Topic
Stochastic game
About: Stochastic game is a research topic. Over the lifetime, 9493 publications have been published within this topic receiving 202664 citations.
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Book•
14 Mar 1996
TL;DR: In this article, the authors present an algorithm for the value of a non-leavable game and the optimality equation for a two-player, zero-sum game.
Abstract: 1 Introduction.- 1.1 Preview.- 1.2 Prerequisites.- 1.3 Numbering.- 2 Gambling Houses and the Conservation of Fairness.- 2.1 Introduction.- 2.2 Gambles, Gambling Houses, and Strategies.- 2.3 Stopping Times and Stop Rules.- 2.4 An Optional Sampling Theorem.- 2.5 Martingale Convergence Theorems.- 2.6 The Ordinals and Transfinite Induction.- 2.7 Uncountable State Spaces and Continuous-Time.- 2.8 Problems for Chapter 2.- 3 Leavable Gambling Problems.- 3.1 The Fundamental Theorem.- 3.2 The One-Day Operator and the Optimality Equation.- 3.3 The Utility of a Strategy.- 3.4 Some Examples.- 3.5 Optimal Strategies.- 3.6 Backward Induction: An Algorithm for U.- 3.7 Problems for Chapter 3.- 4 Nonleavable Gambling Problems.- 4.1 Introduction.- 4.2 Understanding u(?).- 4.3 A Characterization of V.- 4.4 The Optimality Equation for V.- 4.5 Proving Optimality.- 4.6 Some Examples.- 4.7 Optimal Strategies.- 4.8 Another Characterization of V.- 4.9 An Algorithm for V.- 4.10 Problems for Chapter 4.- 5 Stationary Families of Strategies.- 5.1 Introduction.- 5.2 Comparing Strategies.- 5.3 Finite Gambling Problems.- 5.4 Nonnegative Stop-or-Go Problems.- 5.5 Leavable Houses.- 5.6 An Example of Blackwell and Ramakrishnan.- 5.7 Markov Families of Strategies.- 5.8 Stationary Plans in Dynamic Programming.- 5.9 Problems for Chapter 5.- 6 Approximation Theorems.- 6.1 Introduction.- 6.2 Analytic Sets.- 6.3 Optimality Equations.- 6.4 Special Cases of Theorem 1.2.- 6.5 The Going-Up Property of $$ \overline M $$.- 6.6 Dynamic Capacities and the Proof of Theorem 1.2.- 6.7 Approximating Functions.- 6.8 Composition Closure and Saturated House.- 6.9 Problems for Chapter 6.- 7 Stochastic Games.- 7.1 Introduction.- 7.2 Two-Person, Zero-Sum Games.- 7.3 The Dynamics of Stochastic Games.- 7.4 Stochastic Games with lim sup Payoff.- 7.5 Other Payoff Functions.- 7.6 The One-Day Operator.- 7.7 Leavable Games.- 7.8 Families of Optimal Strategies for Leavable Games.- 7.9 Examples of Leavable Games.- 7.10 A Modification of Leavable Games and the Operator T.- 7.11 An Algorithm for the Value of a Nonleavable Game.- 7.12 The Optimality Equation for V.- 7.13 Good Strategies in Nonleavable Games.- 7.14 Win, Lose, or Draw.- 7.15 Recursive Matrix Games.- 7.16 Games of Survival.- 7.17 The Big Match.- 7.18 Problems for Chapter 7.- References.- Symbol Index.
170 citations
TL;DR: In this paper, it was shown that once such doubts are introduced, all that can be justified by an appeal to rationality is one round of deletion of weakly dominated strategies, followed by iterated deletion of strategies that are strongly dominated.
169 citations
Posted Content•
TL;DR: In this paper, the authors characterize the long-run dynamics of such processes in terms of the geometry of the network, but without placing a priori restrictions on the network structure, and show that when agents interact in sufficiently small, close-knit groups, the expected waiting time until almost everyone is playing the stochastically stable equilibrium is bounded above independent of the number of agents and independently of the initial state.
Abstract: We consider processes in which new technologies and forms of behavior are transmitted through social or geographic networks. Agents adopt behaviors based on a combination of their inherent payoff and their local popularity (the number of neighbors who have adopted them) subject to some random error. We characterize the long-run dynamics of such processes in terms of the geometry of the network, but without placing a priori restrictions on the network structure. When agents interact in sufficiently small, close-knit groups, the expected waiting time until almost everyone is playing the stochastically stable equilibrium is bounded above independently of the number of agents and independently of the initial state.
169 citations
Patent•
14 Mar 2007
TL;DR: In this article, the authors present a system that allows a player to wager varying amounts on whether a player will have multiple consecutive wins, losses, or ties of a game of chance.
Abstract: A gaming method and system which allows a player to wager varying amounts on whether that player will have multiple consecutive wins, losses, or ties of a game of chance and having the option of withdrawing from a consecutive wins, loss or tie bet before reaching the number of consecutive wins, losses or ties originally selected and select a reduced payoff or to make a consecutive wins, losses or ties bet without selecting a predetermined number of consecutive wins, losses or ties and which provides a simplified arrangement for monitoring the progress of such bets made by one or more players, as well as providing a multiple outcome bet tracking system and mark matching system to protect against bet tampering.
169 citations
TL;DR: In this article, a model for evolutionary game dynamics in a growing, network-structured population is discussed, where new players can either make connections to random preexisting players or preferentially attach to those that have been successful in the past.
Abstract: We discuss a model for evolutionary game dynamics in a growing, network-structured population. In our model, new players can either make connections to random preexisting players or preferentially attach to those that have been successful in the past. The latter depends on the dynamics of strategies in the game, which we implement following the so-called Fermi rule such that the limits of weak and strong strategy selection can be explored. Our framework allows to address general evolutionary games. With only two parameters describing the preferential attachment and the intensity of selection, we describe a wide range of network structures and evolutionary scenarios. Our results show that even for moderate payoff preferential attachment, over represented hubs arise. Interestingly, we find that while the networks are growing, high levels of cooperation are attained, but the same network structure does not promote cooperation as a static network. Therefore, the mechanism of payoff preferential attachment is different to those usually invoked to explain the promotion of cooperation in static, already-grown networks.
169 citations