Related papers: Nash equilibrium and evolutionary dynamics in semi…
Social dilemmas are situations in which collective welfare is at odds with individual gain. One widely studied example, due to the conflict it poses between human behaviour and game theoretic reasoning, is the Traveler's Dilemma. The…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept…
Nash equilibria are defined using uncorrelated behavioural or mixed joint probability distributions effectively assuming that players of bounded rationality must discard information to locate equilibria. We propose instead that rational…
This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource.…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
In this paper, we consider the competitive diffusion game, and study the existence of its pure-strategy Nash equilibrium when defined over general undirected networks. We first determine the set of pure-strategy Nash equilibria for two…
We discuss stochastic dynamics of finite populations of individuals playing games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of…
Although it has been known since the 1970s that a globally optimal strategy profile in a common-payoff game is a Nash equilibrium, global optimality is a strict requirement that limits the result's applicability. In this work, we show that…
In this paper, I introduce a novel benchmark in games, super-Nash performance, and a solution concept, optimin, whereby players maximize their minimal payoff under unilateral profitable deviations by other players. Optimin achieves…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
Game Theory has been frequently applied in biological research since 1970s. While the key idea of Game Theory is Nash Equilibrium, it is critical to understand and figure out the payoff matrix in order to calculate Nash Equilibrium. In this…
Nash equilibrium has long been a desired solution concept in multi-player games, especially for those on continuous strategy spaces, which have attracted a rapidly growing amount of interests due to advances in research applications such as…
We formulate and study a two-player static duel game as a nonzero-sum discounted stochastic game. Players $P_{1},P_{2}$ are standing in place and, in each turn, one or both may shoot at the other player. If $P_{n}$ shoots at $P_{m}$ ($m\neq…
We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
The Hotelling-Downs model is a natural and appealing model for understanding strategic positioning by candidates in elections. In this model, voters are distributed on a line, representing their ideological position on an issue. Each…
We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed…
The game of \emph{Showcase Showdown} with unlimited spins is investigated as an $n$-players continuous game, and the Nash Equilibrium strategies for the players are obtained. The sequential game with information on the results of the…
We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their…