The Game of Chicken- Strategy, Game Theory and Cases of real life

The game is that two motorists or automobiles are directed against each other at high speed. If one of them departs, he loses as a coward, while the other wins.

If both move apart, none loses nothing, while if both continue, they crash and lose both.

A famous version of this game is that of the movie “Rebel without a cause” where motorists, instead of heading against each other, head towards a cliff with the car. But, as for the game, it does not change much.

We analyze the game according to the concepts of game theory:

* It is a symmetrical game.

* It is not zero-sum.

* There is no dominant strategy for any of the players.

* There are two Nash equilibria in pure strategies: Follow / Set and Move / Follow.

* Depending on how we consider the game, we can take it as sequential or as simultaneous.

When I have to decide whether to continue or to separate, I know that the other, at least until now, has decided to continue. Because if he had decided to leave, I would have won. So from this point of view it is sequential. But for the same reason, we know that both players will continue rushing the decision until the last moment, when we can not wait to see what the other does. Therefore, all initial decisions are trivial, we know that we will both decide to follow. The only decision that matters is the one we made at the last moment. And therefore, we can consider it simultaneous.

Strategy to look like a crazy

What prevents this is the best strategy? This is prevented by the fact that we do not know if the other is crazy and is going to sacrifice himself to punish us.

This is a play on words in English, impossible to translate. Mad means crazy, but they are also the acronym of Mutual Assured Destruction (Mutual Assured Destruction). Sometimes it is also said to “play the crazy card” as a reference to use this strategy, I imagine that in reference to the wild card.

This was the heart of the Cold War: if you attack me, it will start an escalation that will force us both to shoot our nuclear missiles and we will both be destroyed. So do not attack me. Moreover, do not even approach your soldiers to mine, lest there be an accident and we have it.

This result is often called “zero sum”, but not in the same sense in which we used it, but in the sense of 1 + 1 = 0. If both “win” the war, both are destroyed. And all the others, by the way, too.

Curiously, when the Cold War began to cool down (it’s worth the paradox), and both sides began to reduce their arsenal, it was, according to some analysts, when the greatest danger was. At the height of the cold war, there were millions of nuclear warheads on each side (I do not know the number, not even the order of magnitude, and in fact I am not sure that this is really the real situation, but follow the reasoning without stopping in that trifle). If one launched a preemptive attack, it was likely to destroy 99% of the enemy’s warheads while they were still in their silos. But that 1% that remained were still thousands of heads, enough to launch a counterattack of retaliation that annihilated the first without any doubt.

Instead, when both began to reduce their arsenals … for example instead of millions and there were only 1,000 heads on each side … 99% destruction in the first attack would leave 10 heads alive. Enough to launch a counterattack, yes; harmful, yes; but not enough to annihilate the other.

We’re going to leave it here, while we give readers time to go over the movies and readings we’ve recommended, and to dry the tears afterwards. In the second part we will look for another strategy, and we will look for the iteration of the game, ending with another form of chicken game that will be easier for us to analyze.

It is interesting to compare the game of the hen with that of the battle of the sexes. At that time we said that those games were generically called “coordination”, because the best result was when both players chose “good” (remember the paradigmatic example of driving on the left or right). Well, sometimes these games are generically called “anticoordination”, because the worst result is obtained when both decide the same thing (the -100 / -100).

What is the appropriate strategy? Then we will go to that, because first we want to dedicate a few paragraphs to show that, although fortunately there are not many motorists who dedicate themselves to playing this, the game is very, very practical.

We can start with a simple situation. We are looking for parking in a shopping center. We’ve been circling for ten minutes; We started to get tired, and in the back seat the children are getting heavy. Suddenly we see a gap, towards which another driver also heads like a kamikaze. We have two options: try to sneak in first (Follow) or assign the site (Separate us). If we follow and the other moves away, we win a little (if only because our children in the back seat stop sulking). If we separate, we lose a little, because we have to keep looking for another place. If we both continue, in the end we have an accident and instead of losing another ten minutes looking for another place, we have to lose twenty fixing the insurance papers, and the car a week in the workshop. Note that the Move / Move apart combination can not occur, since the last one in Apartarse will change its decision.

Let’s make it a little more serious now. We are negotiating a commercial agreement with a client. He needs us, because he needs our service: if he does not hire him, he will not be able to do his job and will lose money. But of course, we both want to make us hard (us to raise the price and him to lower it). If we press and he gives in, we sell him the service more expensive than normal. If he tightens and we give in, we sell him the service cheaper than normal. If we both press, the deal does not close, we do not earn that money and he can not do his job (losing money too). If we both give a little, it’s the normal situation.

