To Bluff or Not to Bluff
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Economics Strategy Mar 2, 2015

To Bluff or Not to Bluff

Game the­o­ry says it’s pure math­e­mat­ics. But human psy­chol­o­gy mat­ters, too.

Yevgenia Nayberg

Based on insights from

Ehud Kalai

Kent Grayson

From Texas Hold’em to nuclear deter­rence, the bluff is a com­mon strate­gic move, and one that we often think of as a kind of impro­vi­sa­tion — a clever psy­cho­log­i­cal ploy when the odds are stacked against us.

Game the­o­rists take a dif­fer­ent view on bluff­ing. For Ehud Kalai, a pro­fes­sor of man­age­r­i­al eco­nom­ics and deci­sion sci­ences at the Kel­logg School and found­ing edi­tor of Games and Eco­nom­ic Behav­ior, bluff­ing is pri­mar­i­ly com­pu­ta­tion­al, not psy­cho­log­i­cal. To win in any strate­gic game, it pays to be unpre­dictable, and game the­o­ry offers mod­els for how to keep one’s oppo­nent guessing.

It’s straight math­e­mat­ics,” Kalai says. If I bluffed all the time, obvi­ous­ly my bluff­ing would be inef­fec­tive. But it’s not effec­tive to under-bluff, either, because then I’m not mak­ing enough use of my rep­u­ta­tion as a non-bluffer. If you nev­er bluff, or bluff very rarely, you can use this rep­u­ta­tion to bluff more effec­tive­ly and increase your long-term winnings.”

Mix­ing It Up

As Kalai defines it, games of skill are those that require strate­gic moves, with each move ide­al­ly serv­ing to max­i­mize unpre­dictabil­i­ty. In 1984, he had an oppor­tu­ni­ty to prove this in court. When the city of Chica­go for­bade a bar own­er from putting com­put­er­ized pok­er and black­jack machines in his estab­lish­ment — claim­ing that these are games of luck, not skill — the own­er sued, and Kalai tes­ti­fied as an expert wit­ness on his behalf.

If you’re going to bluff, you have to be clear about what kind of game you’re playing.”

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In front of a judge, he played the games in strate­gic and non­strate­gic ways. The point was to show that it is pos­si­ble for some­one to play these games with skill,” he says. The judge was ulti­mate­ly con­vinced — though he did require a brief tuto­r­i­al — and the games were deemed to be legal. A cru­cial part of the skill was bluff­ing — or play­ing unpre­dictably enough to chal­lenge the machine’s algorithms.

Kalai has also applied his exper­tise to pro­fes­sion­al foot­ball. He once had a con­ver­sa­tion with Michael McCaskey, for­mer pres­i­dent of the Chica­go Bears, about using game the­o­ry cal­cu­la­tions to call offen­sive plays. At the time, com­put­ers were banned from the sky­box, but he still thinks the Bears could have paid more atten­tion to probabilities.

Just like in pok­er, you don’t want to be known for doing cer­tain things in cer­tain sit­u­a­tions — in this case, always pass­ing or always run­ning. Even if the sit­u­a­tion calls for run­ning the ball, every once in a while you want to pass the ball to keep the oth­er team unsure. I would ran­dom­ize between pass­ing the ball and run­ning the ball in dif­fer­ent sit­u­a­tions, but for each sit­u­a­tion I would ran­dom­ize with dif­fer­ent prob­a­bil­i­ties. So, for exam­ple, if it’s fourth down and we need ten yards, I would assign a high prob­a­bil­i­ty to pass­ing the ball.”

Game the­o­rists call this a mixed strat­e­gy. It’s a stan­dard game the­o­ry pro­ce­dure to deal with two-per­son, zero-sum games,” Kalai says, and it works for play­ing pok­er against a machine or run­ning an offense. It is based on the assump­tion that your oppo­nent is think­ing (or com­put­ing) as strate­gi­cal­ly as you are. It also assumes, of course, that a team is able to assess its own advantage.

In a mixed strat­e­gy, bluff­ing is con­stant, sus­tained, and sys­tem­at­ic — it takes one’s advan­tage into account but ran­dom­izes just enough to keep that advan­tage work­ing effec­tive­ly. Ran­dom­iza­tion is com­mon prac­tice in any num­ber of games,” from the preda­tor – prey sce­nario of a squir­rel flee­ing a hawk to a government’s approach to air­port secu­ri­ty or tax audit­ing. In most cas­es, suc­cess depends on more than a sin­gle dra­mat­ic bluff. For game the­o­rists, the way to win is to guar­an­tee long-term unpredictability.

Know­ing the Game, Know­ing Yourself

In busi­ness as in pok­er, it can pay to be unpre­dictable, but this is only true for cer­tain com­pet­i­tive sce­nar­ios. Think of two fash­ion com­pa­nies,” Kalai says. One com­pa­ny is a trend­set­ter and one is an imi­ta­tor. If each has to com­mit to the next season’s line with­out pri­or knowl­edge of the other’s style choic­es, then nei­ther the trend­set­ter nor the imi­ta­tor wants to be predictable.”

