This is a brief survey describing some of the recent progress and open problems in the area of cooperative games with incomplete information. We discuss exchange economies, cooperative Bayesian games with orthogonal coalitions, and issues of cooperation in noncooperative Bayesian games.

In this paper, we give a historical overview of the transition from classical game theory to epistemic game theory. To that purpose we will discuss how important notions such as reasoning about the opponents, belief hierarchies, common belief, and the concept of common belief in rationality...

In this paper, we present a matching market in which an institution has to hire a set of pairs of complementary workers, and has a quota that is the maximum number of candidates pair positions to be filled. We define a stable solution and first show that in the unrestricted institution...

A value for games with a coalition structure is introduced, where the rules guiding cooperation among the members of the same coalition are different from the interaction rules among coalitions. In particular, players inside a coalition exhibit a greater degree of solidarity than they are...

A Lyapunov-like (linear) transformation L on a Euclidean Jordan algebra V is defined by the condition $$x \in K,\enspace y\in K^*,\quad \langle x,y\rangle =0\Rightarrow \langle L(x),y\rangle=0,$$where K is the symmetric cone of V. In this paper, we give an elementary proof (avoiding Lie...

This paper contains a survey of cooperative game theory applied to a sports environment. The variety of these applications serves us as a proof of the strength of cooperative game theory introducing successful strategies in sports and explaining the behavior of different actors.

In this paper, we analyze environmental regulation based on tradable emission permits in the presence of strategic interaction in an output market with differentiated products. We characterize firms' equilibrium behavior in the permits and in the output market and we show that both firms adopt...

We present a multistage stochastic procedure that produces a fair allocation of a cake among n-person. In each step players observe the collection of the random offers (x1, …, xn), where x1 + ⋯ + xn = 1. As the proposal emerged players have to make a decision to accept it or reject it. The...

In this paper, we deal with situations arising from markets where an Internet search service provider offers a service of listing firms in decreasing order according to what they have bid. We call these ranking auction situations and introduce the corresponding TU-games. The core, as well as the...

We study games in which the number of players are large, and hence outcomes are independent of the identities of the players. Game models typically study how choices made by individual rational players determine game outcomes. We extend this model to include an implicit player — the society,...