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Showing papers on "Stochastic game published in 1979"


Journal ArticleDOI
TL;DR: In this paper, two abstract game models of coalition formation are proposed and the core and dynamic solution of these abstract games are studied, and the predictions of these models are characterized for games with side payments using various payoff solution concepts such as individually rational payoffs, the core, the Shapley value and the bargaining set M1(i).
Abstract: This paper deals with the question of coalition formation inn-person cooperative games. Two abstract game models of coalition formation are proposed. We then study the core and the dynamic solution of these abstract games. These models assume that there is a rule governing the allocation of payoffs to each player in each coalition structure called a payoff solution concept. The predictions of these models are characterized for the special case of games with side payments using various payoff solution concepts such as the individually rational payoffs, the core, the Shapley value and the bargaining set M1 (i). Some modifications of these models are also discussed.

198 citations


Journal ArticleDOI
TL;DR: It is shown that if a strategy p meets the inclusive fitness criterion this is necessary but not sufficient to ensure that it meets the personal fitness criterion, and ESS's are given for the Hawk-Dove game and the War of Attrition.

97 citations


Posted Content
TL;DR: In this paper, the players in games of incomplete information are not necessarily Bayesian, i.e., a player does not necessarily have any prior probability distribution as to what game is being played.
Abstract: Unlike in the traditional theory of games of incomplete information, the players here arenot Bayesian, i.e. a player does not necessarily have any prior probability distribution as to what game is being played. The game is infinitely repeated. A player may be absolutely uninformed, i.e. he may know only how many strategies he has. However, after each play the player is informed about his payoff and, moreover, he has perfect recall. A strategy is described, that with probability unity guarantees (in the sense of the liminf of the average payoff) in any game, whatever the player could guarantee if he had complete knowledge of the game.

59 citations


Journal ArticleDOI
TL;DR: In contrast to the known fact that there are problems based on a finite state space for which no stationary family of strategies is at all good, this article showed that there always exist £-optimal Markov families (in which the strategy depends only on the current state and the number of times that state has been previously visited).
Abstract: In contrast to the known fact that there are gambling problems based on a finite state space for which no stationary family of strategies is at all good, in every such problem there always exist £-optimal Markov families (in which the strategy depends only on the current state and time) and also t-optimal tracking families (in which the strategy depends only on the current state and the number of times that state has been previously visited). More generally, this result holds for all finite state gambling problems with a payoff which is shift and permutation invariant.

29 citations


Journal ArticleDOI
TL;DR: The payoff constitutes an object of value for the players, or the stakes of the game, the disposition of which becomes a primary focus of bargaining among them as mentioned in this paper, and this is often interpreted to mean that they pursue strategies intended to maximize their individual shares of the available payoff.
Abstract: Central both to formal theories of coalition formation and many, actual, collective decision-making processes is the distribution of some reward, or payoff as it is commonly called, among those participants able to control a decision. The payoff constitutes an object of value for the players, or the stakes of the game, the disposition of which becomes a primary focus of bargaining among them. It is usual to assume that participants in coalition-forming contexts are rational actors, and this is often interpreted to mean that they pursue strategies intended to maximize their individual shares of the available payoff. Theories based upon this general structure have furnished a variety of important propositions, focusing mostly upon the composition of winning coalitions.

18 citations


Journal ArticleDOI
TL;DR: In this paper, the authors employ the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time.
Abstract: This paper employs the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time. Given that a firm's market position expands or deteriorates in a probabilistic way which depends upon the current position, the rate of advertising, and the price the firm charges, we present conditions which ensure that the optimal level of advertising is a monotonic function of the firm's market position, and we discuss the economic meaning of these conditions. Furthermore, although the primary focus is upon a non-competitive environment, we develop the above model as a non-zero sum, two-person stochastic game and show that an equilibrium strategy exists which is simple to compute.

