Estimation of strategies in a markov game

In this paper a two-person Markov game, in discrete time, and with perfect state information, is considered from the point of view of a single player (player A) only. It is assumed that A's opponent (player B) uses the same strategy every time the game is played. It is shown that A can obtain a consistent estimate of B's strategy on the basis of his past experience of playing the game with B. Two methods of deriving such an estimate are given. Further, it is shown that using one of these estimates A can construct a strategy for himself which is asymptotically optimal. A simple example of a game in which the above method may be useful is given.     

Suppression of enemy air defenses (SEAD) as an information duel

Blue strike aircraft enter region ? to attack Red targets. In Case 1, Blue conducts (preplanned) SEAD to establish air superiority. In the (reactive) SEAD scenario, which is Case 2, such superiority is already in place, but is jeopardized by prohibitive interference from Red, which threatens Blue's ability to conduct missions. We utilize both deterministic and stochastic models to explore optimal tactics for Red in such engagements. Policies are developed which will guide both Red's determination of the modes of operation of his engagement radar, and his choice of Blue opponent to target next. An index in the form of a simple transaction kill ratio plays a major role throughout. Published 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 723–742, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10046     

Countering Insurgent-terrorism: Why Nato Chose The Wrong Historical Foundation For Cimic

History teaches that counterinsurgency and counterterrorism campaigns have never been won through purely military action. Defeating an opponent who avoids open battle, but who uses force to reach his goals, including terrorist action, requires a combination of police, administrative, economic and military measures. As a counterinsurgency campaign should pursue a comprehensive political objective, it requires high levels of civil–military cooperation. However, current NATO doctrine for Civil–Military Cooperation (CIMIC) as it emerged from the 1990s is founded in conventional war-fighting and outdated peacekeeping doctrine. CIMIC's focus is on supporting military objectives rather than enabling the military to make a coherent contribution to political objectives. This makes CIMIC unfit for the Alliance's main operational challenges that have expanded from peace operations on the Balkans to countering insurgent terrorism in Afghanistan. When developing CIMIC, the Alliance obviously neglected the historical lessons from counterinsurgency campaigns.     

Continuous-time markov duels: Theory and application

This article extends the previous research on Markov duels (stochastic duels between weapons with Markov-dependent fire) to situations in which the time between rounds fired by each duelist is a continuous random variable that depends on the state of combat. Three starting conditions for the duels are considered: simultaneous detection, surprise by one duelist with continuous time detection by his opponent, and surprise with discrete time detection. The amount of surprise is treated as both a constant and a random variable. An application of these models to an evaluation of armored vehicles is described. The methods used to consider a variety of engagement ranges, tactical situations, and target types (both lethal and nonlethal) are discussed. The procedure for incorporating nonduel attrition into the analysis is described and the exchange rate (the expected number of enemy targets killed per armored vehicle killed) is derived.     

Analysis of artillery shoot‐and‐scoot tactics

Firing multiple artillery rounds from the same location has two main benefits: a high rate of fire at the enemy and improved accuracy as the shooter's aim adjusts to previous rounds. However, firing repeatedly from the same location carries significant risk that the enemy will detect the artillery's location. Therefore, the shooter may periodically move locations to avoid counter‐battery fire. This maneuver is known as the shoot‐and‐scoot tactic. This article analyzes the shoot‐and‐scoot tactic for a time‐critical mission using Markov models. We compute optimal move policies and develop heuristics for more complex and realistic settings. Spending a reasonable amount of time firing multiple shots from the same location is often preferable to moving immediately after firing an initial salvo. Moving frequently reduces risk to the artillery, but also limits the artillery's ability to inflict damage on the enemy.     

Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

Target selection in lanchester combat: Heterogeneous forces and time-dependent attrition-rate coefficients

We develop solutions to two fire distribution problems for a homogeneous force in Lanchester combat against heterogeneous enemy forces. The combat continues over a period of time with a choice of tactics available to the homogeneous force and subject to change with time. In these idealized combat situations the lethality of each force's fire (as expressed by the Lanchester attrition-rate coefficient) depends upon time. Optimal fire distribution rules are developed through the combination of Lanchester-type equations for combat attrition and deterministic optimal control theory (Pontryagin maximum principle). Additionally, the theory of state variable inequality constraints is used to treat the nonnegativity of force levels. The synthesis of optimal fire distribution policies was facilitated by exploiting special mathematical structures in these problems.     

Stochastic duels with bursts

In this analysis we extend the theory of stochastic duels to include the situation where one of the contestants fires a single infinitely long burst at a fixed rate of fire and secondly where he fires fixed-length, fixed-rate of fire bursts randomly spaced. In both cases the opponent fires single rounds randomly spaced. Special cases and parameter effects are considered.     

Inside the Iraqi State Records: Saddam Hussein, ‘Irangate’, and the United States

This article uses captured Iraqi state records to examine Saddam Hussein's reaction to US arms to sales to Iran during the Iran–Iraq War (the Iran/Contra scandal). These records show that ‘Irangate’ marked a decisive departure in Saddam's relations with the United States. Irangate reinforced Saddam's preexisting suspicions of US policy, convincing him that Washington was a strategic enemy that could not be trusted. Saddam concealed his anger to preserve a working relationship with the Reagan administration, but this episode nevertheless cemented his negative views of the United States and forged a legacy of hostility and mistrust that would inform his strategic calculus for years to come.     

