A game theoretic approach to a two firm bidding problem

In this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view.     

Iron Cannot Fight 1 – The Role of Technology in Current Russian Military Theory

Contemporary Russian military theory is dominated by three schools of thought: the ‘traditionalists’, the ‘modernists’ and the ‘revolutionaries’. On the role of technology in future warfare, the traditionalists argue for both high tech and massive forces at the same time. The modernists are ready to trade manpower for technology, whereas the revolutionaries give technology full priority. Both the traditionalists and the modernists believe Russia, because of the country's technological lag and limited resources, should respond asymmetrically to the Western technology challenge. The revolutionaries, on the other hand, maintain that Russia must respond in kind. If not, the country will no longer be able to defend its sovereignty. The currently ongoing radical reform of the Russian military is a partial victory for the modernists, but which model or mix of models that will dominate in the future is first of all dependent on the Russian military's purchasing power and the state of the domestic defence industry.     

Revisiting inspection game and inspector leadership through reaction networks

The inspection game is a two-player noncooperative game that models a situation where an inspector verifies whether the inspectee complies with the rules (on the assumption that the inspectee has the tendency to violate at least one of the rules). The usual approach in the analysis of this game seeks to find an optimal strategic inspection scheme for each of the two players yielding favorable payoffs. Recently, there have been some developments in the study of such games that use a mathematical structure known as reaction network involving a set of molecular species and the existing reactions among these species. In this paper, we use a reaction network to analyze the inspection game giving an alternative way of modeling the social situation. The molecular species play the role of the players' decision moves and their resulting gain or loss, while the reactions are the encounters of the decisions of the players which, as expected, yield payoffs. We reexamine the dynamics of the inspection game through the lens of reaction network theory and consider various situations that call for more detailed analyses such as equal or unequal reaction rates and inspection leadership. Conditions concerning reaction rates, initial population of decision species, benefits, and costs are determined in order to identify strategies that yield better payoffs both for the inspector and inspectee. These results illustrate practical insights rooted from the formulated simple game models.     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.     

Discrete search allocation game with false contacts

This paper deals with a two‐person zero‐sum game called a search allocation game, where a searcher and a target participate, taking account of false contacts. The searcher distributes his search effort in a search space in order to detect the target. On the other hand, the target moves to avoid the searcher. As a payoff of the game, we take the cumulative amount of search effort weighted by the target distribution, which can be derived as an approximation of the detection probability of the target. The searcher's strategy is a plan of distributing search effort and the target's is a movement represented by a path or transition probability across the search space. In the search, there are false contacts caused by environmental noises, signal processing noises, or real objects resembling true targets. If they happen, the searcher must take some time for their investigation, which interrupts the search for a while. There have been few researches dealing with search games with false contacts. In this paper, we formulate the game into a mathematical programming problem to obtain its equilibrium point. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations

We consider the coordination problem between a vendor and a buyer operating under generalized replenishment costs that include fixed costs as well as stepwise freight costs. We study the stochastic demand, single‐period setting where the buyer must decide on the order quantity to satisfy random demand for a single item with a short product life cycle. The full order for the cycle is placed before the cycle begins and no additional orders are accepted by the vendor. Due to the nonrecurring nature of the problem, the vendor's replenishment quantity is determined by the buyer's order quantity. Consequently, by using an appropriate pricing schedule to influence the buyer's ordering behavior, there is an opportunity for the vendor to achieve substantial savings from transportation expenses, which are represented in the generalized replenishment cost function. For the problem of interest, we prove that the vendor's expected profit is not increasing in buyer's order quantity. Therefore, unlike the earlier work in the area, it is not necessarily profitable for the vendor to encourage larger order quantities. Using this nontraditional result, we demonstrate that the concept of economies of scale may or may not work by identifying the cases where the vendor can increase his/her profits either by increasing or decreasing the buyer's order quantity. We prove useful properties of the expected profit functions in the centralized and decentralized models of the problem, and we utilize these properties to develop alternative incentive schemes for win–win solutions. Our analysis allows us to quantify the value of coordination and, hence, to identify additional opportunities for the vendor to improve his/her profits by potentially turning a nonprofitable transaction into a profitable one through the use of an appropriate tariff schedule or a vendor‐managed delivery contract. We demonstrate that financial gain associated with these opportunities is truly tangible under a vendor‐managed delivery arrangement that potentially improves the centralized solution. Although we take the viewpoint of supply chain coordination and our goal is to provide insights about the effect of transportation considerations on the channel coordination objective and contractual agreements, the paper also contributes to the literature by analyzing and developing efficient approaches for solving the centralized problem with stepwise freight costs in the single‐period setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Modified fictitious play