18 citations


Journal ArticleDOI
TL;DR: In this article, the game of R. Isaacs with the players being a hider and a searcher is shown to be solvable in the case of both convex and finite union of convex sets.
Abstract: In this game of R. Isaacs, the players are a hider and a searcher. The payoff is the time until capture. The hider is assumed to be mobile within a bounded set $\mathcal{D}$. The searcher has an arbitrarily small detection radius. There is incomplete information in that neither player knows the present or past location of the other. For various sets $\mathcal{D}$, the value of the game is demonstrated by the presentation of $\varepsilon $-optimal strategies. Specifically, the game is solved in case $\mathcal{D}$ is convex or is the finite union of convex sets in $\mathbb{R}^n $ with $n \geqq 2$. Also the game is discussed in the case where $\mathcal{D}$ is a network. The results settle two conjectures of S. Gal.

16 citations


Journal ArticleDOI
TL;DR: In this paper, an experimental test of three competing theories of payoff allocation (the Shapley, equality, and nucleolus solutions) in n-person conflicts was conducted, where three hundred twenty subjects participated in four-person cooperative core games with side-payments.
Abstract: This paper reports an experimental test of three competing theories of payoff allocation (the Shapley, equality, and nucleolus solutions) in n-person conflicts. These tests apply to decision making in group systems. Three-hundred twenty subjects participated in four-person cooperative, nonconstant sum, nonempty core games with side-payments. The manipulated experimental variables included core size, location of the equality vector with respect to the core, and column difference of payoff matrices. Results show that the Shapley solution is superior to the nucleolus solution in terms of predictive accuracy. Moreover, the Shapley solution is robust to experimental treatments and thus appears to be more useful than the equality solution. Related findings indicate a high percentage of Pareto optimal outcomes (83%) and a higher frequency of outcomes falling in the core when the equality vector is located inside the core than when it is located outside. Findings are discussed in terms of core properties.

13 citations


Journal ArticleDOI
TL;DR: In this article, readily computable strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are developed, and the implications of the payoff relationships are considered.
Abstract: In this paper, readily computable strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are developed. Of particular significance is the fact that the governing differential equations no longer require the solution of an often difficult nonlinear, two-point boundary-value problem, but again satisfy the separation principle of linear-quadratic optimal control. The implications of the payoff relationships are considered.

12 citations


Journal ArticleDOI
TL;DR: In this article, the authors used a coalition game to study coalition formation in decision making of three-person group systems and found that the formation of coalitions tended to depend upon whether the payoff structure of the game made it possible for the partners in a particular coalition to reach an agreement giving both of them relatively large payoffs.
Abstract: Coalition formation in decision making of three-person group systems was studied using a coalition game. This was devised as an analogue for many situations in which groups make decisions, both in “real life” and in laboratory experiments. One of the important findings of the study was that in this game, unlike the games usually employed in coalition research, the “resources” that the triad members possessed had relatively little effect upon which members tended to enter into a coalition or upon which of the partners to a coalition tended to receive the larger payoff. Instead, the formation of coalitions tended to depend upon whether the payoff structure of the game made it possible for the partners in a particular coalition to reach an agreement giving both of them relatively large payoffs. The findings are discussed in relation to previous research on coalitions.

9 citations


Journal ArticleDOI
TL;DR: In this paper, the authors discuss three methods of weighting different information to form a single indicator of "payoff" or "value": explicit weighting and two implicit weighting methods-policycapturing and policy-specifying, which are combined here into a more comprehensive method referred to as policy development.
Abstract: Planning for a computer-based personnel job opportunities system for the Air Force led to a requirement for a procedure to generate a “payoff” or “value” of the assignment of each person to each possible job. This report discusses three methods of weighting different information to form a single indicator of “payoff” or “value”: explicit weighting and two implicit weighting methods-policy-capturing and policy-specifying, which are combined here into a more comprehensive method referred to as policy development. The policy-capturing process presents a series of decision situations to one (or more) policy makers and the policy maker assigns to each situation a number which reflects the value or payoff. Then, a mathematical model is derived by obtaining the regression equation that best predicts the policy maker’s judgments.

