Related papers: Fluctuations around Nash Equilibria in Game Theory
In a many-to-one matching market, we analyze the matching game induced by a stable rule when firms' choice function satisfy substitutability. We show that any stable rule implements the individually rational correspondence in Nash…
Game theory is widely used as a behavioral model for strategic interactions in biology and social science. It is common practice to assume that players quickly converge to an equilibrium, e.g. a Nash equilibrium. This can be studied in…
Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they…
We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…
The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of $N$ player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article we…
We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
We study selection acting on phenotype in a collection of agents playing local games lacking Nash equilibria. After each cycle one of the agents losing most games is replaced by a new agent with new random strategy and game partner. The…
We study stochastic mean-field games among finite number of teams with large finite as well as infinite number of decision makers. For this class of games within static and dynamic settings, we establish the existence of a Nash equilibrium,…
We suggest to look at quantum measurement outcomes not through the lens of probability theory, but instead through decision theory. We introduce an original game-theoretical framework, model and algorithmic procedure where measurement…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
We propose a toy model for a stochastic description of the competition between two athletes of unequal strength, whose average strength difference is represented by a parameter $d$. The athletes interact through the choice of their…
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…
We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk…
We show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse…
We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between…
It is common to assume that agents will adopt Nash equilibrium strategies; however, experimental studies have demonstrated that Nash equilibrium is often a poor description of human players' behavior in unrepeated normal-form games. In this…
We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we…
Observable games are game situations that reach one of possibly many Nash equilibria. Before an instance of the game starts, an external observer does not know, a priori, what is the exact profile of actions that will occur; thus, he…
We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an…