Related papers: Does Nash Envy Immunity
In a society of multiple individuals, if everybody is only interested in maximizing his own payoff, will there exist any equilibrium for the society? John Nash proved more than 50 years ago that an equilibrium always exists such that nobody…
We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players'…
In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an $\epsilon$-Nash equilibrium if no player can gain more than $\epsilon$ by…
Envy, the inclination to compare rewards, can be expected to unfold when inequalities in terms of payoff differences are generated in competitive societies. It is shown that increasing levels of envy lead inevitably to a self-induced…
We extend the study of learning in games to dynamics that exhibit non-asymptotic stability. We do so through the notion of uniform stability, which is concerned with equilibria of individually utility-seeking dynamics. Perhaps surprisingly,…
In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain…
We consider solutions of normal form games that are invariant under strategic equivalence. We consider additional properties that can be expected (or be desired) from a solution of a game, and we observe the following: - Even the weakest…
We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are…
We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a…
This paper proposes a co-evolutionary model of directed graphs and three opinions, i.e., conservative$(+)$, neutral$(\odot)$ and liberal$(-)$. Agents update both opinions and social relationships with bias. We find that an emergent game…
A noncooperative differential (dynamic) game model of opinion dynamics is proposed. In this game, the agents' motives are shaped by their expectations of the nature of others' opinions as well as how susceptible they are to get influenced…
In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the…
Noncooperative games with uncertain payoffs have been classically studied under the expected-utility theory framework, which relies on the strong assumption that agents behave rationally. However, simple experiments on human decision makers…
In this paper, I prove that existence of pure-strategy Nash equilibrium in games with infinitely many players is equivalent to the axiom of choice.
Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the…
In this paper we present a new competitive packet routing model with edge priorities. We consider players that route selfishly through a network over time and try to reach their destinations as fast as possible. If the number of players who…
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…
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…
Due to the lack of coordination, it is unlikely that the selfish players of a strategic game reach a socially good state. A possible way to cope with selfishness is to compute a desired outcome (if it is tractable) and impose it. However…