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and apply it to both symmetric and general games. If the original game is not symmetric, the basic idea is to transform the given matrix game into an equivalent symmetric game (a game with a skew-symmetric matrix) and use the solution properties of symmetric games (the game value is zero and both players have the same optimal strategies). The fictitious play method is then applied to the enlarged skew-symmetric matrix with a modification that calls for the periodic restarting of the process. At restart, both players' strategies are made equal based on the following considerations: Select the maximizing or minimizing player's strategy that has a game value closest to zero. We show for both symmetric and general games, and for problems of varying sizes, that the modified fictitious play (MFP) procedure approximates the value of the game and optimal strategies in a greatly reduced number of iterations and in less computational time when compared to Brown's regular fictitious play (RFP) method. For example, for a randomly generated 50% dense skew-symmetric 100 × 100 matrix (symmetric game), with coefficients |a_ij| ≤ 100, it took RFP 2,652,227 iterations to reach a gap of 0.03118 between the lower and upper bounds for the game value in 70.71 s, whereas it took MFP 50,000 iterations to reach a gap of 0.03116 in 1.70 s. Improved results were also obtained for general games in which the MFP solves a much larger equivalent symmetric game. © 1996 John Wiley & Sons, Inc.     

反恐怖劫持事件中不同目的谈判语言的运用策略

在反劫持谈判中,为了能够解除现场的那种僵持、对抗、凝固的情形,谈判者就得运用不同目的的语言来使劫持者向预期的方向前进。从理论上讲,每一名谈判人员都希望通过和平的方式解决劫持事件。因此,我们必须学会运用反恐谈判讨价的语言、拖延的语言、劝降的语言和摊牌的语言,来使劫持事件得到和平解决或为武力解救行动创造良好时机。     

Zero-sum games with multiple goals

This paper investigates a class of two-person zero-sum multiple payoff games in which each component is deterministic. The problem of minimizing a player's total underachievement of a fixed set of goals is shown to reduce to a linear programming problem. Applications are discussed and illustrative examples are presented.     

Group support for political violence: The role of emotions and expressive choice in creating conflict or providing peace

This paper provides a rationale for group support for political violence which does not provide a material benefit. Rabin’s (1993) theory of fairness is adopted to demonstrate that although group violence may not be a Nash equilibrium it may be a fairness equilibrium in a game containing psychological payoffs. For this to happen the material stakes must be perceived as low and psychological payoffs are expressive. Although the material stakes are actually high, members of each group may choose expressively to support the use of violence because the probability of being decisive is low. The paper also considers the possibility of peace emerging as a fairness equilibrium. This can only happen if each group perceives the other as making some sacrifice in choosing peace.     

Optimizing search with positive information feedback

A search model is formulated in which positive information may be obtained, through the detection of trails, as to the target's earlier whereabouts. The corresponding Bayesian update formulas for target location probabilities are derived. The model does not appear to be amenable to rigorous optimization. A moving-horizon rule, and a heuristic simplification thereof, are, however, derived. In two numerical examples it is demonstrated that actively designing for detecting trail information, through use of these moving-horizon rules, has substantial potential advantage over using, for example, myopic rules even if the positive information is adaptively incorporated into location probabilities before applying the latter rules in each time period.     

Transnational terrorism as a spillover of domestic disputes in other countries

This paper models transnational terrorism as a three‐way strategic interaction involving a government that faces armed opposition at home, which may spill over in the form of acts of terrorism by the state's opponents against the government's external sponsor. The external sponsor also utilises deterrence against potential terrorists, which only lowers terrorism if terrorists are not intrinsically motivated by a deep‐seated sense of humiliation. The model highlights the importance of intrinsic motivation. A rise in the external power's preference for deterrence against terrorism may backfire in these circumstances. Increases in the government's military efficiency against the rebels, who are also terrorists against the government's sponsor, raises overall levels of violence.     