Still, he says, it is impor­tant to rec­og­nize that not all com­pet­i­tive games call for the same strat­e­gy. A mixed strat­e­gy might work best in a two-per­son zero-sum game, but there are also many kinds of nonan­tag­o­nis­tic games — in oth­er words, those that require full or par­tial coop­er­a­tion. It gets com­pli­cat­ed when you cross into dif­fer­ent strate­gic rela­tion­ships,” Kalai says. If you’re going to bluff, you have to be clear about what kind of game you’re playing.”

You also have to be clear about your own rep­u­ta­tion. Kent Grayson, a pro­fes­sor of mar­ket­ing at the Kel­logg School who has stud­ied trust and decep­tion, says that bluff­ing is only effec­tive when it is done with a mea­sure of self-aware­ness. A good rep­u­ta­tion might allow a com­pa­ny to bluff peri­od­i­cal­ly — by, for exam­ple, osten­si­bly mov­ing the date of a prod­uct launch, and there­by rat­tling com­peti­tors — but only if that com­pa­ny has a clear sense of how it is perceived.

A com­pa­ny might want to cap­i­tal­ize on its rep­u­ta­tion for being inno­v­a­tive,” he says, but the bluff would only work if they actu­al­ly have that rep­u­ta­tion — and also if they have a rep­u­ta­tion for telling the truth. In gen­er­al, too much unpre­dictabil­i­ty is like­ly to decrease people’s con­fi­dence in what you are say­ing.” In oth­er words, whether through bluff­ing or out­right decep­tion, over­cap­i­tal­iz­ing on your rep­u­ta­tion can dam­age your rep­u­ta­tion. A well-respect­ed bank can intro­duce hid­den fees for a while — just as a pop­u­lar car sales­man can sell the occa­sion­al lemon — but even­tu­al­ly devi­ous prac­tices will lead to a seri­ous ero­sion of trust.

Our con­cept of trust, Grayson says, is com­prised of three com­po­nents: com­pe­tence, hon­esty, and benev­o­lence. In oth­er words: Do I believe in this person’s abil­i­ty? Do I think he or she is telling the truth? And final­ly, am I sure that he or she has my best inter­ests at heart? In pok­er, foot­ball, and war, only the first two cat­e­gories are in play. When it comes to the mar­ket­place, bluff­ing becomes a much riski­er busi­ness, because a com­pa­ny has to con­sid­er exact­ly whose trust it is manip­u­lat­ing — and whether the pay­off is worth the cost.

High-Stakes Math

It is also not a nat­ur­al move to bluff when the stakes are extreme­ly high. Game the­o­rists say a mixed strat­e­gy has been proven to yield the best results, but there are times when strate­gic ran­dom­iza­tion feels like the wrong approach. Peo­ple under pres­sure tend to be more risk-averse. They also have to deal with the psy­cho­log­i­cal and polit­i­cal fall­out if their bluff does not succeed.

Take for exam­ple the final play of this year’s Super Bowl, when the Seat­tle Sea­hawks had the ball on the goal line against the New Eng­land Patri­ots. Despite hav­ing the best run­ning back in the league, the Sea­hawks chose to pass on sec­ond down, and when the ball was inter­cept­ed there was an out­cry among the team’s fans. Some­times even the best strat­e­gy is deemed incor­rect in hind­sight — that is, if it fails. But if it had worked and the Sea­hawks had won, fans might have thought the play was brilliant.

Ran­dom­iza­tion is espe­cial­ly tough when it comes to war­fare and pol­i­tics — some­thing Kalai, who is Israeli, has wit­nessed him­self. In 1967, dur­ing the Six-Day War between Israel and its Arab neigh­bors, the Israeli mil­i­tary approached a fel­low game the­o­rist with a prob­lem. They knew that some Egypt­ian con­voys were using Israeli sym­bols on the roofs of their trucks to fool the Israeli bombers. This posed a predica­ment for the Israeli pilots, who could not tell the true iden­ti­ty of such con­voys before mak­ing a deci­sion about whether to bomb.

My friend, being a game the­o­rist, told them that you can com­pute it. You bomb accord­ing to such-and-such prob­a­bil­i­ties. Of course, there was no way the gen­er­al was going to do that, even if it was the right deci­sion, because to bomb peo­ple by the flip of a coin would be polit­i­cal suicide.”

The British faced a sim­i­lar dilem­ma dur­ing World War II. When Alan Tur­ing broke the wartime Ger­man code, Enig­ma, the mil­i­tary used a math for­mu­la to deter­mine how many inter­ven­tions the Allied forces could plau­si­bly make with­out reveal­ing their secret advan­tage. This, of course, was classified.

So while game the­o­ry has a lot to teach about strate­gic decep­tion, there are lim­i­ta­tions. Some­times the math is too com­plex to rec­om­mend a course of action. If we take a restrict­ed pok­er game,” Kalai says, I can com­pute the opti­mal bluff­ing prob­a­bil­i­ties. But if it was a full pok­er game as played by a group of play­ers in the casi­no, I could not com­pute the absolute­ly opti­mal strat­e­gy. The same goes for oth­er sit­u­a­tions. Some­times it is a solv­able prob­lem, and some­times it is just an estimate.”

Featured Faculty

Ehud Kalai

Professor of Managerial Economics & Decision Sciences, Emeritus

Kent Grayson

Associate Professor of Marketing; Bernice and Leonard Lavin Professorship

About the Writer

Drew Calvert is a freelance writer based in Chicago.

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