When is the value of public information positive in a game?

The value of public information is studied by considering the equilibrium selections that maximize the weighted sum of players' payoffs. We show that the value of information can be deduced from the deterministic games where the uncertain parameters have given values. If the maximal weighted sum of equilibrium payoffs in deterministic games is convex then the value of information in any Bayesian game derived from the deterministic games is positive with respect to the selection. We also show the converse result that positive value of information implies convexity. Hence, the convexity of maximal weighted sum of payoffs in deterministic games fully characterizes the value of information with respect to considered selections. We also discuss the implications of our results when positive value of information means that for any equilibrium in a game with less information there is a Pareto dominant equilibrium in any game with more information.     

Metric adjusted skew information and uncertainty relation

We show that an uncertainty relation for Wigner-Yanase-Dyson skew information proved by Yanagi (2010) [10] can hold for an arbitrary quantum Fisher information under some conditions. This is a refinement of the result of Gibilisco and Isola (2011) [4].     

A model of interim information sharing under incomplete information

We propose a two-person game-theoretical model to study information sharing decisions at an interim stage when information is incomplete. The two agents have pieces of private information about the state of nature, and that information is improved by combining the pieces. Agents are both senders and receivers of information. There is an institutional arrangement that fixes a transfer of wealth from an agent who lies about her private information. In our model, we show that (1) there is a positive relation between information revelation and the amount of the transfers, and (2) information revelation has a collective action structure, in particular, the incentives of an agent to reveal decrease with respect to the amount of information disclosed by the other.     

Wigner-Yanase skew information vs. quantum Fisher information

Among concepts describing the information contents of quantum mechanical density operators, both the Wigner-Yanase skew information and the quantum Fisher information defined via symmetric logarithmic derivatives are natural generalizations of the classical Fisher information. We will establish a relationship between these two fundamental quantities and show that they are comparable.

     

Mode hunting through active information

We propose a new method to find modes based on active information. We develop an algorithm called active information mode hunting (AIMH) that, when applied to the whole space, will say whether there are any modes present and where they are. We show AIMH is consistent and, given that information increases where probability decreases, it helps to overcome issues with the curse of dimensionality. The AIMH also reduces the dimensionality with no resource to principal components. We illustrate the method in three ways: with a theoretical example (showing how it performs better than other mode hunting strategies), a real dataset business application, and a simulation.     

Securitizing and tranching longevity exposures

We consider the problem of optimally designing longevity risk transfers under asymmetric information. We focus on holders of longevity exposures that have superior knowledge of the underlying demographic risks, but are willing to take them off their balance sheets because of capital requirements. In equilibrium, they transfer longevity risk to uninformed agents at a cost, where the cost is represented by retention of part of the exposure and/or by a risk premium. We use a signalling model to quantify the effects of asymmetric information and emphasize how they compound with parameter uncertainty. We show how the cost of private information can be minimized by suitably tranching securitized cashflows, or, equivalently, by securitizing the exposure in exchange for an option on mortality rates. We also investigate the benefits of pooling several longevity exposures and the impact on tranching levels.     

Uncertainty principle and quantum Fisher information

A family of inequalities, related to the uncertainty principle, has been recently proved by S. Luo, Z. Zhang, Q. Zhang, H. Kosaki, K. Yanagi, S. Furuichi and K. Kuriyama. We show that the inequalities have a geometric interpretation in terms of quantum Fisher information. Using this formulation one may naturally ask if this family of inequalities can be further extendend, for example to the RLD quantum Fisher information. We show that this is impossible by producing a family of counterexamples.     

