A note on uncertainty and cooperation in a finitely repeated prisoner's dilemma

An intuitive expectation is that in a finitely repeated prisoner's dilemma, the players will achieve mutual cooperation in at least some periods. Existing explanations for equilibrium cooperation (with agents perfectly informed of one another's characteristics) require that the number of repetitions be unknown, which is in many cases an uncomfortably strong uncertainty assertion. This paper demonstrates that if agents have private information concerning the number of repetitions (as opposed to being completely uninformed), equilibrium mutual cooperation can occur in a finitely repeated game. This appears to be a weaker and more palatable assumption then that of complete uncertainty, and hence provides a natural and useful alternative foundation for mutual cooperation.     

Reciprocal cooperation in the Prisoner's Dilemma repeated with random horizon

Summary A standard assumption on the Iterated Prisoner's Dilemma is that the probability of further interaction is constant. Then, cooperation via reciprocity can be guaranteed if and only if this probability is sufficiently high. In this paper we analyze a more realistic model: a discrete random variable, not necessarily geometric, governs the number of interactions. We obtain necessary conditions and sufficient conditions for reciprocal cooperation based on the use of TFT strategy by both players. The obtained conditions are particularized to classes of distributions with monotonous failure rate and to some relevant probability models.     

Fractal interpolation: a sequential approach

Fractal interpolation is a modern technique to fit and analyze scientific data. We develop a new class of fractal interpolation functions which converge to a data generating(original) function for any choice of the scaling factors. Consequently, our method offers an alternative to the existing fractal interpolation functions(FIFs). We construct a sequence of α-FIFs using a suitable sequence of iterated function systems(IFSs). Without imposing any condition on the scaling vector, we establish constrained interpolation by using fractal functions. In particular,the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data. The existence of Cr-α-FIFs is investigated. We identify suitable conditions on the associated scaling factors so that α-FIFs preserve r-convexity in addition to the C~r-smoothness of original function.     

A note on the value of zero-sum sequential repeated games with incomplete information

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 sequencev _n is monotonic,v _n being the value of then shot game. Moreover the speed of convergence is bounded byK/n, and this is the best bound.     

Parallel and sequential computation: a statistician's view

I borrow themes from statistics—epsecially the Bayesian ideas underlying average-case analysis and ideas of sequential design of experiments—to discuss when parallel computation is likely to be an attractive technique.     

Asymmetric potentials and motor effect: a homogenization approach

We provide a mathematical analysis for the appearance of motor effects, i.e., the concentration (as Dirac masses) at one side of the domain, for the solution of a Fokker–Planck system with two components, one with an asymmetric potential and diffusion and one with pure diffusion. The system has been proposed as a model for motor proteins moving along molecular filaments. Its components describe the densities of different conformations of proteins.     

Coalition-proof equilibria in a voluntary participation game

We examine the coalition-proof equilibria of a participation game in the provision of a (pure) public good. We study which Nash equilibria are achieved through cooperation, and we investigate coalition-proof equilibria under strict and weak domination. We show that under some incentive condition, (i) a profile of strategies is a coalition-proof equilibrium under strict domination if and only if it is a Nash equilibrium that is not strictly Pareto-dominated by any other Nash equilibrium and (ii) every strict Nash equilibrium for non-participants is a coalition-proof equilibrium under weak domination.     

The centrifugal instability of a stokes layer: Asymmetric disturbances

The influence of the asymmetry of the perturbations on the instability of viscous incompressible flow originated by a circular cylinder performing harmonic oscillations around its axis is investigated in the linear regime. The critical values of the Taylor number (based on the amplitude of the cylinder tangential velocity and on the thickness of the basic flow) and of the axial wavenumber are found to increase monotonically as the asymmetry parameter (azimuthal wavenumber) increases. This result agrees with previous experimental observations of the author.

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Sommario Si esamina l'influenza che l'asimmetria dei disturbi esercita sulla stabilità lineare del moto indotto da un cilindro, oscillante in modo armonico intorno al suo asse, in un fluido viscoso incomprimibile posto nella regione esterna al cilindro. I valori critici del numero di Taylor (costruitocon l'ampiezza della velocità tangenziale del cilindro e lo spessore dello strato interessato dal moto base) e del numero d'onda assiale si trovano essere monotonicamente crescenti al crescere del parametro che caratterizza l'asimmetria (numero d'onda circonferenziale). Ciò risulta in accordo con osservazioni sperimentali precedenti dell'autore.

     

Regulation under partial cooperation: The case of a queueing system

Socially optimal behavior can be achieved through the cooperation of the participating agents with a central planner. What happens when only a fraction of the population cooperates? We investigate this question in a Markovian single server queue. The main result is non-intuitive: the optimal control of cooperative customers is independent of their proportion. We also conclude that the gain from controlling cooperative customers after they join the queue is relatively small.     

Optimal cargo allocation on board a plane: a sequential linear programming approach

We examine a case study of an airline company whose problem is to plan cargo allocations on board a plane. Given the volume, weight, and structural constraints, the problem of finding the optimal load layout is formulated as a fractional programming problem. An algorithm is suggested to solve the linearized problem as a sequence of linear programming problems whose optimal solutions converge to the optimum (with a predetermined level of tolerance).     

