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Register Log inInsights & Publications Latest thinking Industries Functions Regions ThemesArticleMaking game theory work for managersA new model, rejecting solutions optimal only for a single precisely defined future, generates answers representing the best compromise between risks and opportunities in all likely futures.December 2009| byHagen Lindstdt and Jrgen MllerIn times of uncertainty,game theory should come to the forefront as a strategic tool, for it offers perspectives on how players might act under various circumstances, as well as other kinds of valuable information for making decisions. Yet many managers are wary of game theory, suspecting that its more theoretical than practical. When they do employ this discipline, its often misused to provide a single, overly precise answer to complex problems.Our work on European passenger rail deregulation and other business issues shows that game theory can provide timely guidance to managers as they tackle difficult and, sometimes, unprecedented situations. The key is to use the discipline to develop a range of outcomes based on decisions by reasonable actors and to present the advantages and disadvantages of each option. Our model shifts game theory from a tool that generates a specific answer to a technique for giving informed support to managerial decisions.Several factors in todays economic environment should propel game theory to a prominent place in corporate strategy. The global downturn and uncertain recovery, of course, have prompted radical shifts in demand, industrial capacity, and market prices. Some companies, emboldened by the crisis, have tried to steal market share. New global competitors from emerging economies, particularly China and India, are disturbing the established industrial order. They use new technologies and business models and even have novel corporate objectives, often with longer-term horizons for achieving success.These uncertainties can paralyze corporate decision making or, perhaps worse, compel managers to base their actions on gut feelings and little else. Game theory can revitalize and contribute clear information to decision makingbut only if its users choose a set of inputs detailed enough to make the exercise practical and analyze a range of probable scenarios.Decades oldand misunderstoodGame theory as a management tool has been around for more than 50 years. Today, most university business students are introduced to the idea through the classic prisoners dilemma. This and similar exercises have instilled the idea that game theory generates a single solution representing the best outcome for reasonable players.In academic settings, game theory focuses on logically deriving predictions of behavior that are rational for all players and seem likely to occur. It does so by seeking some form of equilibrium, or balance, based on a specific set of assumptions: the prisoners arent aware of each others actions, can give only one answer, and so on.But the real world is messier than the neat environment of the prisoners dilemma, and game theory loses some traction when faced with practical, dynamically evolving business problems. Companies using this approach often fail to strike the right balance between simplifying a problem to make it manageable and retaining enough complexity to make it relevant. In addition, decision makers often get a single proposed solution without understanding clearly the assumptions that went into its formulation. This problem is especially troublesome because solutions that seek a universal equilibrium among players in a sequence are sensitive to the initial conditions presented and to the assumptions used in deriving an answer.We have developed a model that addresses these objections. Instead of predicting a single outcome, with all factors balanced, the model first generates a narrow set of strategic options that can be adjusted to account for changes in various assumptions. Instead of solving an individual game, the model automatically involves a sequence of several games, allowing players to adjust their actions after each of them, and finds the best path for different combinations of factors. As one result, it supports executive decisions realistically by presenting managers with the advantages and disadvantages of the strategic options that remain at each stage of the progression. In a second step, the model finds the best robust option, considering its upside potential and downside risks under all likely scenarios, assumptions, and sensitivities as time elapses. This approach is different from attempts to look for equilibrium in an artificially simplified world.Lets say, for example, that two companies in the global machinery market face an attacker from China planning to open its own multipurpose factory. Depending on myriad assumptions about cost structures, customer demand, market growth, and other factors, the best strategy in one scenario could be for the incumbents to cut prices. In a second scenario, using slightly different assumptions, it could be best to wait until the entrant acts and then to secure the greatest value by reacting appropriately.Traditional game theory delivers the best answers and