Routing in Queues with Delayed Information

We compare two routing-control strategies in a high-speed communication network with c parallel channels (routes), where information on service completions in down-stream servers is randomly delayed. The controller can either hold arriving messages in a common buffer, dispatching them to servers only when the delayed information becomes available (Wait option), or route jobs to the various channels, in a round-robin fashion, immediately upon their arrival. Interpreting the delays as servers's vacations and considering overall queue sizes as a measure of performance, we show that the Wait strategy is superior as long as the mean information delay is below a threshold. We calculate threshold values for various combinations of load and c and show that, for a given load, the threshold increases with c and, for fixed c, the threshold decreases with an increasing load. If information is delayed on arrival instants, rather than on service completions, we show that the system can be viewed as a tandem queue and derive a generalization of a queue-decomposition result obtained by Altman, Kofman and Yechiali.     

Juche versus Sadae: Game-theoretic approach

We argue that to some degree Juche is represented by the concept of Nash equilibrium, and Sadae by Thompson and Faith's truly perfect information equilibrium. We characterize the latter, and show that for a Pareto optimal Nash equilibrium, Juche is as good as, or better than Sadae. This includes the game of brinkmanship.     

Uncertainty relation associated with a monotone pair skew information

We derive a trace inequality leading to an uncertainty relation based on the monotone pair skew information introduced by Furuichi. As the monotone pair skew information generalizes the Wigner-Yanase-Dyson skew information as well as some other skew information, our result also extends a few known results on the uncertainty relations. Particularly it reduces to that of Luo, Yanagi, and Furuichi et al. in the special cases.     

Optimal Conditional Estimation: Average Case Setting

We consider an estimation problem which appears in the identification of systems by means of restricted complexity models: find the optimal approximation to an element of a linear normed space (a system) based on noisy information, subject to the restriction that approximations (models) can be selected from a prescribed subspace M of the problem element space. In contrast to the worst-case optimization criterion, which may be pessimistic, in this paper the quality of an identification algorithm is measured by its local average performance. Two types of local average errors are considered: for a given information (measurement) y and for a given unknown element x, the latter in two versions. For a wide spectrum of norms in the measurement space, we define an optimal algorithm and give expressions for its average errors which show the dependence on information, information errors, unmodelled dynamics, and norm in the measurement space.     

Sequence of opponents and reduced strategies

We consider the framework of repeated two-person zero-sum games with lack of information on one side. We compare the equilibrium payoffs of the informed player in two cases: where he is facing either a) a single long-lived uninformed player, or b) a sequence of short-lived uninformed players. We show: 1) that situation b) is always (weakly) better than a), 2) that it can be strictly better in some cases, 3) that the two cases are equivalent if the long uninformed player has an optimal strategy independent of his own moves. Received: March 1999/Revised: May 2000     

Information Algebras and Consequence Operators

We explore a connection between different ways of representing information in computer science. We show that relational databases, modules, algebraic specifications and constraint systems all satisfy the same ten axioms. A commutative semigroup together with a lattice satisfying these axioms is then called an “information algebra”. We show that any compact consequence operator satisfying the interpolation and the deduction property induces an information algebra. Conversely, each finitary information algebra can be obtained from a consequence operator in this way. Finally we show that arbitrary (not necessarily finitary) information algebras can be represented as some kind of abstract relational database called a tuple system. Mathematics Subject Classification (2000): Primary 03B22; Secondary 03G15 03G25 08A70 68Q99 94A99 03C950     

信息代数紧扩张的一种新方法

本文研究了从一般信息代数获取紧信息代数的一种新方法.通过在一个信息代数的定向集族上建立一个等价关系,证得相应的等价类全体之集关于联合和聚焦两种运算构成了原信息代数的一个紧扩张.     

On the quality of algorithms based on spline interpolation

The qualityq of a numerical algorithm using some specified information is the ratio of its error to the smallest possible error of an algorithm based on the same information. We use as information function values at equidistant points, periodicity and a bound for therth derivative. We show thatq is rather small, if the algorithm is based on spline interpolation.     

Quantum Gaussian memory channels

We study the information transmission through two different models of Gaussian memory channels: an additive Gaussian channel and a lossy bosonic memory channel. We then show that entangled inputs can enhance the transmission rate in such channels. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 390–404, August, 2007.     

