Related papers: Statistical Games
We consider multiplayer stochastic games in which the payoff of each player is a bounded and Borel-measurable function of the infinite play. By using a generalization of the technique of Martin (1998) and Maitra and Sudderth (1998), we show…
We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
Conventional game theory assumes that players are perfectly rational. In a realistic situation, however, players are rarely perfectly rational. This bounded rationality is one of the main reasons why the predictions of Nash equilibrium in…
In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…
The paper studies one-shot two-player games with non-Bayesian uncertainty. The players have an attitude that ranges from optimism to pessimism in the face of uncertainty. Given the attitudes, each player forms a belief about the set of…
Bayesian games model interactive decision-making where players have incomplete information -- e.g., regarding payoffs and private data on players' strategies and preferences -- and must actively reason and update their belief models (with…
Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…
Stochastic two-player games model systems with an environment that is both adversarial and stochastic. The adversarial part of the environment is modeled by a player (Player 2) who tries to prevent the system (Player 1) from achieving its…
We introduce a new paradigm for game theory -- Bayesian satisfaction. This novel approach is a synthesis of the idea of Bayesian rationality introduced by Aumann, and satisfaction games. The concept of Bayesian rationality for which, in…
Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and…
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
Empirically, many strategic settings are characterized by stable outcomes in which players' decisions are publicly observed, yet no player takes the opportunity to deviate. To analyze such situations in the presence of incomplete…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
Classical results of Decision Theory, and its extension to a multi-agent setting: Game Theory, operate only at the associative level of information; this is, classical decision makers only take into account probabilities of events; we go…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
We introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been…