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The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…
In an earlier experiment, participants played a perfect information game against a computer, which was programmed to deviate often from its backward induction strategy right at the beginning of the game. Participants knew that in each game,…
Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of…
Games are complex, multi-faceted systems that share common elements and underlying narratives, such as the conflict between a hero and a big bad enemy or pursuing a goal that requires overcoming challenges. However, identifying and…
Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…
Inspired by applications such as supply chain management, epidemics, and social networks, we formulate a stochastic game model that addresses three key features common across these domains: 1) network-structured player interactions, 2)…
Trust and reciprocation of it form the foundation of economic, social and other interactions. While the Trust Game is widely used to study these concepts for interactions between two players, often alternating different roles (i.e.,…
Consider the following probabilistic one-player game: The board is a graph with $n$ vertices, which initially contains no edges. In each step, a new edge is drawn uniformly at random from all non-edges and is presented to the player,…
A closed form is found for the expected number of rolls of a fair n-sided die until three consecutive increasing values are seen. The answer is rational, and the greatest common divisor of the numerator and denominator is given in terms of…
An-ever increasing number of social media websites, electronic newspapers and Internet forums allow visitors to leave comments for others to read and interact. This exchange is not free from participants with malicious intentions, which do…
Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…
We study random convex cones defned as positive hulls of $d$-dimensional random walks and bridges. We compute expectations of various geometric functionals of these cones such as the number of $k$-dimensional faces and the sums of conic…
Understanding the evolution of human social systems requires flexible formalisms for the emergence of institutions. Although game theory is normally used to model interactions individually, larger spaces of games can be helpful for modeling…
Noga Alon and Yaakov Malinovsky recently studied the following game: you start at 0, and keep rolling a fair standard die, and add the outcomes until the sum happens to be prime. We generalize this in several ways, illustrating the power of…
Schelling's famous model of segregation assumes agents of different types who would like to be located in neighborhoods having at least a certain fraction of agents of the same type. We consider natural generalizations that allow for the…
Using a probabilistic model, based on random walks on the additive group $\mathbb{Z}/m\mathbb{Z}$, we prove that the values of certain real character sums are uniformly distributed in residue classes modulo $m$.
We study the mathematical properties of probabilistic processes in which the independent actions of $n$ players (`causes') can influence the outcome of each player (`effects'). In such a setting, each pair of outcomes will generally be…
When selfish users share a road network and minimize their individual travel costs, the equilibrium they reach can be worse than the socially optimal routing. Tolls are often used to mitigate this effect in traditional congestion games,…
TV series such as HBO's Game of Thrones have seen a high number of dedicated followers, mostly due to the dramatic murders of the most important characters. In our work, we try to predict killer and victim pairs using data about previous…
Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and…