4 présentations

• 
  16h10 - 16h35

  Time consistent dynamic bargaining in continuous time with asymmetric players

  • Jesus Marin-Solano, prés., Universitat de Barcelona
  • Anna Castañer, Universitat de Barcelona
  • Carmen Ribas, Universitat de Barcelona

  A dynamic Nash bargaining procedure is studied in a continuous time setting. Decision rules of players are derived as the maximizers of a Nash welfare function. Special attention is paid to the choice of the threat point in case of disagreement. Agents can arrive to a partial commitment, in the sense that, if they decide not to cooperate at a given time, the threat is that they will not cooperate along a fixed and known time period. Attention is centered in the limit when this time period goes to zero. This means that agents do not make any commitments for the future. The solution obtained in that case, if it exists, becomes subgame perfect, avoiding in this way the time/dynamic inconsistency problems arising in previous proposals of Nash bargaining solutions in differential games. The theoretical approach is then applied to two common property resource games with asymmetric players. Asymmetries can be the result of using different utility functions and/or different discount rates. In particular, harvest rates and steady states are compared for different solution concepts in a renewable resource model with logarithmic utilities for both players. Analytical expressions are also derived in the problem of management of a common property nonrenewable resource with general isoelastic utilities.

• 
  16h35 - 17h00

  Dynamic games applied to common resources: modeling and experimentation.

  • Murielle Djiguemde, prés., CEE-M, Univ. Montpellier, CNRS, INRA, SupAgro
  • Dimitri Dubois, CEE-M, Univ. Montpellier, CNRS, INRA, SupAgro
  • Mabel Tidball, INRAE

  We study the exploitation behavior of two symmetrical farmers using groundwater table as in Rubio & Casino (2003), where water extraction is the only input in the production process of these farmers, and the dynamic is given by the evolution of the level of the water table. In our model, strategic interaction is introduced through extraction costs which negatively depend on the level of the water table. We made the assumption that the groundwater has a flat bottom, parallel sides, and that its natural recharge is provided by a constant and positive amount of rain. Another assumption is that farmers behave non cooperatively, by maximizing their actualized utilitarian criteria.

  We study this model in continuous time with an infinite horizon, and consider the equilibrium paths of the four following types of behavior : myopic, feedback, open-loop and social optimum. We also studied the same model in discrete time in order to see if our results will approch those in continuous time. Unlike some articles in the literature that find different results between continuous time and discrete time, we found that the discrete time model gives results equivalent to those of the continuous time, but with the condition that discretization in time is small enough.

  We test the behaviors using two different protocols in the laboratory (experimental economics) for both treatments in continuous and discrete time.

  References
  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.

• 
  17h00 - 17h25

  Strategic inaction: Asymmetric feedback Nash equilibria in a symmetric mitigation game

  • Florian Wagener, prés., University of Amsterdam
  • Colin Rowat, Department of Economics, University of Birmingham

  We study a symmetric linear-quadratic mitigation game. To prevent a stock of pollutants to increase exponentially, players have to perform costly mitigation activities. If the stock grows slowly, there is a symmetric stationary Nash equilibrium in linear strategies. If the rate of growth is however sufficiently large, two additional non-symmetric stationary Nash equilibria appear. These are characterised by one of the players reducing its mitigation efforts relative to the symmetric benchmark, forcing the other player to increase its efforts. We show that this behaviour is the outcome of a reasonable learning process. Finally, we demonstrate that there is a family of non-stationary Nash equilibria that can bring the play back to the more efficient symmetric situation.

• 
  17h25 - 17h50

  Subgame Perfect Nash Equilibrium as solution of an optimal control problem

  • Juan Pablo Rincon-Zapatero, prés., Universidad Carlos III de Madrid

  The computation of Nash equilibrium in differential games is a difficult task, due to the interactions in the players' strategies. A class of games, known as Potential Games, has the feature that the open loop Nash equilibrium is the solution of a suitable single-player control problem. This facilitates the analysis of the equilibrium and allow to use standard techniques of Control Theory to prove existence and to characterize the solution. Unfortunately, strategies based on open loop rules are most often not temporally consistent, in the sense that they prescribe suboptimal solutions at intermediate stages of the game. Feedback rules prevent this difficulty, but the study of Nash equilibrium in this case is much more difficult. To our knowledge, the problem of characterizing Subgame Perfect Nash Equilibrium as the solution of a control problem has not been addressed in the literature. We develop in this paper a method for doing this and show its applicability in a problem arising in economics, when noncooperative players exploits a resource in common access.