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non‐linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low‐dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Extensions and reductions in the von neumann model of an expanding economy

This paper introduces an extension of the v. Neumann model of an expanding economy. In addition to the conventional nonnegative input and output matrices A₁, B₁ representing technology, two matrices A₂, B₂ represent socio-political evaluations and show that there exist solutions to the 4-matrix model. The proof is based on an extension of a constructive proof given by O. Morgenstern and G. L. Thompson. It is shown that this proof is valid only under an additional assumption. The transformation of v. Neumann models (taking consumption into account) into 1 or 2 games is shown and adds an additional condition to M. Morishima's model to guarantee a solution. The equivalence of the v. Neumann model to a maximization problem under a (efficiency) constraint is presented. It is shown that E. Malinvaud's maximality and efficiency criterion - if based on the same assumptions (model) - are equivalent and specify the assumptions which will make the MT-model efficient. The economic evaluation is considered to be of utmost importance.     

A multi‐objective model for bank ATM networks

In this paper we present an application of the core solution concepts for multi‐objective games to a bank ATM network model. In these games, the worth of a coalition is given by a subset of vectors of the k‐dimensional space rather than by a scalar. The paper investigates how an ATM network model based on multi‐objective cooperative game theory could be used as an alternative way of setting interchange fees paid by the customer's bank to the one that owns the ATM. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

A strategic model for state compliance verification

The theory of directed graphs and noncooperative games is applied to the problem of verification of State compliance to international treaties on arms control, disarmament and nonproliferation of weapons of mass destruction. Hypothetical treaty violations are formulated in terms of illegal acquisition paths for the accumulation of clandestine weapons, weapons‐grade materials or some other military capability. The paths constitute the illegal strategies of a sovereign State in a two‐person inspection game played against a multi‐ or international Inspectorate charged with compliance verification. The effectiveness of existing or postulated verification measures is quantified in terms of the Inspectorate's expected utility at Nash equilibrium. A prototype software implementation of the methodology and a case study are presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 260–271, 2016     

One-person games of economic survival

This paper discusses the one-person economic survival game model with a discrete probability distribution for the contribution to surplus variable. The general game model and strategies in these games are examined, and necessary conditions which an undominated, stationary strategy must satisfy are obtained. For a special class of these games a mathematical formulation of the value of the game is given, and examples and theorems which relate to undominated strategies in this class are presented. This paper, in some sense, is a sequel to a portion of a paper by Shubik and Thompson [7] which appeared in this journal.     

Optimal dynamic rules for assigning customers to servers in a heterogeneous queuing system

We consider a queuing system in which both customers and servers may be of several types. The distribution of a customer's service time is assumed to depend on both the customer's type and the type of server to which he is assigned. For a model with two servers and two customer types, conditions are presented which ensure that the discounted number of service completions is maximized by assigning customers with longer service times to faster servers. Generalizations to more complex models are discussed.     

Risk preference,multiple attributes,and multiple criteria in bayesian acceptance sampling plans

Although there has been considerable research directed toward developing Bayesian acceptance sampling plans, little consideration has been given to incorporating a decision-maker's risk attitude or treating such problems in terms of multiple-type defects and multiple criteria. We review our own work which is focused on the above issues. A model incorporating risk preference is shown to yield substantial differences in the characteristics of an optimal sampling plan relative to a typical Bayesian linear cost (risk neutral) model. Bayesian models and optimization schemes for a variety of multiple-type defect plans are reviewed. A bicriterion acceptance model, employing average outgoing quality and average inspection cost is also formulated. Traditional versus interactive optimization procedures are compared empirically in terms of ease of use, satisfaction with solutions, and insight gained into the problem.     

COOPERATION,SIGNALS, AND SANCTIONS

This paper uses game theory and modeling to address the role of incentive structures and information dynamics in nuclear inspections. The traditional argument is that compliant states should be willing to allow inspections to prove their innocence, while proliferating states are likely to impede inspections. This argument does not take into account the historical variation in inspection, signaling, and sanctioning behaviors. Using a game theoretic analysis and model, it is shown that the separation of proliferators from nonproliferators only occurs when the likelihood of proliferation is high and punishment costs are moderate. The model assumes that states can choose how much to cooperate with inspectors and must pay opportunity or secrecy costs when inspections are effective. The results are tested against a set of real-life cases, providing support for the claims of historical variation and the model's deductive propositions.