Showing papers on "Stochastic game published in 1985"

Volunteer's dilemma.

Abstract: A conflict game simulating social traps in which a collective good can be provided by a volunteer is discussed and some solution concepts are analyzed. There is a greater incentive for “free riding” than for the production of the collective good at the cost of the volunteer. However, if everybody defects, all players will lose. Such a result is frequently produced by “diffusion of responsibility” as described by Darley and Latane (1968). In contrast to other social traps, a dominant strategy does not exist. Also, the mixed-equilibrium strategy yields very low payoffs. The expected gain is not greater than the payoff achieved by the nonequilibrium maximum strategy. Superrationality might be a way out of the trap. However, this concept lacks the desirable equilibrium property. Only in the free communication version of the game can a definitive answer to the question of a rational strategy be given.

Bargaining Theory and Portfolio Payoffs in European Coalition Governments 1945–83

Abstract: Coalition formation has been the subject of much theoretical work in the past decade or so. The theories that have been way or another, upon assumptions about the ways in accruing to a particular coalition is distributed among its less empirical work has been done on the process of payoff some of the fundamental assumptions of coalition theories, at their practical application to coalition governments, have tested. Several theories of payoff distribution have been however. It is the purpose of this article to test the application theories to the practice of coalition government in Europe. We begin by looking in more detail at the role of payoff theories formation. We then review both the theoretical and coalition payoffs, especially those payoffs denominated in posts. This sets the scene for a comparative testing of three proportional payoffs, the bargaining set and the kernel, in terms of each theory to predict portfolio payoffs in twelve post-systems. This study is conducted both on a general and a basis, since past analyses have demonstrated that differences are at least as significant as those between theories.

Existence of equilibrium stationary strategies in discounted noncooperative stochastic games with uncountable state space

Abstract: This paper considers discounted noncooperative stochastic games with uncountable state space and compact metric action spaces. We assume that the transition law is absolutely continuous with respect to some probability measure defined on the state space. We prove, under certain additional continuity and integrability conditions, that such games have e-equilibrium stationary strategies for each e>0. To prove this fact, we provide a method for approximating the original game by a sequence of finite or countable state games. The main result of this paper answers partially a question raised by Parthasarathy in Ref. 1.

On stochastic games with additive reward and transition structure

Abstract: In this paper, we introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which depends only on the action of the first player and a part dependent only on the action of the second player. For the zero-sum games in this class, we prove that the orderfield property holds in the infinite-horizon case and that there exist optimal pure stationary strategies for the discounted as well as the undiscounted payoff criterion. For both criteria also, finite algorithms are given to solve the game. An example shows that, for nonzero sum games in this class, there are not necessarily pure stationary equilibria. But, if such a game possesses a stationary equilibrium point, then there also exists a stationary equilibrium point which uses in each state at most two pure actions for each player.

Definition and Properties of Cooperative Equilibria in a Two-Player Game of Infinite Duration

Abstract: A two-player multistage game, with an infinite number of stages is considered. The concepts of overtaking and weakly overtaking payoff sequences are introduced. The class of strategies considered consists of memory strategies, which are based on the past history of the control and the initial state from where the game has been played. Weak equilibria are defined in this class of strategies. It is then shown how such equilibria can be constructed by composing into a trigger strategy a nominal cooperative control sequence and two threat strategies representing the announced retaliation by each player in the case where the other player does not play according to the nominal control. When the threats consists of a feedback equilibrium pair, the resulting cooperative equilibrium is perfect. Another result shows that, if each player can use a most effective threat based on a saddle-point feedback strategy, then any weak equilibrium in the class of memory strategies is in some sense related to this particular kind of equilibrium in the class of trigger strategies.

Player aggregation in the traveling inspector model

Abstract: We consider a model of dynamic inspection/surveillance of a number of facilities in different geographical locations. The inspector in this process travels from one facility to another and performs an inspection at each facility he visits. His aim is to devise an inspection/ travel schedule which minimizes the losses to society (or to his employer) resulting both from undetected violations of the regulations and from the costs of the policing operation. This model is formulated as a noncooperative, single-controller, stochastic game. The existence of stationary Nash equilibria is established as a consequence of aggregating all the inspectees into a single "aggregated inspectee." It is shown that such player aggregation causes no loss of generality under very mild assumptions. A notion of an "optimal Nash equilibrium" for the inspector is introduced and proven to be well-defined in this context. The issue of the inspector's power to "enforce" such an equilibrium is also discussed.

An exponential differential game which admits a simple Nash solution

Abstract: This paper deals with a class ofN-person nonzero-sum differential games where the control variables enter into the state equations as well as the payoff functionals in an exponential way. Due to the structure of the game, Nash-optimal controls are easily determined. The equilibrium in open-loop controls is also a closed-loop equilibrium. An example of optimal exploitation of an exhaustible resource is presented.

Coordinating Coordination Failures in Keynesian Models

Abstract: This paper focuses on the importance of strategic complementarity in agents' payoff functions as a basis for macroeconomic coordination failures. We first analyze an abstract game and find that inefficient equilibria and a multiplier process may arise in the presence of strategic complementarities (essentially positively sloped reaction curves). We then place additional economic content on complementarities arising from production functions, matching technologies and commodity demand functions in a multi-sector economy.

