Game theory and agent-based modeling augmentation of the “rational inattention” concept.

This part of project is aimed at studying coordination of agents when they are allowed to endogenously choose what information to process. In other words, these agents do not just passively receive signals, they actively choose what to pay attention to. This research builds on the rational inattention in Sims (2003), which is already an extremely highly cited paper, yet very few researchers followed directly in the way rational inattention was proposed. We will introduce rational inattention to game-theoretical setups. Not only we apply this feature to standard noncooperative games with Nash equilibria, we will also study bargaining and communication in two-person games. We assume that several classical results of game theory, such as Betrand paradox, might be altered, when the endogenous information is introduced. What changes in the game’s structure is that we add a new mechanism of coordination “how agents process information”. This topic has been particularly important in recent years, since coordination issues are by many economists considered to be the main drivers of financial crisis.

Cooperative games based on restricted information sharing

We plan to extend the methods for evaluating coalition games of networks by the analysis of the evolution of information nets, depending on real coalition formation. We apply the Coalitional Skill Games on collective action that depend on work with information. We examine the possibility to estimate the coalition capacity of a net using the intersectional dimensions of graphs technique.

Possibilities of using the techniques of the cooperative game theory, especially the technique Values of Games (Shapley & another) for the analysis of the information price

The value of information, no matter how measured, may increase or decrease in the context of other information. This creates a situation parallel to cooperative games. In the project, we will test the possibility of the decomposition of a cooperative game to the sum of games with different complexity. Formally, for a characteristic function v of a game: v(S) = Σ Lk(S), where Lk(S) is a linear function of values dependent on sub-coalitions S of size k. For the theory of information, we expect the contribution in a possibility to measure quantitatively gains and losses caused by simplification of a concrete prediction task, compared to the acceptation of its full complexity. The approach will be an alternative step towards non-atomic games. In the literature they are understood as a limit of complicated finite games, here alternatively as a limit of simple infinite games with bounded Lk. Further research will focus on the approximation of computational complexity of evaluation of classes of games with restricted measure of complexity, i.e. fulfilling Lk = 0 for large k.

Fuzzy cooperation game theory

The main attention will be paid to the analysis of the influence of various types of uncertainty and vagueness in input data on the stability of cooperation among agents, and on the determinism of the expected results.

Public good games with complementarities and spillovers

This part of the project investigates non-cooperative games of agents who produce public goods out of complementary inputs in the presence of input and output spillovers. A first particular problem is how the Stackelberg leader exploits commitment power by implementing an arbitrary structure of contributions in these games. We aim to show that since the equilibrium provision and the players' utilities are discontinuous and non-monotonic if income is redistributed in these games, a valuation paradox exists. This research thus aims to demonstrate that the leader benefits from commitment not only for the usual reasons identified in neutral allocations, but also from the power to induce an arbitrary structure of the contribution profile. In addition, this power generates extra gains through voluntary transfers from the follower. These effects exist only in the joint presence of non-substitutable inputs, an opportunity for both agents to contribute to all inputs, and the non-resaleability of the inputs. A second problem is to build explicit spatial microfoundations for the functional forms used in the non-cooperative game-theoretic analysis of inter-jurisdictional public spending spillovers. This part of the project should build a model that distinguishes between three stages: multiple public inputs (intermediary goods) production, multiple public outputs (final goods) production with asymmetries and aggregation, and their consumption with asymmetries and preferences for variety. It should identify conditions for the different combinations of features to be isomorphic. Additionally, it should analyze which interactions of the inter-jurisdictional spillovers with non-additive aggregations lead to asymmetrically structured demands in Nash equilibrium.