equilibriums, which could be completely different for each scenario. Then it tries to predict the most likely scenario. But you cant analyze uncertainty away, and the traditional approach actually offers management a series of snapshots, not a recommendation based on the overall picture. Our model, in contrast, examines how assumptions and actions might change and looks at possible gains and losses for each player in a dynamic world. In the example of the machinery companies, the best robust option could be to leave room for the entrant in a particular niche, where the incumbents are weakest and theres little risk that the entrant could expand into other segments.Our model seeks to balance simplicity and relevance by considering a likely set of actions and their effect on important metrics such as demand and profit. Experience and an understanding of the various actors sensitivities to different situations guide the analysis. By considering only the most relevant factors, the model manages complexity and, at the same time, creates transparency around important break points for the key drivers. One such break point could be how strongly the market must react to an attackers move before an incumbents best strategy shifts from coexistence to counterattack.The best way to understand the model is to examine it in action.Game theory and European railAfter years of debate and delay, the deregulation of passenger railways in the European Union appears to be gaining momentum. Cross-border passenger service is to be fully open to competition from January 2010. Some member states, including Germany, Italy, Sweden, and the United Kingdom, have taken the initiative and begun opening domestic long-distance passenger rail service to competition, as well.The experience of other deregulated industries provides rail operators with some lessons, such as the futility of price wars, which generally destroy an industrys profitability. But the unique characteristics of rail make it exceptionally difficult to predict how competition will alter the playing field. In passenger rail service, for instance, network effects are prevalent, as routes connecting passengers to numerous cities and towns tend to be highly interdependent.Certainly, new entrants will try to skim off some of the most profitable point-to-point routes. Despite significant upfront capital expenditures, these challengers will probably try to use lower operating costs to undercut the incumbents fares. Beyond that, it remains to be seen how and where the attackers will attack and how incumbents will defend themselves.Besides mutually destructive price wars, what options do the incumbents have? Should they rewrite their schedules to compete with the attackers timetables head-to-head? Would it make sense for them to emphasize their superior service or to compete on price by stripping away frills? Should they concede some minor routes to the new entrants in hopes of limiting the damage or fight for every passenger?To address these questions, the model we developed uses game theory to understand the dynamics of the emerging competition in long-haul passenger rail routes. It breaks down the complex competitive dynamics into a set of sequential games in which an attacker makes a move and an incumbent responds.From the perspective of the attackers, the range of options available can be distilled into four main choices. The attackers could imitate the incumbents by providing similar or identical service. They could go on the offensive with a more attractive servicefor instance, one that is cheaper or more frequent. They could specialize by offering a niche service, probably only at peak hours, that isnt intended to compete with the incumbents across the schedule. Finally, they could differentiate by providing a clearly distinctive service, such as a low-cost offer focused on leisure travelers, with suitable timetables and less expensive, slower rolling stock.Likewise, the range of responses available to incumbents on each route under challenge can be broken down to their essence: to ignore the attackers by not reacting at all; to counterattack by contesting the entry through changes in price, frequency of service, and schedules; to coexist by ceding some routes and learning to share them; or to exit a route by stopping service on it.These initial steps in setting up a game theory model are straightforward. The crucial element is to create a list that is both exhaustive and manageable. But the world is dynamic, and the payoffs for each player depend heavily on the details. Four factors, which must also be included in the rail model, can significantly affect the outcome. Total changes in demand.What will happen to demand with each move by an attacker and response by an incumbent? When offered a broader, more comprehensive choice of rail links, passengers could change their behaviorfor instance, travelling by train instead of car or plane. Cost differences.New players typically have significantly lower operating costs than incumbents, which, however, generally enjoy economies of scale. But a higher degree of complexity and public-service obligations, such as maintaining uneconomical routes, often negate this advantage. Network advantages.Incumbents almost always have