New characteristic function for multistage dynamic games

Abstract

The finite stage dynamic n-person games with transferable payoffs are considered. The cooperative version of the game is defined, and a new approach for constructing characteristic functions in multistage games based on characteristic functions defined in stage games is proposed. It is proved that the values of this new characteristic function dominate the values of characteristic function constructed using the min-max approach. This allows constructing the subcore of the classical core in the multistage game under consideration and guarantees that this new approach leads to time-consistent (works L. Petrosyan, G. Zaccour, 2003; L. Petrosyan, 1991) and in some cases strongly time-consistent solutions (paper L. Petrosyan, 1993). The example is provided showing the construction of this newly defined characteristic function and the time-consistency and strong time-consistency of the core.

Cooperative Solutions in Multi-Star Network Games

“…(Petrosyan and Bulgakova, 2020) is dedicated to the study of multi-stage games with pairwise interactions under the consideration of complete graphs, constructing characteristic functions, and calculating Shapley values. In (Bulgakova, 2019) and (Pankratova, 2018), studies on the construction of the characteristic function are carried out. (Hernandez, Munoz-Herrera and Sanchez, 2013) considered the interaction model between cooperation and coalition in network games.…”

Cooperation in the Multi-Agent System with Different Types of Interactions

“…This paper researches the new equilibrium principle of behavior in terms of "nperson prisoner's dilemma" game. We investigate the new characteristic function (Petrosyan, 2019) to consider the different optimality principles in the dynamic "n-person prisoner's dilemma" model, particularly the subcore of dynamic game (Petrosyan and Pankratova, 2018) that contains the Shapley value.…”