Related papers: Random Initialization Solves Shapley's Fictitious …
We study a Stackelberg variant of the classical discrete-time Dynkin game, in which Player 1 (the leader) commits to a stopping strategy first and Player 2 (the follower) responds optimally. This leader-follower structure induces an optimal…
We study the following game. Three players start with initial capitals of $s_{1},s_{2},s_{3}$ dollars; in each round player $P_{m}$ is selected with probability $\frac{1}{3}$; then \emph{he} selects player $P_{n}$ and they play a game in…
The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called \emph{weak saddle}. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence,…
Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…
In the framework of finite games in extensive form with perfect information and strict preferences, this paper introduces a new equilibrium concept: the Perfect Prediction Equilibrium (PPE). In the Nash paradigm, rational players consider…
We simulate behaviour of two independent reinforcement learning algorithms playing the Crawford and Sobel (1982) game of strategic information transmission. We adopt memoryless algorithms to capture learning in a static game where a large…
The term rational has become synonymous with maximizing expected payoff in the definition of the best response in Nash setting. In this work, we consider stochastic games in which players engage only once, or at most a limited number of…
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the…
In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by…
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.…
We introduce set packing games as an abstraction of situations in which $n$ selfish players select subsets of a finite set of indivisible items, and analyze the quality of several equilibria for this class of games. Assuming that players…
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,…
When modeling robot interactions as Nash equilibrium problems, it is desirable to place coupled constraints which restrict these interactions to be safe and acceptable (for instance, to avoid collisions). Such games are continuous with…
We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large $N$-player stochastic differential games. Following the idea of fictitious play, we recast the $N$-player game into $N$ decoupled…
Deception plays a critical role in many interactions in communication and network security. Game-theoretic models called "cheap talk signaling games" capture the dynamic and information asymmetric nature of deceptive interactions. But…
Counterfactual Regret Minimization (CFR) and its variants are widely recognized as effective algorithms for solving extensive-form imperfect information games. Recently, many improvements have been focused on enhancing the convergence speed…
Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…