4 Presentations

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  02:00 PM - 02:25 PM

  Dynamically Consistent Cooperative Solution of a Dynamic Game with Coalitional Blocs

  • D.W.K. Yeung, presenter, Hong Kong Shue Yan University
  • Leon Petrosyan, St.Petersburg State University

  In many real-life scenarios, groups or nations with common interest form coalition blocs by agreement for mutual support and joint actions. This paper presents a dynamic game with coalitional blocs in which common interests of players within a bloc are reflected through (i) their common preference which is not shared by players outside the bloc, (ii) resources exclusively owned and controlled by players in the bloc, and (iii) some state dynamics can only be affected by actions of players inside the bloc. The coalitional equilibrium between different blocs is derived. Dynamically consistent payoff distribution to players within each bloc is derived. A grand coalition cooperation of the coalitional blocs is studied. Dynamically consistent payoff distributions between coalitions and among players are derived for this double-level cooperation scheme. This is the first time that dynamically consistent solution is derived for coalitional bloc cooperation.

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  02:25 PM - 02:50 PM

  Cooperation with asymmetric environmental valuation and responsibility in a dynamic setting

  • Francisco Cabo, presenter, Universidad de Valladolid
  • Mabel Tidball, INRAE

  When an environmental agreement between two countries is regarded from a dynamic perspective, it is very often observed that cooperation does not lead to an immediate reward. More to the contrary, an agreement to reduce the emissions of pollutants is usually associated with lower flows of production income. However in a profitable agreement the current costs are more than compensated by a future cleaner environment. While this is true globally (for the two countries), neither the costs from lower emissions nor the value of a cleaner environment need to be
  identical for the two parts. Because the uneven benefits from cooperation are delayed, it is the cost of compliance what needs to be distributed between the signing countries. This paper analyzes a sharing mechanism satisfying two
  main properties. Firstly, a benefit-pay-principle or fairness axiom: the greater the benefit one country gets from cooperation, the greater must be its share of the costs. And secondly, assuming that the responsibility from the initial environmental problem is not even across countries, a responsibility axiom requires that a country's share of the costs increases with its responsibility. Moreover, the sharing scheme must be defined to guarantee time consistency.
  At any intermediate instant of time, no country can do better by deviating from cooperation with the sharing mechanism presented in the paper.

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  02:50 PM - 03:15 PM

  Strong time-consistent core for a class of linear-state games

  • 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

  Time consistency is an important property of any solution to a cooperative dynamic game. If the solution satisfies this property, players do not need to revise it and break a cooperative agreement. Strong time consistency is a stricter property which is applicable to cooperative set solutions. In this paper, we examine a class of linear-state games which come into use in many applications of dynamic games. Considering the core as the solution of the game, we provide sufficient conditions for its strong time consistency. In case of its inconsistency, we show how core elements can be realized using a strong time-consistent imputation distribution procedure.

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  03:15 PM - 03:40 PM

  Time-Consistency, Subgame Consistency, Subgame Perfection and Dynamic Stability of Solutions in Dynamic Games

  • Leon Petrosyan, presenter, St.Petersburg State University
  • D.W.K. Yeung, Hong Kong Shue Yan University

  In classical control theory an important property is the time-consistency of optimal solutions. In particular, Richard Bellmann’s optimality principle and dynamic programming techniques are based on this property. In dynamic games (both continuous-time and discrete-time) the notion of Subgame Perfection for Nash Equilibrium was introduced. The concept of time-consistency was extended to the analysis of cooperative dynamic games, and it happens that most solution concepts taken from classical one-shot cooperative game theory will not be time-consistent when applied to a dynamic framework. For stochastic games, the cooperative trajectory is non-unique and there can be a large set of cooperative trajectories. The term subgame-consistency was used since subgames occurring along the cooperative trajectories do not depend only on the single parameter -- time, but also on the realized random state variables. We investigate the relationships between these notions and provide examples explaining their differences.