The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexi...

In this paper we review some recent results on non-cooperative and semicooperative differential games. For the n-person non-cooperative games in one-space dimension, we consider the Nash equilibrium solutions. When the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic, we show that the weak solution of a corresponding system of hyperbolic conservation laws deter...

Numerous studies have shown that playing violent video games alone increases subsequent aggression. However, social game play is becoming more popular than solo game play, and research suggests cooperative game play is beneficial for players. The current studies explore the effects of cooperative game play on player’s subsequent aggressive behaviors toward video game partners (Experiment 1) and...

We examine the impact of independent agents failures on the solutions of cooperative games, focusing on totally balanced games and the more speci c subclass of convex games. We follow the reliability extension model, recently proposed in [1] and show that a (approximately) totally balanced (or convex) game remains (approximately) totally balanced (or convex) when independent agent failures are ...

Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the reliability extension, each agent only “survives” with a certain probability, and a coalition’s value is the probability that its surviving members would be a win...

In certain multi-agent systems, the interactions between agents result in the formation of relationships, which can be leveraged for cooperative or collaborative activities. These relationships generally constrain individual-agent actions, since relationships imply that at least one contract (or mutual agreement) between the agents must exist. There is always some uncertainty as to whether or n...

The chief problem in the theory of the general n-person game seems to be that of determining the proper definition of a solution for them. The cooperative theories in which the players are expected to form coalitions, developed by von Neumann-Morgenstern, Shapley and others, have the shortcoming that the notion of solution does not give much insight into how the games should be played. The coop...

We examine a solution concept, called the “value,” for n-person strategic games. In applications, the value provides an a-priori assessment of the monetary worth of a player’s position in a strategic game, comprising not only the player’s contribution to the total payoff but also the player’s ability to inflict losses on other players. A salient feature is that the value takes account of the co...

I introduce cooperative product games (CPGs), a cooperative game where every player has a weight, and the value of a coalition is the product of the weights of the players in the coalition. I only look at games where the weights are at least 2. I show that no player in such a game can be a dummy. I show that the game is convex, and therefore always has a non-empty core. I provide a simple metho...

Parrondo’s paradox [1–4] shows that the combination of two losing strategies can lead to a winning result. The paradox can be phrased in terms of very simple gambling games in which some unit (say, 1 euro) is won or lost with a given probability. We can imagine that the games consist on tossing different biased coins and that a “capital” C(t) is built. Every time a game is played (a coin is tos...