Individual headstart strategies for combating congestion

This paper examines the process by which a user of a queueing system selects his arrival time to the system to compensate for unpredictable delays in the system if he wishes to complete service at a particular time. Considering the case in which all the system users have already decided on their arrival times to the system and will not change these times, this paper investigates how a new user of this system develops his strategy for selecting his arrival time. The distribution of this customer's arrival time is then obtained for a special case.     

On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

New results on a stochastic duel game with each force consisting of heterogeneous units

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force—knowing which units are still alive in real time—decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 56–65, 2014     

Survival and effectiveness of a weapon system against a superior force (guerrilla warfare)

Stochastic models are developed for a weapon system which attacks at a certain rate, but withdraws when attacked (guerrilla warfare). The models yield as output the distributions and mean values in closed form of the survival period and number of attacks made. As input are, for the weapon system, attack rate or amount of ammunition and time horizon, and, for the opponent, kill rate and probability of killing the weapon system, given the opponent has been attacked (strike back performance of the opponent). One model allows, however, for strike back also by the weapon system, when attacked by the opponent. This model is then used to determine, when the weapon system should strike back. The models are based on the Poisson and the binomial processes. Consistency among the models is shown and an example is provided.     

On a search for a moving target

We consider the problem of searching for a target that moves in discrete time and space according to some Markovian process. At each time, a searcher attempts to detect the target. If the searcher's action at each time is such as to maximize his chances of immediate detection, we call his strategy “myopic.” We provide a computationally useful necessary condition for optimality, and use it to provide an example wherein the myopic strategy is not optimal.     

Boko Haram and the challenges of Nigeria's war on terror

Boko Haram terrorism has been recognized by Nigerian President Jonathan as the most threatening and complex security issue in Nigeria since independence. In response, the Federal Government of Nigeria has committed itself to different counterterrorism measures, which are largely dominated by “hard politics” and military mobilization. Spending heavily on defense to upgrade military hardware and train personnel in a counterterrorism role, Nigeria has also boosted its strategic importance in the “Global War on Terror”. However, this attempt has become unpopular as it has failed to contain Boko Haram within a short time frame and has made insufficient headway against unabated terror, with human rights costs among the host communities and amidst a surge of stakeholders' discordance. As a matter of concern, this article seeks to assess Boko Haram as an opponent in Nigeria's war on terror (WOT) and to ascertain the challenges the country faces, the alternative measures open to it, and possible ways forward.     

Eisenhower,science and the nuclear test Ban Debate 1953–56

Though historians debate whether Eisenhower seriously pursued a nuclear test ban agreement at the close of his presidency, few have closely examined his consideration of the issue during his first term in office. Publicly, his administration ridiculed Democratic presidential candidate Adlai E. Stevenson's highly publicized test ban proposal in 1956. In fact, Eisenhower's private inclination to ban testing antedated Stevenson's campaign proposal by two years. A review of the administration's techniques of countering Stevenson's test ban proposal reveals the use of heated rhetoric, clever deception, and outright lies to manipulate public understanding of the test issue and to conceal the depth of Eisenhower's own sincere desire to limit, or even cease, tests.     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

On models for business failure data

It is pointed out in this paper that Lomax's hyperbolic function is a special case of both Compound Gamma and Compound Weibull distributions, and both of these distributions provide better models for Lomax's business failure data than his hyperbolic and exponential functions. Since his exponential function fails to yield a valid distribution function, a necessary condition is established to remedy this drawback. In the light of this result, his exponential function is modified in several ways. It is further shown that a natural complement of Lomax's exponential function does not suffer from this drawback.     

‘Troops were then forced to fire’: British army crowd control in Palestine,November 1945

In November 1945, British army shooting during street riots and search operations in Palestine resulted in the death of 13 Jews and the injuring of dozens. The most costly in casualties caused by army fire during the whole Jewish insurgency, these incidents have nevertheless not received detailed attention in literature on the British army's counterinsurgency campaign in postwar Palestine. This article outlines British military use of firepower to control civilian crowds and the difficulties involved during these incidents, contributing to the debate on the army's principal of ‘minimum force’. It also highlights the serious problem of legitimizing opening of fire on unarmed protestors, epitomized in the army's fabricated account justifying shooting at a large crowd rushing a military cordon at Givat Hayim.     

Operation Messiah: Did Christianity Start as a Roman Psychological Counterinsurgency Operation?

Through examining the life and work of the man who is generally known as the Apostle Paul, I hope to challenge the idea that the founder of Christianity was a saint and replace it with the possibility that he really was an agent-provocateur working for the Roman administration in Palestine and various other parts of the Empire. Paul's biography and his own letters, both of which were taken up in the New Testament, hold numerous clues to the effect that this former persecutor, originally named Saul of Tarsus, never left the ranks of the government, but instead went undercover after his famous ‘conversion’ en route to Damascus. The self-proclaimed successor-to-Jesus was not only treated dramatically differently from Jesus by the Romans, but they were his friends and allowed him to live and work for 20 years instead of crucifying him. Jesus' original followers distrusted Paul, and made various attempts to kill him throughout his life. I will conclude by arguing that Paul's claim that Jesus, this candidate-king of the Jews, was the Messiah and had been crucified as the will of God (the prime assumption upon which Christianity is based) should be read as a sadistic mockery of Jewish faith, meant to divide a Jewish resistance organisation and pacify it.