On a repeated game with state dependent signalling matrices

Abstract: We prove the existence of the minmax and the maxmin for a repeated game with lack of information on both sides and signalling matrices which depend on the state.

The completely mixed single-controller stochastic game

Abstract: We consider a zero-sum stochastic game with finitely many states and actions. Further we assume that the transition probabilities depend on the actions of only one player (player II, in our case), and that the game is completely mixed. That is, every optimal stationary strategy for either player assigns a positive probability to every action in every state. For these games, properties analogous to those derived by Kaplansky [4] for the completely mixed matrix games, are established in this paper. These properties lead to the counterintuitive conclusion that the controller need not know the law of motion in order to play optimally, but his opponent does not have this luxury.

On stochastic games with additive reward and transition structure

Abstract: In this paper, we introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which depends only on the action of the first player and a part dependent only on the action of the second player. For the zero-sum games in this class, we prove that the orderfield property holds in the infinite-horizon case and that there exist optimal pure stationary strategies for the discounted as well as the undiscounted payoff criterion. For both criteria also, finite algorithms are given to solve the game. An example shows that, for nonzero sum games in this class, there are not necessarily pure stationary equilibria. But, if such a game possesses a stationary equilibrium point, then there also exists a stationary equilibrium point which uses in each state at most two pure actions for each player.

A comparison of the alpha‐ and beta‐characteristic functions in cooperative non‐sidepayment n‐person games 1

Abstract: This article reports a test of theories of payoff allocation in n‐person game‐theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4‐person, 2‐strategy non‐sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α‐effectiveness (von Neumann‐Morgenstern) and β‐effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the g‐imputation set was more accurate than the a‐imputation set, the β‐stable set was more accurate than the α‐stable set, and the (3‐core was more accurate than the α‐core; in other words, for each of the solutions tested, the prediction from any solution concept based on (β‐effectiveness was more accurate than the prediction from the same solution based on a‐effectiveness. Second, the β‐core was the most accurate of the six theories tested. Res...

Distributed learning of the global maximum in a two-player stochastic game with identical payoffs

Abstract: Little is known about the distributed learning of the global maximum in a stochastic framework when there is no communication between the decision-makers. The case of two decision-makers is considered, and prior knowledge is assumed about the expected rewards. The prior knowledge captures the asymmetries that may be present in the rewards. It is shown that each decision-maker completely unaware of the other converges to the global optimum with arbitrary accuracy over time.

A game locating a needle in a circular haystack

Abstract: A complete solution of the following Hider-Seeker zero-sum game is obtained. The hider hides a needle of lengtha, 0

Plausible Outcomes for Games in Strategic Form

Abstract: This is the first in a projected series of papers on solutions to games in matrix and extensive form The predominant solution concept in the literature is that of the noncooperative equilibrium put forward by Nash (1951)

The sequence method for finding solutions to infinite games: A first demonstrating example

Abstract: A noncooperative infinite game can be approached by a sequence of discrete games. For each game in the sequence, a Nash solution can be found as well as their limit. This idea and procedure was used before as a theoretical device to prove existence of solutions to games with continuous payoffs and recently even for a class of games with discontinuous ones (Dasgupta and Maskin, 1981). No one, however, used the method for the actual solution of a game. Here, an example demonstrates the method's usefulness in finding a solution to a two-person game on the unit square with discontinuous payoff functions.

A Note on the Characterization of Optimal Return Functions and Optimal Strategies for Gambling Problems

Abstract: We consider finite state gambling problems with the Dubins and Savage payoff and with the $\lim\inf$ payoff. For these models we show that the optimal return function with respect to all stationary strategies can be characterized similarly to the optimal return function. This enables us then to characterize those stationary strategies which are optimal within the set of all stationary strategies in the same way as it was done for optimal strategies by Dubins and Savage.

An analysis of decision making processes in a multi-person experimental game

Abstract: An experimental analysis of voting behavior based on a new matrix game paradigm defined by Takigawa (1983) is reported. Five experimental conditions defined by 2×2 payoff matrices were adopted, where the first row represented the player's vote for the first party and the second row the vote for the second party. The first column corresponded to the winning of the first party and the second column to the winning of the second party. Eight successive elections were performed in the course of an hour. The result showed the effectiveness of the payoff matrices used. The selection distributions converged upon the first party acceleratively, which we called an avalanche phenomenon, as shown in Figs. 2 and 3. Further analysis suggested that there were two stages in decision making in this kind of situation, i. e., the subjects tended to control the outcome of the voting by voting to realize the best score cell initially in each election and shifted their choice by voting for the other party which they predicted would win at the next vote in order to realize some score.

On the learning algorithm of 2-person zero-sum markov game with expected average reward criterion

Abstract: We develop a method for learning the optimal strategies of 2-person zero-sum Markov game with expected average reward criterion. To do this, at each stage the players play a modified matrix game with relation to each state, and then receive an information about the result of the game from a teacher. Using the information, the players generate a pair of mixed strategies with relation to each state used at next stage. Then, such a pair of mixed strategies generated by the players converges with probability one and in mean square to a pair of the optimal stationary strategies. Further, when the learning is stopped at some stage by the teacher, the probability of error is estimated.