Showing papers on "Stochastic game published in 1969"

Equilibrium points for games with infinitely many players.

Abstract: : Conditions that guarantee the existence of equilibrium points for games with infinitely many players are discussed; essentially what is needed is that the payoff functions are continuous in an appropriate sense. If the continuity assumption does not hold then one shows by an example that equilibrium points may not exist. (Author)

Optimal stopping rules for multinomial observations

Abstract: Many times sampling from a known or an unknown population results in observations that are integers and there is a payoff which depends on the observations. Thus, the experimenter is tempted to continue sampling in the hope of increasing his payoff. On the other hand, usually each observation costs a fixed amount and thus the experimenter also is reluctant to continue sampling because each additional sample increases the total sampling cost. The problem is to determine a place to stop making observations such that thenet payoff is a maximum. This paper considers stopping rules which will maximize the net payoff to the experimenter when the observations come from a multinomial population.

ON ASYMPTOTIC BEHAVIOR OF SOME NUCLEI OF n-PERSON GAMES AND THE PIECEWISE LINEARITY OF THE NUCLEOLUS.

Abstract: : In a previous paper the authors developed a new class of solution concepts in n-person game theory as optimal solutions to specially constructed linear programming problems whose constraint matrices and hence optimal solutions depend on a certain parameter, c. In this paper asymptotic results are obtained for the limiting payoff configuration as c approaches infinity. It is shown that the limiting payoff configuration in general shares some properties with Schmeidler's solution concept of the nucleolus and under additional assumptions does converge to the nucleolus. By using recent results of Kohlberg, a new proof is obtained for the author's theorem of the piecewise linearity of the nucleolus as a function of the characteristic function of n-person games. (Author)

Effects of Different Payoff Matrices on Arithmetical Estimation Tasks: An Attempt to Produce “Rationality”:

Abstract: 5 experiments were conducted in an attempt to produce a shift in the decision pattern in a forced-choice arithmetical estimation task. The expected shift was related to a change in the payoff matrix attached to the possible outcomes of the decision. The experiments varied in the amount of payoff, clarity of the explanation of the payoff matrix, difficulty of the task, feedback after decision and the length of decision time. None of these manipulations produced the expected rational shift. The role of payoff matrices in decisions in tasks involving skill is discussed.

Median two-person game theory for median competitive games

Abstract: A form of discrete two-person game theory based on median con­ siderations is developed in [1]. Median game theory has very strong application advantages over expected value game theory [2]. In particular, the class of median competitive games, where both players can be simultaneously protective and vindictive, is huge compared to the corresponding class for expected value game theory_ Moreover, the median approach is usable for games where the numbers in one or both payoff matrices do not satisfy the arithmetical operations (but can be ranked within each matrix)_ A subclass of the median competitive games is identified in [1]. The complete class is specified in this paper and a method is given for determining median optimum strategies. In addition, the class of games where a given player (but not necessarily the other one) can be simultaneously protective and vindictive is identi­ fied_ Also, a way of finding a median optimum strategy for this player is developed_ The evaluation methods given are oriented toward mini­ mum application effort (and do not use preferred sequences)_

Arithmetical estimation under conditions of different payoff matrices

Abstract: A forced-choice arithmetical estimation task was devised. The task included three units of 50 addition problems each. To each unit of the task a different payoff matrix was attached. Twenty Ss participated in the experiment. It was found that estimation under severe time limits was correct in about 70% of the items. No effects of the different payoff matrices was found. Ss showed perfect probability matching in their estimation behavior.

Personality impression formation in a Maximizing Difference game

Abstract: Introduction Investigators interested in behavior in the Prisoner's Dilemma game situation have focused a good deal of attention on the effects of sending the subjects "programmed" strategies. The subject, while believing that he is playing against another subject, is actually playing against a strategy selected by the experimenter. Becker and McClintock (1967) have summarized the findings of such studies by noting that, at best, such strategies have a small effect upon the behavior of the players. These experiments have, for the most part, employed a standard Prisoner's Dilemma matrix. However, McClintock and Messick (1965) have suggested that a relaxed version of the Prisoner's Dilemma game, known as the Maximizing Difference game, may be more sensitive to factors which could induce greater cooperation. A Maximizing Difference matrix is shown in Figure 1. This matrix has the advantage of establishing a unitary motive for the competitive response, i.e., the desire to maximize the difference between one's own payoff and that of one's opponent. Gallo (1966), using a Maximizing Difference matrix, compared the results of fair games, random strategies of from 80 to 100

Effects of payoff information in multistage mixed‐motive games

Abstract: A two-person multistage mixed-motive game (MMG) simulates the basic characteristics of interdependent conflicts. MMG is composed of several interconnected subgames in each of which a joint decision by the two players determines a payoff for each of them as well as the next subgame to be played. Three groups of subjects played the MMG, differing from one another in the amount of information possessed about the payoffs of the other player. It was found that as the amount of information decreased the percent of cooperative choices and the difference in gain within dyads increased. A model for MMG accounted for the stated policies of the majority of the subjects. Difficulties encountered in testing the model are discussed briefly.

Values of non-atomic games, part ii: the random order approach,

Abstract: : The paper reports the second study in a series concerned with the value of participation in a non-atomic game A non-atomic game is a special type of infinite-person game in which no individual player has significant influence on the outcome The work develops the concept of mixing value and presents a new approach based on mixing transformations A program is outlined for imposing a probability measure on the space of all measurable orders Some consideration is given to the asymptotic approach, in which a game with a continuum is treated as a limit of games with finitely many players It is significant that all values defined in the axiomatic, mixing, and asymptotic approaches possess a common diagonal property

Prisoner’s Dilemma with A Payoff-Adjusting Option

Abstract: To study the effects of a payoff-adjusting option on game behavior, 30 subject pairs played a 63-trial prisoner’s dilemma game under either individualistic, competitive, or competitive plus simulated-war instructions. All Ss had the opportunity to escalate or de-escalate the payoffs to themselves and the other players by factors from 10 to 1/10. In the competitive groups, an escalation or de-escalation tended to be countered by a response of the opposite kind. All group mean scale value choices were positive, but Ss in the individualistic condition chose higher scale values and made fewer scale value changes. No group showed a trend in scale value level across trials. The 2 competitive groups showed no behavioral differences. Game performance for Ss in all groups was unrelated to F-scale score.

Artifacts in the Siegel-Fouraker Study of Bargaining and Group Decision Making

Abstract: Siegel and Fouraker 1960 hypothesize and purport to show experimentally that players in bilateral monopoly will tend toward contracts at the Paretian optimum quantity P.O. under conditions of incomplete information players know only their own payoff functions, even though the theory implicitly assumes complete information both players know both functions. Their results contain artifacts which severely limit the generality of any inferences that might be drawn from them. The theory prediction that players will tend toward P.O. must be based on the explicit, not implicit, assumption of complete information. In this paper it is demonstrated that under conditions of incomplete information it is very likely that players will tend toward contracts at the P.O. only when it can be assumed that they meet the very restrictive condition of behaving like perfect competitors. Also, in an experiment measuring the degree to which players did in fact bid along their marginal functions, some 48% of the variance in behavior was explained by this model.