Related papers: A Theoretical Study of Mafia Games
In many cases the Nash equilibria are not predictive of the experimental players' behaviour. For some games of Game Theory it is proposed here a method to estimate the probabilities with which the different options will be actually chosen…
The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…
In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states.…
We present the results of detailed numerical study of a model for the sharing and sorting of informations in a community consisting of a large number of agents. The information gathering takes place in a sequence of mutual bipartite…
In mix-game which is an extension of minority game, there are two groups of agents; group1 plays the majority game, but the group2 plays the minority game. This paper studies the change of the average winnings of agents and volatilities vs.…
Game theory, as an analytical tool, is frequently utilized to analyze human behavior in social science research. With the high alignment between the behavior of Large Language Models (LLMs) and humans, a promising research direction is to…
A puzzle about prisoners trying to identify the color of a hat on their head leads to a version where there are k more hats than prisoners. This generalized puzzle is related to the independence number of the arrangement graph A(m, n) and…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…
In studies of social dynamics, cohesion refers to a group's tendency to stay in unity, which -- as argued in sociometry -- arises from the network topology of interpersonal ties between members of the group. We follow this idea and propose…
We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be…
We study the value of a two-player zero-sum game on a random matrix $M\in \mathbb{R}^{n\times m}$, defined by $v(M) = \min_{x\in\Delta_n}\max_{y\in \Delta_m}x^T M y$. In the setting where $n=m$ and $M$ has i.i.d. standard Gaussian entries,…
We study discrete preference games in heterogeneous social networks. These games model the interplay between a player's private belief and his/her publicly stated opinion (which could be different from the player's belief) as a strategic…
In this article we study the organizational structure of a large group of members of the Sicilian Mafia by means of social network analysis and an econometric analysis of link formation. Our mains results are the following. i) The Mafia…
The minority game is a simple congestion game in which the players' main goal is to choose among two options the one that is adopted by the smallest number of players. We characterize the set of Nash equilibria and the limiting behavior of…
The minority model was introduced to study the competition between agents with limited information. It has the remarkable feature that, as the amount of information available increases, the collective gain made by the agents is reduced.…
The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…
We analyze the two-player game of Knock 'em Down, asymptotically as the number of tokens to be knocked down becomes large. Optimal play requires mixed strategies with deviations of order sqrt(n) from the naive law-of-large numbers…
Condorcet's paradox is a fundamental result in social choice theory which states that there exist elections in which, no matter which candidate wins, a majority of voters prefer a different candidate. In fact, even if we can select any $k$…
We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…
We study a static game played by a finite number of agents, in which agents are assigned independent and identically distributed random types and each agent minimizes its objective function by choosing from a set of admissible actions that…