The influence of face-to-face communication: a principal-agent experiment

The principal-agent problem is an interesting problem involved in many everyday relationships, such as the one between company owners and their delegates. Our experiment simulates such a relationship, whereby the task of participating pairs is to negotiate labor contracts. Our aim is to find the effects of face-to-face communication and negotiation on contract framing. We argue that including pre-play communication into the principal-agent problem leads to a significant improvement of agent’s effort and results in changes of the compensation scheme. We show that incentives are not the only possibility to induce high effort. We use content analysis of the video-taped negotiations to find some characteristics of the communication process.     

On a repeated game without a recursive structure

The solution is given here for the infinitely repeated two-person zero-sum games of incomplete information characterized by 2×2 games, with information matrices $\left( {{*{20}c} a & b \\ b & b \\ } \right)$\left( {\begin{array}{*{20}c} a & b \\ b & b \\ \end{array} } \right) for the first game and $\left( {{*{20}c} b & b \\ b & a \\ } \right)$\left( {\begin{array}{*{20}c} b & b \\ b & a \\ \end{array} } \right) for the second game.     

Asymmetric stokes flow past a spherical cap

Ranger's solution of the asymmetric streating Stokes' flow past a spherical cap is analyzed in detail. It is found that most caps exhibit wakes within their concavities, but the dividing streamsurface does not always emanate from the rim. Drag and torque formulae valid for all cap angles are derived and these are in agreement with the known results in the limiting cases when the cap becomes a sphere and a circular disc.

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Zusammenfassung Die Lösung von Ranger für die unsymmetrische Stokes-Strömung um eine Kugelhaube wurde im Detail analysiert. Es wurde gefunden, dass die meisten Kugelhauben in ihrem Hohlraum Albösungsgebiete aufweisen, doch beginnt die Ablösungs-Stromfläche nicht immer am Rand der Haube. Widerstand und Moment wurde für alle Haubenformen berechnet; die bekannten Resultate der Kugel und der Kreisscheibe ergeben sich als Grenzfälle.

     

Unbiased sequential estimation of1/p: Settlement of a conjecture

Summary We present a complete characterization of the class of (unbounded) sampling plans providing unbiased (sequential) estimation of the reciprocal of the Bernoulli parameterp. This settles a conjecture set forth by Sinha and Sinha (1975,Ann. Inst. Statist. Math.,27, 245–258) regarding the nature of such plans as sought out by Gupta (1967,Ann. Inst. Statist. Math.,19, 413–416). Incidentally, a special type of sampling plans (termed ‘infinite-step generalizations of the inverse binomial plans’), studied by Sinha and Bhattacharyya (1982, Institute of Statistics Mimeo Series, Raleigh), are seen to play a central role in this study.     

On repeated games without a recursive structure: Existence of limV n

We consider repeated zero-sum games with symmetric incomplete information where at each stage the common signal is either non-revealing or completely revealing. We prove that the sequence of values ofn-stage games converges by approximating the repeated game by a sequence of games in continuous time.     

Multiple criterion management of a sequential fishery

A static stochastic simulation was used to assess the performance of alternative management strategies in the satisfaction of multiple objective criteria in the context of a sequentially exploited transboundary resource. The model was applied to the Yukon River chum salmon (Oncorhynchus keta) fishery. Four strategies were evaluated using three criteria: probability of satisfying escapement objectives; probability of jointly satisfying escapement and subsistence harvest objectives; and probability of simultaneously reaching escapement, subsistence and commercial harvest objectives. The modeled strategies were also compared with the actual performance of the fishery for 1980–1995. The results indicate that satisfaction of escapement and subsistence harvest goals in the middle Yukon depends on imposing restrictive limits on commercial harvests in the lower Yukon. However, even with full information, escapement objectives in the upper drainage are only satisfied 65–70% and 75–80% of the time for summer and fall chum, respectively. The model was also used to explore the effects of increased average run strength that could arise from reduced bycatch of Yukon origin chum in marine fisheries. The results suggest that reduced marine interceptions are unlikely to substantially increase the probability of satisfying catch and escapement goals for the middle and upper Yukon.     

On a model of sequential point patterns

A finite point process motivated by the cooperative sequential adsorption model is proposed. Analytical properties of the point process are considered in details. It is shown that the introduced point process is useful for modeling both aggregated and regular point patterns. A possible scheme of maximum likelihood estimation of the process parameters is briefly discussed. V. Shcherbakov is on leave from Laboratory of Large Random Systems, Faculty of Mathematics and Mechanics, Moscow State University, Moscow.     

Multiagent cooperation for solving global optimization problems: an extendible framework with example cooperation strategies

This paper proposes the use of multiagent cooperation for solving global optimization problems through the introduction of a new multiagent environment, MANGO. The strength of the environment lays in its flexible structure based on communicating software agents that attempt to solve a problem cooperatively. This structure allows the execution of a wide range of global optimization algorithms described as a set of interacting operations. At one extreme, MANGO welcomes an individual non-cooperating agent, which is basically the traditional way of solving a global optimization problem. At the other extreme, autonomous agents existing in the environment cooperate as they see fit during run time. We explain the development and communication tools provided in the environment as well as examples of agent realizations and cooperation scenarios. We also show how the multiagent structure is more effective than having a single nonlinear optimization algorithm with randomly selected initial points.     

A dynamic Cournot–Nash game: a representation of a finitely repeated feedback game

This paper studies market outcome equivalence of two dynamic production-capital investment games under uncertainty. One is played under complete information, while the other, feedback (FB) game, is played under incomplete information about the opponents’ costs and market demand. The FB game structure may be observed in some newly initiated industries, in which a homogeneous good is exchanged via an auction mechanism. In that case, the FB game setting may predict the complete information equilibrium market outcomes.