a network advantage, since attackers rarely replicate an incumbents entire system. (Many routes, intrinsically unprofitable by themselves, are valuable only as feeders to the larger network.) Passengers generally prefer seamless connectionsa preference that plays to the incumbents strengths, especially to and from points beyond the major routes. Price sensitivity.Attackers typically charge lower fares, and the degree of difference needed for passengers to switch lines or modes of transport (from cars to trains, for instance) is critical to the outcome.In the common approach to game theory, analysts look at dozens of permutations of actions and reactions, choosing those they feel are consistent and mutually balanced, as well as most likely to occur. Then they make assumptions about these or other factors. The result is a solution, with one particular set of assumptions, derived from all the interests of all the players. The solution could, for instance, be to fight the new entrant tooth and nail on all fronts.But in looking at the problem, we found several conditions in which the players interests could be seen as consistent and mutually balanced. Just as interesting, the results were sensitive to our initial assumptions: in other words, when we slightly modified an assumption about, say, changes in demand, the results would be very different. From this perspective, our model resembles a business simulator, allowing executives to get a clear understanding of the likely evolution of competition under differing conditions. It helps companies to generate the best option as the moves of competitors become clear.The outcome of the rail analysisWhat did the model say about European passenger rail?Consider, first, one set of conditions. In this scenario, the incumbent operates a fairly large network and has enjoyed monopoly advantagesin particular, relatively high profits. But because of the monopoly legacy, the incumbent suffers from operational inefficiencies and a sizeable cost base. Overall demand is elastic: customers are likely to travel more by rail if service improves and quite likely to accept low-price offers. A new company with a substantially lower cost base considers cherry-picking a few of the more attractive routes by offering improved service.This model suggests that although the attacker enjoys lower costs and seems to have a favorable starting position, it will probably take only a sliver of market share, and that thanks largely to a general increase in rail use. The incumbent will remain dominant. Seeing the likely outcome of the attackers specialized or niche entry, the incumbents executives should conclude that a strategy of tolerance would be best. Only a small share of the market is at stake, and the incumbent could lose much more if it engaged in a costly battle for this sliverfor instance, by waging a destructive price war or using other expensive tactics. If the attacker is more aggressive, the incumbents best answer would be to fight back with tactics including aggressive price competition, targeted marketing activities, and more frequent and better service on the routes under attack. Note, however, that this would substantially lower profits for both players.To cover the full range of possibilities, the model can manipulate each variable. Under certain circumstances (if the demand reaction is muted, the incumbents cost disadvantage high, and its network advantage small) entrants have the inside track and could probably take control of the market. When circumstances favor the incumbent a little more (because its network advantage is stronger or its cost disadvantage smaller) it will probably have strong incentives to lower prices preemptively to prevent a possible attackers entry. If conditions are more ambiguous, the incumbent may have to settle for coexistence, although it can probably retain market leadership. The attackers share of the industrys profits would vary significantly, depending mainly on the incumbents network advantage (Exhibit 1).Exhibit 1Three scenariosThree scenarios depict the interrelatedness of customer demand, the incumbents cost disadvantage, and the strength of network effects. Enlarge

When we run the European passenger rail model through an array of different situations, a critical factor appears to be the way demand reacts to liberalization. Will the new offerings seduce travelers to take trains rather than cars or jetliners, or will overall demand remain stagnant, leaving rail companies to battle for an unchanged pool of customers (Exhibit 2)?Exhibit 2The inuence of pricingThe competitive scenarios change slightly if the passengers are highly price sensitive. Enlarge

