Elena M. Parilina

Node-consistent core for games played over event trees

We consider a class of dynamic games played over an event tree, where the players cooperate to optimize their expected joint payoff. Assuming that the players adopt the core as the solution concept of the cooperative game, we devise a node-decomposition of the imputations in the core such that each player finds it individually rational at each node to stick to cooperation rather than switching to a noncooperative strategy. We illustrate our approach with an example of pollution control.

Approximated cooperative equilibria for games played over event trees

We consider the class of stochastic games played over event trees. We suppose that the players agree to cooperate and maximize their joint payoff. To sustain cooperation over the event tree, we use trigger strategies. As we are dealing with a finite horizon, it is known that deviation from cooperation in the last stage cannot be deterred, as there is no possibility for punishing the deviator(s). Consequently, we focus on epsilon equilibria. We prove the existence of an epsilon-perfect equilibrium.

Soil acidity adaptive control problem

Problem of soil acidity regularization is modeled as stochastic adaptive control problem with a linear difference equation of the dynamics of a field pH level. Stochastic component in the equation represents an individual time variability of soil acidity of an elementary section. We use Bayesian approach to determine a posteriori probability density function of the unknown parameters of the stochastic transition process. The Kullback–Leibler information divergence is used as a measure of difference between true distribution and its estimation. Algorithm for the construction of an adaptive stabilizing control in such a linear control system is proposed in the paper. Numerical realization of the algorithm is represented for a problem of a field soil acidity control.

Stable cooperation in stochastic games

The paper considers stochastic games with random duration in the class of stationary strategies. The cooperative version for such class of stochastic games is constructed, and the cooperative solution is found. The conditions of stable cooperation for stochastic games are obtained. The principles of stable cooperation include three conditions, viz., the subgame consistency (dynamic stability), strategic stability and irrational behavior proofness of the cooperative agreement. And finally, the paper presents an example for which the cooperative agreement is found and the conditions of stable cooperation are checked.

Node-Consistent Shapley Value for Games Played over Event Trees with Random Terminal Time

We consider a class of dynamic games played over an event tree, with random terminal time. We assume that the players wish to jointly optimize their payoffs throughout the whole planning horizon and adopt the Shapley value to share the joint cooperative outcome. We devise a node-consistent decomposition of the Shapley value, which means that in any node of the event tree, the players prefer to stick to cooperation and to continue implementing the Shapley value rather than switching to noncooperation. For each node and each player, we provide two payment values, one that applies if the game terminates at that node and the other if the game continues. We illustrate our results with an example of pollution control.

Consensus in a social network with two principals

This paper considers a model of opinion dynamics in a social network with two principals, in which the members may affect the opinions of each other and their opinions evolve according to a time-homogeneous Markov chain. We study the existence of a consensus in this network for two types of influence models, namely, when the principals may or may not affect the opinions of each other directly. In addition, we find the values of social network parameters under which a consensus is reached. For the cases without a consensus in its standard definition, we introduce the notion of a consensus of the majority and find the parameter values under which it is reached. Two numerical examples illustrate the obtained theoretical results.

Strategic Support of Node-Consistent Cooperative Outcomes in Dynamic Games Played Over Event Trees

In this paper, we show that cooperative outcomes in a dynamic game played over an event tree can be supported strategically, that is, to be part of a subgame perfect e-equilibrium. A numerical example illustrates our results.

Strongly Subgame-Consistent Core in Stochastic Games

This paper investigates stochastic games on finite tree graphs. A given n-player normal-form game is defined at each node of a tree. Transition to a next node of the tree is random and depends on the strategy profile realized in a current game. We construct a cooperative solution of the game by maximizing the total expected payoff of the players. The core is used as the solution concept of the cooperative game. We introduce the definition of a strongly subgame-consistent (strongly time-consistent) core. Finally, we suggest a method for designing a cooperative distribution procedure of an imputation from the core that guarantees its strong subgame consistency.

Stable cooperation in oligopoly

We study a problem of stable cooperation on a single-product market where firms are in competitive relationship. Firms compete in quantities, but the maximum quantity of the product to be produced by any firm is bounded which is common knowledge. We assume that firms may cooperate forming coalitions, and the firms belonging to the same coalition choose their quantities to maximize the joint profit. The problem is to find a partition of the firms — a coalition structure — which is stable against unilateral deviations of any firm. For this reason, we first determine the worth of any coalition taking into account the joint profit of the firms involved, and second allocate this worth in accordance with a cooperative solution.

Price of anarchy in a linear-state stochastic dynamic game

We consider a linear-state dynamic game played over an event tree and determine analytically the price of anarchy (PoA), which is given by the ratio of player’s outcome in the cooperative game to her outcome in the noncooperative game. Next, we illustrate our findings in the context of a pollution control problem. We conduct a sensitivity analysis to assess the impact on PoA, and its lower and upper bounds, of varying the different parameter values.