On the tradeoff between optimal order-base-stock levels and demand lead-times

We investigate the tradeoff between finished-goods inventory and advance demand information for a model of a single-stage make-to-stock supplier who uses an order-base-stock replenishment policy to meet customer orders that arrive a fixed demand lead-time in advance of their due-dates. We show that if the replenishment orders arrive in the order that they are placed, then the tradeoff between the optimal order-base-stock level and the demand lead-time is “exhaustive”, in the sense that the optimal order-base-stock level drops all the way to zero if the demand lead-time is sufficiently long. We then provide a sufficient condition under which this tradeoff is linear. We verify that this condition is satisfied for the case where the supply process is modeled as an M/M/1 queue. We also show that the tradeoff between the optimal order-base-stock level and the demand lead-time is linear for the case where the supply process is modeled as an M/D/1 queue. More specifically, for this case, we show that the optimal order-base-stock level decreases by one unit if the demand lead-time increases by an amount equal to the supplier’s constant processing time. Finally, we show that the tradeoff between the optimal order-base-stock level and the demand lead-time is exhaustive but not linear in the case where the supply process is modeled as an M/D/∞ queue. We illustrate these results with a numerical example.     

Optimality of monotonic policies for two-action Markovian decision processes,with applications to control of queues with delayed information

We consider a discrete-time Markov decision process with a partially ordered state space and two feasible control actions in each state. Our goal is to find general conditions, which are satisfied in a broad class of applications to control of queues, under which an optimal control policy is monotonic. An advantage of our approach is that it easily extends to problems with both information and action delays, which are common in applications to high-speed communication networks, among others. The transition probabilities are stochastically monotone and the one-stage reward submodular. We further assume that transitions from different states are coupled, in the sense that the state after a transition is distributed as a deterministic function of the current state and two random variables, one of which is controllable and the other uncontrollable. Finally, we make a monotonicity assumption about the sample-path effect of a pairwise switch of the actions in consecutive stages. Using induction on the horizon length, we demonstrate that optimal policies for the finite- and infinite-horizon discounted problems are monotonic. We apply these results to a single queueing facility with control of arrivals and/or services, under very general conditions. In this case, our results imply that an optimal control policy has threshold form. Finally, we show how monotonicity of an optimal policy extends in a natural way to problems with information and/or action delay, including delays of more than one time unit. Specifically, we show that, if a problem without delay satisfies our sufficient conditions for monotonicity of an optimal policy, then the same problem with information and/or action delay also has monotonic (e.g., threshold) optimal policies.     

Efficacy,Beliefs, and Investment in Step-Level Public Goods

A central concept for understanding social dilemma behavior is the efficacy of an actor's cooperative behavior in terms of increasing group well-being. We report a decision and game theoretical analysis of efficacy in step-level public goods (SPGs). Previous research shows a positive relation between efficacy and contributions to SPGs and explains this relation by a purely motivational account. We show, however, that from a decision and game theory perspective an increasing relationship is not general, but only follows from very specific assumptions about players’ information and beliefs. We offer 3 examples of how the predicted efficacy–contribution relation depends on players’ information and beliefs. We discuss the implications of our results for the social psychology of efficacy in social dilemmas.     

技术许可下信息分享和政府补贴对闭环供应链的影响分析——基于经销商再制造模式

研究了信息分享对制造商许可经销商从事再制造模式下闭环供应链的影响。分别建立了无信息分享和信息分享下经销商再制造和制造商再制造两种模式下的闭环供应链模型并分析了政府补贴对废旧产品回收量和渠道成员决策的影响。研究发现,当经销商对制造商进行信息分享时,经销商的利润减少,而制造商的利润增加。渠道领导者制造商总是能从再制造活动中抽取利润,在经销商再制造模式下,制造商通过收取许可费分享再制造的利润;在制造商再制造模式下,制造商设定适当的批发价格及回收价格协调正向流和逆向流,从而实现利润最大化。同时表明了政府补贴的刺激会显著地提高废旧产品的回收量。