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...

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,...

This paper studies situations in which companies can cooperate in order to decrease the earliest completion time of a project that consists of several tasks. This is beneficial for the client who wants the project to be completed as early as possible. The client is willing to pay more for an...

In cooperative stochastic dynamic games a stringent condition — subgame consistency — is required for a dynamically stable solution. A cooperative solution is subgame consistent if an extension of the solution policy to a situation with a later starting time and any feasible state brought...

In this note, we give a straightforward and elementary proof of a theorem by Aumann and Maschler stating that in the well-known bankruptcy problem, the so-called CG-consistent solution described by the Talmud represents the nucleolus of the corresponding coalitional game. The proof nicely fits...

We propose a theory of the interaction between knowledge and games. Epistemic game theory is of course a well-developed subject but there is also a need for a theory of how some agents can affect the outcome of a game by affecting the knowledge which other agents have and thereby affecting their...

A linear-quadratic zero-sum singular differential game, where the cost functional does not contain the minimizer's control cost, is considered. Due to the singularity, the game cannot be solved either by applying the MinMax principle of Isaacs, or by using the Bellman–Isaacs equation method....