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Download Article © October 2017 | IJIRT | Volume 4 Issue 5 | ISSN: 2349-6002 The Analogous Application of Game Theory and Monte Carlo Simulation Techniques from World War II to Business Decision Making Dhriti Malviya1, Disha Gupta2, Hiya Banerjee3, Dhairya Shah4, Eashan Shetty5 1, 2,3,4,5 Narsee Monjee Institute of Management Studies, Mumbai, India Abstract- The Second World War, one of the most ‗Operations Research‘ only came up in the year 1940. gruelling events in the history of mankind, also marks During World War II, a team of humans referred to the emergence of one of modern-day’s most widely used as the Blackett‘s Circus in UK first applied scientific scientific disciplines – Operations Research (OR). techniques to analyze military operations to win the Rather than defining OR as a ‘part of mathematics’, a war and thus developed the scientific discipline – better characterization of the sequence of events would be that some mathematicians during World War II Operations Research. Operations Research includes were coerced into mixed disciplinary units dominated plenty of problem-solving techniques like by physicists and statisticians, and directed to mathematical models, statistics and algorithms to participate in an assorted mix of activities which were assist in decision-making. OR is used to analyze clubbed together under the rubric of ‘Operations advanced real-world systems, typically with the Research’. Some of these activities ranged from target of improving or optimizing the tasks. curating a solution for the neutron scattering problem The aim during WWII was to get utmost economical in atomic bomb design to strategizing military attacks usage of restricted military resources by the by means of choosing the best possible route to travel. Thus arose two major Operations Research techniques application of quantitative techniques. Ever since – Monte Carlo Simulation and Game Theory. More then, OR has developed into a theme oftentimes used than 70 years later, managers face business problems in industries, economics and businesses together with that often seem as complicated as the design of an petrochemicals, logistics, airlines, government, etc. atomic bomb. Models of pricing buy-back and revenue- The Second World War had sparked scientific sharing negotiations, product decisions, principal-agent advances in the study of communication, decisions, supply chain design, advertising decisions, computation, & control which produced the options and futures trading or allocation of funds are technological grounds for automation. usually too complex to solve in simple mathematical Modern challenges related to a worldwide economy terms. In the first part of this paper, we discuss in- and also the growth of technology have magnified the depth, how mathematicians leveraged the two aforementioned OR techniques during World War II. complexness of the business setting. Modern firms In the latter part of the paper, we map both these usually attempt to serve a worldwide, instead of a techniques to the current business scenario and suggest regional or national, client base and face worldwide ways of using them to make better managerial competition. By relying on refined mathematical decisions. models and advanced software tools, Operations Index terms: Game Theory, Nash Equilibrium, Monte Research can assess all available options facing a Carlo Simulation, Managerial Decision Making, Second firm, project possible outcomes and analyze risks World War, Operations Research associated with particular decisions. Companies I. INTRODUCTION collect large amounts of data but may feel It is often seen that history is not clear cut. This is the overwhelmed by the volume and lack the time or classic example where different people have diverse expertise to fully analyze these data, transforming views of the same event. Based on the history of OR, them into useful information on which to base it is believed that Sir Charles Babbage (1791-1871) is decisions. Operations research uses advanced the father of Operations Research, but the name mathematical and statistical techniques, such as linear IJIRT 144872 INTERNATIONAL JO URNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 177 © October 2017 | IJIRT | Volume 4 Issue 5 | ISSN: 2349-6002 programming and regression analysis, to help Stage 1: Analysing the use of Monte Carlo organizations make the most of their data. Through Simulation and Game Theory in World War II detailed analysis of the data, operations research Stage 2: Mapping both the techniques and their uses analysts can help uncover options that lead to higher to the modern world and managerial decision profits, more-efficient operations and less risk. making. Business managers who find that projects always Methods used: seem to run late, cost overruns are all too common, I. Game Theory and actual results are not even close to projections (i) Zero-sum Games: may sometimes feel the need to use methods akin to In Zero-sum games, most