Journal ArticleDOI
TL;DR: In this article, eight quartets of subjects each played eight different versions of a 4-person apex game twice, in a computer-controlled coalition formation experiment, and the data were analyzed from the point of view of coalition frequencies, payoff allocations, and a bargaining process examination of the computer-recorded protocols.
Abstract: Eight quartets of subjects each played eight different versions of a 4-person apex game twice, in a computer-controlled coalition formation experiment. The eight games were cast into a 2 × 2 factorial mold in which (i) the central apex player was either weak or strong in terms of the outcomes available to Apex coalitions, and (ii) the outcomes to players not in coalitions varied, such that the outside opportunities of the Base players were not necessarily equal. The data were analyzed from the point of view of coalition frequencies, payoff allocations, and a bargaining process examination of the computer-recorded protocols. The H competitive bargaining set is shown to be a first-order predictor of payoff allocations, but differences not accountable by that model are also manifest. The manipulation of the strength of the Apex player affected coalition frequencies such that strong Apex players were in more coalitions than weak Apex players. Somewhat contrary to expectation, no effect for differential outside opportunities of Base players were shown. The analysis of the bargaining protocols revealed structural and psychological factors not considered in present mathematical models that must be incorporated into any model aspiring to provide a coherent description of coalition formation processes.

Journal ArticleDOI
S. Sorin1
TL;DR: In this article, the authors consider repeated two-person zero-sum games with lack of information on both sides and prove that the sequence is monotonic and the speed of convergence is bounded by K/n.
Abstract: We consider repeated two-person zero-sum games with lack of information on both sides If the one shot game is played sequentially, it is proved that the sequencevn is monotonic,vn being the value of then shot game Moreover the speed of convergence is bounded byK/n, and this is the best bound

Journal ArticleDOI
TL;DR: In this paper, structural equilibrium and stable payoffs are derived from the application of ψ-stability to the core and to the bargaining set, respectively, for games without side payments.

Book ChapterDOI
01 Jan 1979
TL;DR: In this article, six quartets of players participated in a sequence of 16 4-person nonconstant-sum characteristic function games in which one player (the monopolist) was necessarily a member of any coalition that could form.
Abstract: Six quartets of players participated in a sequence of 16 4-person nonconstant-sum characteristic function games in which one player (the monopolist) was necessarily a member of any coalition that could form. The sixteen games were four repetitions each of four game types, arranged in a 2 x 2 design depending on (i) whether or not the grand coalition of all four players was allowed to form, and (ii) whether or not the monopolist players were symmetric. The outcomes of these games were compared to predictions derived from the M 1 (i) bargaining set [Maschler, 1963b], and from a modification of Maschler’s [1963a] power model. The results indicated that each quartet established a standard for the range of the monopolist’s payoff early in the sequence, and that this standard took on the function of a norm in defining the legitimate bargaining ground for that quartet for the remainder of the sequence. Two quartets’ standards were well within the prediction of the bargaining set; one quartet supported the power model. Analysis of the patterns of coalition structure and rudimentary analyses of the bargaining processes indicate that the central concept of standards of fairness underlying the power model is appropriate and timely.

Journal ArticleDOI
TL;DR: In this article, the authors used the tools of differential geometry to study two-person games in normal form and their "ordinary" points, i.e. the points which are not equilibria in any sense, and defined the concept of reversibility in terms of the derivatives of the payoff functions.
Abstract: Using the tools of differential geometry two-person games in normal form and their “ordinary” points, i.e. the points which are not equilibria in any sense, are studied. The concept of reversibility if defined and characterized in terms of the derivatives of the payoff functions. Reversible points appear as those points at which the behavior may become cooperative. In the second part of the paper, three-person games in normal form are considered. All the concepts defined depend only on the preference preorderings associated with the payoff functions and do not depend on the metric of the strategy spaces.

