4 Presentations

• 
  09:00 AM - 09:25 AM

  Construction of M-strongly time-consistent subcore in the game with spanning tree

  • Yin Li, presenter,
  • Liyang Wu, Herzen State Pedagogical University of Russia, St.Petersburg, Russia

  In the paper the multistage N-person minimum cost spanning tree game is considered. The cooperative behavior of players is defined. Selecting strategies, players build a minimum cost spanning tree at each stage. On the bases of values of characteristic function, a new characteristic function V is constructed for each coalition in subgames. The function V is defined as in [L. A. Petrosjan, Y. B. Pankratova, 2017]. With the help of this newly constructed characteristic function, an analogue of the core is defined. This analogue of the core can be considered a new optimality principle. It is proved that this constructed optimality principle has the property of M-strongly time-consistent in the game with spanning tree.

• 
  09:25 AM - 09:50 AM

  Mechanisms for Cooperative Truck Routing

  • Ioannis Kordonis, presenter, NTUA
  • Aristotelis-Angelos Papadopoulos, USC
  • Maged Dessouky, USC
  • Petros Ioannou, USC

  Freight transport vehicles represent a significant part of the road network load, especially in roads near ports or commercial hubs. Today routing decisions are made in an uncoordinated, selfish manner and affect travel times, pollution and fuel consumption of both trucks and passenger vehicles. This work studies the problem of designing incentive schemes for the truck drivers inducing cooperative behaviors and leading to an efficient use of the road network. At first, static models are considered. The basic characteristics of the mechanisms we design are budget balance, voluntary participation, and the fact that they do not penalize the truck drivers compared to the user equilibrium. We then move to models with many time intervals, in which the drivers choose both their departure time and their route. We design a coordination-incentive scheme where the truck drivers declare their desired departure time and the coordinator provides suggestions including a suggested departure time and a suggested route, as well as a monetary incentive or fee. For this case, in addition to the other requirements, it is necessary to ensure that the mechanism induces a truthful revelation of the preferred departure times. In all cases, we give a special emphasis on the fairness of the outcomes of the designed mechanisms. Efficient algorithms for the computation of the suggested routes and fees are also presented. Finally, the mechanisms designed are tested in a medium scale network (the Sioux-Falls network). The numerical results illustrate that the proposed mechanisms may approach the efficiency of the SO solution, while concurrently offering individual incentives for participation.

• 
  09:50 AM - 10:15 AM

  On the existence of IDP-core in Cooperative Differential Games

  • Ovanes Petrosian, presenter, Student, Saint-Petersburg State University
  • Victor Zakharov, Saint Petersburg University

  Presentation is devoted to study the new cooperative solution for differential games called IDP-core. It is proved that this new cooperative solution is a subset of Core in differential game and possesses the property of strong time consistency by construction.

  Concept of time consistency of cooperative solutions was mathematically formalized by L. Petrosyan [3]. In [4], he introduced the notion of imputation distribution procedure (IDP), which is used for constructing time consistent solutions.

  Notion of IDP-core was introduced in the paper [1]. In this work, we consider cooperative differential game with transferable payoffs and study non-emptiness conditions of IDP-core presented in [1]. In order to do that we use the approach proposed in [2] and used for Core and SC-core in static TU-cooperative games. Corresponding theorem for n-player differential game is proved and special conditions for a case of 3-players differential game are presented.

  V. Zakharov in [2] proposed necessary and sufficient conditions for non-emptiness of Core, which simplify test whether single-point solutions, such as Shapley's vector, Banzaf's influence index and others, belong to Core. The approach implies that non-emptiness property of Core can be verified by solving the linear programming problem constructed using a system of constrains from definition of Core.

  References:
  [1] O. Petrosian, E. Gromova, S. Pogozhev. Strong Time-consistent Subset of Core in Cooperative Differential Games with Finite Time Horizon // Mathematical Game Theory and its Applications. 2016. V. 8. N. 4. P. 79-106.
  [2] V. Zakharov, O-Hun Kwon. Linear programming approach in cooperative games // J. Korean Math. Soc. 1997. V. 34. N 2. P. 423-435.
  [3] L. Petrosyan Time-consistency of solutions in multi-player differential games // Vestnik Leningrad State University. 1977. V. 4. N. 19. P. 46-52.
  [4] L. Petrosyan, N. Danilov Stability of solutions in non-zero sum differential games with transferable payoffs // Vestnik Leningrad State University. 1979. V. 1. P. 52-79.

• 
  10:15 AM - 10:40 AM

  Faking Patience in a Stochastic Prisoners' Dilemma

  • Elena Parilina, presenter, Saint-Petersburg State University
  • Alessandro Tampieri, University of Florence Department of Economics

  This paper analyses a stochastic Bayesian prisoners' dilemma where players' discount factor is private information. We consider an infinitely repeated game where two states of the world may occur. Players may choose a cooperative behaviour in both states (patient), in none of the states (impatient) or in one state only (mildly patient). There are two phases in the game: during the first phase players update information about the other players discount factors, in the second phase they realise the behaviour strategies depending on the beliefs which are formed by the end of the first phase. The presence of different states of the world affects the strategic role of beliefs. A mildly patient player has an incentive in "faking patience", which increases with the competitor's belief that the player is patient. Interestingly, this effect prevents cooperative equilibria to occur when the belief in patience is strong.