If the attackers entry doesnt stimulate demand, two operators cannot profitably share most routes: high fixed costs make many of them natural monopolies supporting only a certain level of capacity. A weak incumbentfor instance, one with major cost disadvantages or few network benefitscould be squeezed out by an agile attacker. A strong incumbent could cut fares before the attacker committed itself to any investment, dissuading it from making the challenge. In the end, the competitors will face a winner-takes-all situation, with only one left in the market.When rail demand can be stimulated, players will probably coexist profitably. But the model suggests that even when the attacker enjoys the best conditions, the incumbent is likely to retain market leadership. Reasonable attackers will have an incentive to enter only on a small scale that the incumbent can usually tolerate. More aggressive moves from either side would trigger ruinous price wars or service expansions, destroying the industrys overall profitability.Finally, at each moment, incumbents almost always have one best robust option that conserves much more of their profits than any other course. Quite often, deviating from that option reduces the entire industrys profits significantly. But unlike a solution based on traditional game theorya solution optimal only for a single precisely defined futureour model generates an answer that represents the best compromise between risks and opportunities across all likely futures. Unlike the answers suggested by traditional game theory, this one does not require all competitors to behave according to a narrowly defined rational equilibrium at each moment. The transparency of our approach helps executives understand the break points of a strategy: how much reality must differ from its assumptions before a new strategy is needed.Although we focus here on European passenger rail, our model shows how game theory can be applied to many complex environments and produce results informing many strategic decisions. Weve applied the model to other problems, with similarly enlightening results. In health care, for example, we examined the dynamics of the commoditization of certain drugsin particular, after Asian manufacturers offered higher-quality versions of them. We also looked at the strategic options of companies in the chemical industry in the wake of recent overcapacity and reduced demand. Game theory is a powerful framework that enables managers to analyze systematically the ties among interactions between actors in a market and to develop appropriate competitive strategies. But its helpful only if executives expect a tool that helps them make informed decisions based on a range of market actions by each player, not a single answer that solves the whole riddle.About the authorsHagen Lindstdtis the head of the Institute for Management at Karlsruhe University, andJrgen Mlleris a principal in McKinseys Stockholm office.In Salary Negotiations

Since receiving an increase in salary often affects other salaries in the company, more people are involved and these types of games are more complex than simple one on one negotiations. The more people involved the more difficult it is to negotiate, so breaking negotiations down to one partner and using game theory with him is advised rather than attempting to negotiate with multiple people.In order to attain a higher salary in negotiations using game theory, one must attempt to minimize risk, make the first offer, beware of precedence, have credibility, maintain continuity, and have a reciprocal relationship with the partner being negotiated with.There first must be a need for your services, so you cannot simply receive a raise just because you want one. But if you are up for a raise and in negotiations, you can work down the chain at the potential responses from your employer and have a counter-argument ready for each. You must know the partner well and understand the path to the optimal amount you are seeking.

Read more:http://www.businessinsider.com/how-to-use-game-theory-to-your-benefit-2012-4?op=1#ixzz32c2kOhJr

Game theory in practiceComputing: Software that models human behaviour can make forecasts, outfox rivals and transform negotiationsSep 3rd 2011|From the print edition

FOR a man who claims to lack expertise in the field, Bruce Bueno de Mesquita, an academic at New York University, has made some impressively accurate political forecasts. In May 2010 he predicted that Egypt's president, Hosni Mubarak, would fall from power within a year. Nine months later Mr Mubarak fled Cairo amid massive street protests. In February 2008 Mr Bueno de Mesquita predicted that Pakistan's president, Pervez Musharraf, would leave office by the end of summer. He was gone before September. Five years before the death of Iran's Ayatollah Khomeini in 1989, Mr Bueno de Mesquita correctly named his successor, and, since then, has made hundreds of prescient forecasts as a consultant both to foreign governments and to America's State Department, Pentagon and intelligence agencies. What is the secret of his success? I don't have insightsthe game does, he says.Mr Bueno de Mesquita's game is a computer model he developed that uses a branch of mathematics called game theory, which is often used by economists, to work out how events will unfold as people and organisations act in what they perceive to be their best interests. Numerical values are placed on the goals, motivations and influence of playersnegotiators, business leaders, political parties and organisations of all stripes, and, in some cases, their officials and supporters. The computer model then considers the options open to the various players, determines their likely course of action, evaluates their ability to influence others and hence predicts the course of events. Mr Mubarak's