Journal ArticleDOI
TL;DR: A revision to the OPTSA model for optimal allocation of aircraft sorties that shortens its running time is presented, using the fact that not all payoff entries of a game matrix need be known to determine the game solution.
Abstract: This note presents a revision to the OPTSA model for optimal allocation of aircraft sorties that shortens its running time. The new procedure uses the fact that not all payoff entries of a game matrix need be known to determine the game solution, and that the computer time spent in simplex operations is insignificant compared to the time spent computing payoff entries. Estimates of the computational savings are given. When the procedure was implemented in a three-stage behavioral game, computational savings of up to 95% over the original model were observed.

01 Jan 1979
TL;DR: In this paper, the authors employ the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time.
Abstract: This paper employs the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time. Given that a firm's market position expands or deteriorates in a probabilistic way which depends upon the current position, the rate of advertising, and the price the firm charges, we present conditions which ensure that the optimal level of advertising is a monotonic function of the firm's market position, and we discuss the economic meaning of these conditions. Furthermore, although the primary focus is upon a non-competitive environment, we develop the above model as a non-zero sum, two-person stochastic game and show that an equilibrium strategy exists which is simple to compute.

Journal ArticleDOI
TL;DR: In this paper, the concepts of priorcommitment and delayed-commitment strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are applied to a detailed example of a pursuit-evasion game.
Abstract: In this paper, the concepts of prior-commitment and delayed-commitment strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are applied to a detailed example of a pursuit-evasion game. Quasilinearization is used to solve the nonlinear two-point boundary-value problem of the prior-commitment game. A closed form solution is obtained for the delayed-commitment strategies. Comparison of the payoff functionals confirms the relationships discussed in Ref. 1.

Journal ArticleDOI
TL;DR: In this article, it was shown that the upper and lower values of a deterministic differential game with terminal payoff are independent of the length of the memory of the player's memory.
Abstract: It is shown that, in differential games, strategies can be defined for the players in such a way that their controls depend, for each timet, on a finite section of the past of the trajectoryx(t). In particular,s-delay,r-memory strategies can be defined as in the Varaiya-Lin approach. It is shown that, for deterministic differential games with terminal payoff, the upper and lower values of the game so defined, are independent of the lengthr of the memory. Lettingr → 0, a feedback strategy is obtained which depends only on the present (and infinitesimal past) of the trajectoryx(t).


Journal ArticleDOI
TL;DR: This paper presented an experiment derived from social exchange theory, designed to explore the question of how people deal with multiple and possibly conflicting sources of information about rewards and costs in a binary choice two-person game.
Abstract: This paper presents an experiment derived from social exchange theory, designed to explore the question of howpeople deal with multiple and possibly conflicting sources of information about rewards and costs. Twenty female and 20 male dyads participated in a binary choice two-person game that was cooperative in nature but required coordination. Independent variables were: goal structure (established by two different payoff matrices); exchange rules (established by six different "bonus rules "); order of presentation of exchange rules; sex; and subject position (subjects were randomly assigned to "table 1" or "table 2"). Dependent variables were the choices made by the subjects in the game and their responses on questionnaires that tested their attitudes and intentions. The general theoretical assumption was that the less certain (that is, more ambiguous, difficult to coordinate, or contradictory to social expectations) a source of information is, the less it will affect behavior. Several hypotheses drawn ...

Journal ArticleDOI
TL;DR: An alternative to, or extension of, the chance-constrained method of stochastic programming is presented whereby an expected cost of infeasibility is included in the objective function.
Abstract: In this paper an alternative to, or extension of, the chance-constrained method of stochastic programming is presented whereby an expected cost of infeasibility is included in the objective function. The problem is to select a solution to implement before the available resources are known where the adaption of a non-feasible solution to the resources available involves a system cost. While increasing the amount of computation required, the model enables the decision maker to more effectively trade off increased payoff for decreased likelihood of feasibility.