相关论文: Temperatures of Robin Hood

This study introduces a novel cooperative game theory model designed to improve the United Nations' current funding mechanisms, which predominantly rely on voluntary contributions. By shifting from a Nash equilibrium framework, where member…

Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to…

Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the…

The core is a dominant solution concept in economics and cooperative game theory; it is predominantly used for profit, equivalently cost or utility, sharing. This paper demonstrates the versatility of this notion by proposing a completely…

We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the…

We propose a type of non-cooperative game, termed multi-cluster aggregative game, which is composed of clusters as players, where each cluster consists of collaborative agents with cost functions depending on their own decisions and the…

We study the transport properties of a large class of locally confined Hamiltonian systems, in which neighboring particles interact through hard core elastic collisions. When these collisions become rare and the systems large, we derive a…

Humans possess innate collaborative capacities. However, effective teamwork often remains challenging. This study delves into the feasibility of collaboration within teams of rational, self-interested agents who engage in teamwork without…

The Optional Public Goods Game is a three-strategy game in which an individual can play as a cooperator or defector or decide not to participate. Despite its simplicity, this model can effectively represent many human social dilemmas, such…

A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…

In Combinatorial Game Theory, the fundamental relation of game equivalence, denoted by $=$, is introduced early on and overrides the notion of set equality. We explore what happens if set equality is given its due before game equivalence is…

We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…

The emergence of cooperation in the thermodynamic limit of social dilemmas is an emerging field of research. While numerical approaches (using replicator dynamics) are dime a dozen, analytical approaches are rare. A particularly useful…

In this paper, we introduce a family of games called concave pro-rata games. In such a game, players place their assets into a pool, and the pool pays out some concave function of all assets placed into it. Each player then receives a…

Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…

We consider heat transfer across an arbitrary harmonic network connected to two heat baths at different temperatures. The network has $N$ positional degrees of freedom, of which $N_L$ are connected to a bath at temperature $T_L$ and $N_R$…

Several different "hat games" have recently received a fair amount of attention. Typically, in a hat game, one or more players are required to correctly guess their hat colour when given some information about other players' hat colours.…

The cordiality game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting \track{unlabeled} vertices of $G$. Admirable labels the selected vertices by $0$ and Impish by $1$, and the resulting label…

We study a type of generalized recursive game introduced by Castronova, Chen, and Zumbrun featuring increasing stakes, with an emphasis on continuous guts poker and $1$ v. $n$ coalitions. Our main results are to develop practical numerical…

Partizan subtraction games are combinatorial games where two players, say Left and Right, alternately remove a number n of tokens from a heap of tokens, with $n \in S_L$ (resp. $n \in S_R$) when it is Left's (resp. Right's) turn. The first…