Related papers: Berk-Nash Rationalizability
Complexity and limited ability have profound effect on how we learn and make decisions under uncertainty. Using the theory of finite automaton to model belief formation, this paper studies the characteristics of optimal learning behavior in…
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 present a framework that incorporates the idea of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is characterized, in general, by its (Nash) equilibria in feedback form. However,…
The problem of making sequential decisions in unknown probabilistic environments is studied. In cycle $t$ action $y_t$ results in perception $x_t$ and reward $r_t$, where all quantities in general may depend on the complete history. The…
A description of the environment cognition process by intelligent systems with a fixed set of system goals is suggested. Such a system is represented by the set of its goals only without any models of the system elements or the environment.…
This article introduces a class of $Nash$ games among $Stackelberg$ players ($NASPs$), namely, a class of simultaneous non-cooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a…
The Nash equilibrium paradigm, and Rational Choice Theory in general, rely on agents acting independently from each other. This note shows how this assumption is crucial in the definition of Rational Choice Theory. It explains how a…
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…
The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of two formalisms used for different purposes and in different…
We consider any network environment in which the "best shot game" is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A…
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…
Level-k thinking has been widely applied as a solution concept for games in normal form in behavioral and experimental game theory. We consider level-k thinking in games in extensive form. Player's may learn about levels of opponents'…
Federated learning is a distributed learning paradigm where multiple agents, each only with access to local data, jointly learn a global model. There has recently been an explosion of research aiming not only to improve the accuracy rates…
This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…
Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are…
Since the 1990s, AI systems have achieved superhuman performance in major zero-sum games where "winning" has an unambiguous definition. However, most social interactions are mixed-motive games, where measuring the performance of AI systems…
This note shows that under the unrestricted domain, there exists a choice liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A…
Here we present a ground-breaking new postulate for game theory. The first part of this postulate contains the axiomatic observation that all games are created by a designer, whether they are: e.g., (dynamic/static) or…
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…
We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…