instances involve repetitive those used in the design of the atomic bomb. So they solution. The winner receives the entire amount of created a wholly new approach -- plugging in payoff which is contributed by the loser. Therefore, indiscriminately chosen numbers into the equations two-person zero-sum games are simply those games and scheming the results. This new approach came to which involves only two players where one person‘s be known as the ‗Monte Carlo Simulation‘ approach. gain is exactly balanced by the other person‘s loss. Though the scientists during WWII solely checked Thus, we obtain a sum of zero when adding up the thousands and trillions of combos of numbers, by total gains and subtracting the total loss. sampling random numbers to hide the various We analyze a two-person zero-sum game with a dimensions of the matter, and analyzing the results simple mathematical description of a game, the with statistics, they were ready to create excellent strategic form. predictions -- and in fact guide the design of an The strategic form of a two-person zero-sum game is atomic bomb that ultimately ended WWII. Similarly, given by a triplet (X, Y, A), where the ‗Theory of Games‘ also known as ‗Game Theory‘ X being a nonempty set, the set of strategies of originated to solve problems like finding the best Player I route for military attacks and making strategic Y being a nonempty set, the set of strategies of military decisions. Today, the application of Game Player II Theory has scaled from just military decisions to A being a real-valued function defined on X × Y crucial managerial decisions in the competitive (Thus, A(x, y) is a real number for every x ∈ X and corporate world. every y ∈ Y.) Research Objectives: Meaning, suppose Player I chose x ∈ X and Player II 1. To discuss the following applications of Game chose y ∈ Y concurrently, and each player oblivious Theory and Monte Carlo Simulation: of the choice of the other. (i) Historical applications (World War II) The amount Player I could win from Player II will (ii) Current applications (in the business belong to the set A(x, y). If A < 0, Player I will lose scenario) this amount. Therefore, A(x, y) indicates the 2. Under Game Theory, to enunciate the uses of the winnings of Player I and the losses of Player II. The following types of strategies in various business maximin value of a player is the largest value that the applications and managerial decision making: player can be sure to get without knowing the actions (i) Zero-sum Games of the other players. The minimax value of a player is (ii) Dominance Strategy and Pay-off the smallest value that the other players can force the Matrices player to receive, without knowing his actions. (iii) Nash Equilibrium and Prisoner‘s Encounters where we obtain the same maximin and Dilemma minimax values, the outcome is called an equilibrium 3. To similarly enunciate the uses of Monte Carlo outcome and we obtain a saddle point. Thus, when Simulation in various business applications and the maximin and minimax are said to be in managerial decision making particularly in equilibrium, the outcome associated with them is making complex product decisions. called a saddle point. Methodology: (ii) Nash Equilibrium We carried out our analysis in two stages: The Nash Equilibrium is a concept of game theory where the optimal outcome of a game is one IJIRT 144872 INTERNATIONAL JO URNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 178 © October 2017 | IJIRT | Volume 4 Issue 5 | ISSN: 2349-6002 where no player has an incentive to deviate from his (Strategies curated and applied during WWII chosen strategy after considering an opponent's particularly in the Battle of the Bismarck Sea) choice. The Battle of the Bismarck Sea took place in the (iii) Dominance Strategy & Pay-off Matrix South West Pacific Area during World War II in In game theory, strategic dominance (commonly 1943 when aircraft of the U.S. Fifth Air Force and called simply dominance) occurs when one strategy the Royal Australian Air Force attacked a Japanese is better than another strategy for one player, no convoy carrying troops to New Guinea. This part of matter how that player's opponents may play. the paper talks about the fundamental concepts of A strategy is said to be weakly dominated if there Game Theory like the two-person zero-sum game and exists some other strategy for a player which is some Nash Equilibrium dominance ideas as well as possibly better and never worse, yielding a higher the strategies applied to the Battle of the Bismarck payoff in some strategy profile and never yielding a Sea based on the actual military operation. lower payoff. The Japanese Admiral, Imamura, who was the An iterated-dominance equilibrium is a strategy commander of the Japanese Navy ordered for profile found by deleting a weakly dominated reinforcements to be delivered to Japanese soldiers strategy from the strategy set of one of the players, fighting in Papua New Guinea.
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