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In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…
We study discrete two player all-pay auction with complete information. We provide full characterization of mixed strategy Nash equilibria and show that they constitute a subset of Nash equilibria of discrete General Lotto game. We show…
In this short note we give an example of a four-person finite positional game with perfect information that has no positions of chance and no Nash equilibria in pure stationary strategies. The corresponding directed graph has only one…
We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…
We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on…
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…
We present a quantum approach to a signaling game; a special kind of extensive games of incomplete information. Our model is based on quantum schemes for games in strategic form where players perform unitary operators on their own qubits of…
We study a finite-horizon two-person zero-sum risk-sensitive stochastic game for continuous-time Markov chains and Borel state and action spaces, in which payoff rates, transition rates and terminal reward functions are allowed to be…
The paper addresses a problem of sequential bilateral bargaining with incomplete information. We proposed a decision model that helps agents to successfully bargain by performing indirect negotiation and learning the opponent's model.…
We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…
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…
This paper introduces risk-revising players to a class of games with incomplete information. These players enter the game with ex ante risk preferences represented by coherent risk measures and develop time-consistent interim revisions of…
In the paper we present a model of discrete-time mean-field game with several populations of players. Mean-field games with multiple populations of the players have only been studied in the literature in the continuous-time setting. The…
It was shown in Flesch and Solan (2022) with a rather involved proof that all two-player stochastic games with finite state and action spaces and shift-invariant payoffs admit an $\epsilon$-equilibrium, for every $\epsilon>0$. Their proof…
We introduce a stochastic learning process called the dampened gradient approximation process. While learning models have almost exclusively focused on finite games, in this paper we design a learning process for games with continuous…
A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information…
This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical…
We propose a new dynamics for equilibrium selection of finite player discrete strategy games. The dynamics is motivated by optimal transportation, and models individual players' myopicity, greedy and uncertainty when making decisions. The…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of…