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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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TL;DR: In this article, the Shapley value is defined for games involving a fixed finite set of players, and the authors present an axiomatic development of value functions for games with a fixed number of players.
Abstract: Introduction The study of methods for measuring the “value” of playing a particular role in an n -person game is motivated by several considerations One is to determine an equitable distribution of the wealth available to the players through their participation in the game Another is to help an individual assess his prospects from participation in the game When a method of valuation is used to determine equitable distributions, a natural defining property is “efficiency”: The sum of the individual values should equal the total payoff achieved through the cooperation of all the players However, when the players of a game individually assess their positions in the game, there is no reason to suppose that these assessments (which may depend on subjective or private information) will be jointly efficient This chapter presents an axiomatic development of values for games involving a fixed finite set of players We primarily seek methods for evaluating the prospects of individual players, and our results center around the class of “probabilistic” values (defined in the next section) In the process of obtaining our results, we examine the role played by each of the Shapley axioms in restricting the set of value functions under consideration, and we trace in detail (with occasional excursions) the logical path leading to the Shapley value
488 citations
TL;DR: In this paper, the authors report laboratory data for games that are played only once, and show that a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior, which is consistent with simple intuition based on the interaction of payoff asymmetries and noisy introspection about others' decisions.
Abstract: This paper reports laboratory data for games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment in which behavior conforms nicely to predictions of the Nash equilibrium or relevant refinement. In each case, however, a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior. These contradictions are generally consistent with simple intuition based on the interaction of payoff asymmetries and noisy introspection about others' decisions.
483 citations
TL;DR: In this paper, the authors analyzed a sequential game of coalition formation when the division of the coalitional surplus is fixed and the payoffs are defined relative to the whole coalition structure and showed that any core stable coalition structure can be attained as a stationary perfect equilibrium of the game.
480 citations
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TL;DR: In this paper, the authors study allocation rules, which are functions mapping conference structures to payoff allocations, and describe how the outcome of a cooperative game might depend on which groups of players hold cooperative planning conferences.
Abstract: To describe how the outcome of a cooperative game might depend on which groups of players hold cooperative planning conferences, we study allocation rules, which are functions mapping conference structures to payoff allocations. An allocation rule is fair if every conference always gives equal benefits to all its members. Any characteristic function game without sidepayments has a unique fair allocation rule. The fair allocation rule also satisfies a balanced contributions formula, and is closely related to Harsanyi's generalized Shapley value for games without sidepayments. If the game is superadditive, then the fair allocation rule also satisfies a stability condition.
479 citations
TL;DR: In this article, the authors study allocation rules, which are functions mapping conference structures to payoff allocations, and describe how the outcome of a cooperative game might depend on which groups of players hold cooperative planning conferences.
Abstract: To describe how the outcome of a cooperative game might depend on which groups of players hold cooperative planning conferences, we study allocation rules, which are functions mapping conference structures to payoff allocations. An allocation rule is fair if every conference always gives equal benefits to all its members. Any characteristic function game without sidepayments has a unique fair allocation rule. The fair allocation rule also satisfies a balanced contributions formula, and is closely related to Harsanyi's generalized Shapley value for games without sidepayments. If the game is superadditive, then the fair allocation rule also satisfies a stability condition.
468 citations