelberg leader. We consider the feedback information structure of both players, while the Poacher also knows the current decision of the Owner, who is the first mover.

  If the game is one stage only, the informational advantage of the Owner, results in the fact that his catch and payoff are larger than the Poacher's.

  If the game has two stages, the far-sightedness of the Leader becomes costly---for certain levels of the initial biomass of fish, his first-stage catch, payoff and value function are substantially lower than Poacher's. Besides, the equilibrium strategies are discontinuous for both players and the Owner's optimal strategy is nonunique, although the value function of the Owner is continuous and unique.

  Moreover, the value function of the Owner is not monotone in the initial biomass of fish even in one stage.

  By this example, we illustrate difficulties which appear in calculation of Stackelberg equilibria in presence of contraints which may be active at the optimum.

  We also compare these myopic-follower-Stackelberg equilibria to the symmetric Nash equilibria in the same game.

• 
  02:30 PM - 03:00 PM

  Optimal and Markov-perfect Nash equilibria in harvesting age-structured populations

  • Olli Tahvonen, University of Helsinki, Department of Economics, Department of Forest Sciences
  • Martin Quaas, presenter, Leipzig University

  We specify an analytically solvable age-structured harvesting model for collectively optimal and Markov-perfect Nash equilibria in both deterministic and stochastic settings. The model has any number of age-classes and is assumed to be harvested from one or two age classes. The collectively optimal harvests are obtained in closed form as functions of the number of individuals in the given age class. The existence of sustainable solutions is shown to depend on fundamental biological factors and rate of discount in addition to the internal delays in the age-structured system. In a symmetric game all actors harvest both age classes and the existence of sustainable Nash equilibrium depends on the objective functional properties besides the rate of discount. In an asymmetric game, the sustainability depends on how the number of actors are divided into groups harvesting population age classes in different locations. The collectively optimal and Nash equilibria are shown to be globally asymptotically stable for optimal feedback solutions. Stochastic recruitment makes harvesting more conservative in both the optimal solution and various Nash equilibria.

• 
  03:00 PM - 03:30 PM

  A model of river pollution as a dynamic game with network externalities

  • Artem Sedakov, presenter, Saint Petersburg State University
  • Han Qiao, School of Economics and Management, University of Chinese Academy of Sciences
  • Shouyang Wang, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

  In network games, a network is an important attribute of players' strategies: each player adopts her behavior not only by taking into account standard information about her opponents such as objectives, game dynamics, and information structure; but she also evaluates the communication structure of players represented by the network. We investigate a dynamic game with network externalities in which a state variable of each player is influenced by her own decision and the decisions of her predecessors in the network. For the game under consideration, we identify Nash equilibrium and cooperative behavior. Next, we use our findings to take in the important environmental problem of river pollution. We analyze this model in detail by incorporating a firm's location and analytically comparing equilibrium and cooperative behavior.

• 
  03:30 PM - 04:00 PM

  Strong rarity value in view of hysteresis in an ETP-ESP fishery game model

  • Reinoud Joosten, presenter, University of Twente

  ETP-ESP are stochastic games with endogenous transition probabilities and endogenous state payoffs, i.e., depend on the action choices made by the players in the past. These stochastic games developed from games with frequency dependent stage payoffs in a series of generalizations inspired by efforts to model replenishable resource extraction games such as fishery games.
  Strong rarity value in a fishery is a phenomenon In which an increase in scarcity or rarity of a species, and the subsequent decrease in landing sizes, is more than compensated by price effects for the exploiters of the resource. Simply stated, despite decreasing catches and increasing search costs the profits of the agents (continue to) grow if the resource is sufficiently scarce. Rarity value is well documented in the context of managing endangered species where it is seen as a major if not fatal threat to the survival of the species at hand. A real world candidate of this phenomenon if fisheries might be bluefin tuna.
  Hysteresis in the same context can be seen as a regime shift in which overfishing moves the system into a stable low resource-level state after some time, but it takes a surprising amount of time, certainly much longer than the time to get into this stable state, for the system to move out of it again if measures to restore the resource are adopted.
  Recent progress in the speed of algorithms to find large sets of feasible limiting average rewards in ETP-ESP games, and the advent of an algorithm to establish threat points in the same class enable us to do an analysis of strong rarity value if the players are able to manipulate the system into a temporarily stable state in which the resource is made sufficiently scarce in order to profit from this optimally. The evaluation criterion underlying our analysis is the limiting average reward criterion, i.e., agents care for their long term average payoffs. Our method of analysis is closely related to the dominant mode of analysis for repeated games, i.e., we derive Folk-Theorem type of results.