Related papers: Blackwell Equilibrium in Repeated Games
Cooperation through repetition is an important theme in game theory. In this regard, various celebrated ``folk theorems'' have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
A real-valued function $\varphi$ that is defined over all Borel sets of a topological space is \emph{regular} if for every Borel set $W$, $\varphi(W)$ is the supremum of $\varphi(C)$, over all closed sets $C$ that are contained in $W$, and…
We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by…
We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from…
We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no…
It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…
We study multiplayer Blackwell games, which are repeated games where the payoff of each player is a bounded and Borel-measurable function of the infinite stream of actions played by the players during the game. These games are an extension…
While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
The Team-maxmin equilibrium prescribes the optimal strategies for a team of rational players sharing the same goal and without the capability of correlating their strategies in strategic games against an adversary. This solution concept can…
Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage…
We study infinitely repeated games in settings of imperfect monitoring. We first prove a family of theorems that show that when the signals observed by the players satisfy a condition known as $(\epsilon, \gamma)$-differential privacy, that…
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…
The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…
Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…
We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…
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…
Under the assumption of complete rationality, Nash equilibrium is the only reasonable strategy (set) of the finitely repeated prisoner's dilemma. In fact, some strategies only slightly deviate from the so-called rationality, and the…