influence, for example, waned as cuts in American aid threatened his ability to keep cronies in the army and security forces happy. Underemployed citizens then realised that disgruntled officials would be less willing to use violence to put down street protests against the ailing dictator.Technology Quarterly Cameras get cleverer Drops to drink Formula 1 goes sailing Zapping fakes with lasers Particle physic A golden fleece Joining the drones club Reducing the barnacle bill What would Jesus hack? Worrying about wireless Changes in the air Game theory in practice Muscling in on motors Put your thinking cap on Disrupting the disruptersReprintsRelated topics Pakistan Hosni Mubarak Technology Software Science and technologyMesquita & Roundell, Mr Bueno de Mesquita's company, is just one of several consulting outfits that run such computer simulations for law firms, companies and governments. Most decision-making advice is political, in the broadest sense of the wordhow best to outfox a trial prosecutor, sway a jury, win support from shareholders or woo alienated voters by shuffling a political coalition and making legislative concessions.But feeding software with good data on all the players involved is especially tricky for political matters. Reinier van Oosten of Decide, a Dutch firm that models political negotiations and vote-trading in European Union institutions, notes that forecasts go astray when people unexpectedly give in to non-rational emotions, such as hatred, rather than pursuing what is apparently in their best interests. Sorting out people's motivations is much easier, however, when making money is the main object. Accordingly, modelling behaviour using game theory is proving especially useful when applied to economics.Follow the moneyModelling auctions has proved especially successful, says Robert Aumann, an academic at the Hebrew University of Jerusalem who received a Nobel prize in 2005 for his work in game-theory economics. Bids, being quantified, facilitate analysis, and predicting the right answer can be very lucrative. Consulting firms are popping up to help clients design profitable auctions or win them less expensively. In the run-up to an online auction in 2006 of radio-spectrum licences by America's Federal Communications Commission, Paul Milgrom, a consultant and Stanford University professor, customised his game-theory software to assist a consortium of bidders. The result was a triumph.When the auction began, Dr Milgrom's software tracked competitors' bids to estimate their budgets for the 1,132 licences on offer. Crucially, the software estimated the secret values bidders placed on specific licences and determined that certain big licences were being overvalued. It directed Dr Milgrom's clients to obtain a patchwork of smaller, less expensive licences instead. Two of his clients, Time Warner and Comcast, paid about a third less than their competitors for equivalent spectrum, saving almost $1.2 billion.

Advances in game theory have picked up dramatically in recent years as it has become apparent that failing to do a proper analysis can be costly, says Sergiu Hart, a colleague of Dr Aumann's at Hebrew University. For example, a few years ago Israel's government added a novel twist to an auction of oil-refinery facilities. To encourage more and higher bids, the government offered a $12m prize to the second-highest bidder. It was an expensive mistake. Without the incentive, the highest bid would have been about $12m higher, an analysis showedparticipants bid low because the loser would strike it rich. Combine that sum with the prize payout, and the government's loss amounted to roughly $24m. The conclusion, then, is don't presume you know what the solution is without help from modelling software, says Brad Miller, senior modeller at Charles River Associates, a consultancy in Boston. It designs game-theory software to model industrial auctions and the plotting of corporate mergers and acquisitions.The use of modelling makes business clients more inclined to adopt longer-term strategies.Software is not always needed. A student at Hebrew University, for example, demonstrated the Israeli government's $24m loss using pen and paper. It took him about two days, however, according to a professor there. Software, naturally, is far faster. But gathering and handling the necessary data can require expensive expertise or training. Decide, the Dutch consultancy, usually charges 20,000-70,000 ($28,000-100,000) to solve a problem using its software, called DCSim, because it must first conduct lengthy interviews with experts. Its clients include government bodies in the Netherlands and abroad, and big companies including IBM, a computer giant, and ABN AMRO, a Dutch bank.PA Consulting, a British firm, designs bespoke models to help its clients solve specific problems in areas as diverse as pharmaceuticals, fossil-fuel energy and the production of television shows. British government agencies have asked PA Consulting to build models to test regulatory schemes and zoning rules. To give a simple example: if two shrewd, competing ice-cream sellers share a long beach, they will set up stalls back-to-back in the middle and stay put, explains Stephen Black, a modeller in the firm's London headquarters. Unfortunately for potential customers at the far ends of the beach, each seller prevents the other from relocatingno other spot would be closer to more people. Introduce a third seller, however, and the stifling equilibrium is broken as a series of market-energising relocations and pricing changes kick in. The use of modelling makes business clients more inclined to adopt longer-term strategies, Dr Black says.But game-theory software can also work well outside the sphere of economics. In 2007 America's military provided Mr Bueno de Mesquita with classified information to enable him to model the political impact of moving an aircraft carrier close to North Korea (he will not reveal the findings). Game-theory software can even help locate a terrorist's hideout. To run simulations, Guillermo Owen of the Naval Postgraduate School in Monterey, California, uses intelligence data from the US Air Force to estimate on a 100-point scale the importance a wanted man attaches to his likes (fishing, say) and priorities (remaining hidden or, at greater risk of discovery, recruiting suicide-bombers). Such factors determine where and how terrorists decide to live. Game-theory software played an important role in finding Osama bin Laden's hideout in Abbottabad, Pakistan, says Mr Owen.Where is all this heading? Alongside the arms race of increasingly elaborate modelling software, there are also efforts to develop software that can assist in negotiation and mediation. Two decades ago Clara Ponsat, a Spanish academic, came up with a clever idea while pondering the arduous Israeli-Palestinian peace process. As negotiators everywhere know, the first side to disclose all that it is willing to sacrifice (or pay) loses considerable bargaining power. Bereft of leverage, it can be pushed back to its bottom line by a clever opponent. But if neither side reveals the concessions it is prepared to make, negotiations can stall or collapse. In a paper published in 1992, Dr Ponsat described how software could be designed to break the impasse.

Difficult negotiations can often be nudged along by neutral mediators, especially if they are entrusted with the secret bottom lines of all parties. Dr Ponsat's idea was that if a human mediator was not trusted, affordable or available, a computer could do the job instead. Negotiating parties would give the software confidential information on their bargaining positions after each round of talks. Once positions on both sides were no longer mutually exclusive, the software would split the difference and propose an agreement. Dr Ponsat, now head of the Institute of Economic Analysis at the Autonomous University of Barcelona, says such mediation machines could lubricate negotiations by unlocking information that would otherwise be withheld from an opponent or human mediator.Such software is now emerging. Barry O'Neill, a game theorist at the University of California, Los Angeles, describes how it can facilitate divorce settlements. A husband and wife are each given a number of points which they secretly allocate to household assets they desire. The wife may inform the software that her valuation of the family car is, say, 15 points. If the husband puts the car's value at 10 points, he cannot later claim that he deserves more compensation for not getting the car than she would be entitled to.Predicting an end to conflictParticipants need to be sure that such mediation technology is fully neutral. For large deals, audit firms closely monitor the development and use of such software to ensure that no party secretly obtains information about another's bargaining positions, says Benny Moldovanu, a game theorist at the University of Bonn. He advises firms that design negotiation software for privatisation schemes and wholesale-electricity markets. This approach will spread to other utility markets, such as water, he believes.Could software-based mediation spread from divorce settlements and utility pricing to resolving political and military disputes? Game theorists, who consider all these to be variations of the same kind of problem, have developed an intriguing conceptual model of war. The principle of convergence, as it is known, holds that armed conflict is, in essence, an information-gathering exercise. Belligerents fight to determine the military strength and political resolve of their opponents; when all sides have converged on accurate and identical assessments, a surrender or peace deal can be hammered out. Each belligerent has a strong motivation to hit the enemy hard to show that it values victory very highly. Such a model might be said to reflect poorly on human nature. But some game theorists believe that the model could be harnessed to make diplomatic negotiations a more viable substitute for armed conflict.Today's game-theory software is not yet sufficiently advanced to mediate between warring countries. But one day opponents on the brink of war might be tempted to use it to exchange information without having to kill and die for it. They could learn how a war would turn out, skip the fighting and strike a deal, Mr Bueno de Mesquita suggests. Over-optimistic, perhapsbut he does have rather an impressive track record when it comes to predicting the future.