Ransom Mel Gibson Movie and Game Theory

Ransom is a smarter-than-usual kidnapping thriller, starring ” Mel Gibson as an airline owner whose child is kidnapped, and who tries to outsmart the kidnappers with a risky plan that might work, or might lead to the loss of his child. Everything depends on his hunch that the child is doomed anyway-unless his desperate scheme pays off.

Gibson plays a former fighter pilot who has built an airline from scratch, and is now under investigation for bribing union officials. He lives with his wife on Central Park, where they take their young son (Brawley Nolte) to a science fair. The boy is kidnapped, a ransom note arrives by anonymous e-mail, and the FBI is called even though, as Gibson observes, The FBI just spent three months trying to bury us. The movie makes little mystery about the identity of the kidnappers; we need to know who they are in order to appreciate the cat-and-mouse game that takes place. The gang is masterminded by Gary Sinise, a crooked police detective, and includes his girlfriend Lili Taylor), who once worked for Gibson and knows the family’s routine. Other members include a computer whiz and a couple of lowlife thugs.

The FBI kidnapping expert wants Gibson to pay the ransom. He tries to, but an FBI helicopter interrupts the ransom drop, and Gibson becomes convinced (by the look in a gang member’s eyes) that the kidnappers have no plans to return the child alive. That’s when he devises his daring plan, which horrifies his wife and angers the FBI, but puts the ball squarely in Sinise’s court.

Instead of developing this material along pure thriller lines, “Ransom” also involves intriguing side issues. It’s clear, for example, that Gibson *did* bribe a union official (who becomes one of the kidnapping suspects). At one point, talking to Sinise, he asks the question that eventually occurs to everyone in such a situation: Why me? “Because you buy your way out of trouble,” Sinise tells him. “You’re a payer. You did it once, and now you’re gonna do it again.” The movie spends a lot of time examining the dynamics inside the kidnap gang, but there’s the feeling that scenes have been dropped that might have made things clearer. When Sinise and Lili Taylor confront each other at the end of the film, for example, we would have liked to know more about the real nature of their relationship.

The screenplay, by Richard Price and Alexander Ignon (based on the 1956 Glenn Ford movie of the same name), also hints at depths of Gibson’s character: He’s a self-made man with a temper, who needs to control it in order to win. But the movie sets up more elements than it deals with.

And a final scene–the closing confrontation between Gibson and Sinise-has the potential to be more clever and suspenseful than it is. The director, Ron Howard, obviously has a notion of how to handle the material, but somehow the timing and the logic are off. Without giving away the situation, I’ll point out that Gibson’s moment of realization is hammered too hard (there are too many close-ups of narrowing eyes), and the charade inside a bank has ironic promise, but could have been great, and is only adequate.

Brinkmanship

Another case is that of the Cuban missile crisis. Two countries (which in that article were the USSR and the US) are facing an escalation of violence: the first kills one soldier by accident, the other attacks a patrol for spite, the first one bombs a base, the other a city, the first launches its nuclear missiles … and the second also. Game over.

Anyone can give (Move) at any time, or Keep climbing. The one that yields when the other threat suffers a political damage, which is the reward of the other. But if both keep climbing, both are annihilated.

And then, is there an adequate strategy?

Well, there are some, but their success is not guaranteed at all.

One of the ways to deal with this game is to eliminate one of our options. For example, in the game of hen with cars, we can chain the wheel so that it is impossible to turn it to Move away. That way the other player has no doubt about what our decision is going to be, and he only has one rational decision:

To move away.

This is what the commercial does many times when it tries to sell something: “it’s not that I do not want to lower the price, it’s that I can not, it’s not in my hand. The price is fixed to me from the central, I can not lower it anymore “. Or when the client negotiates: “if I like what you offer me, but at that price I can not buy it, I would lose money”. Whether it’s true or not … that does not depend on this article anymore.

The expression “burn the ships” seems to come from the invasion of the Aztec empire by Hernán Cortes, with only 300 or 400 Spanish soldiers. In order to prevent his men from being tempted to return to the safety of Havana, he ordered that the ships’ helmets that had brought them to New Spain be drilled, so that they only had the option of going forward. The grace is not only that the Spaniards know that they can not retreat, and therefore fight better, but that the enemies also know that they can not retreat, and therefore they know that the Spaniards will fight like lions, favoring that they withdraw themselves.

If you ever find it, the English use the expression “burn the bridges” (burn the bridges) to represent this.

Related to this is the strategy of “who gives first, gives twice”. If the game is not completely simultaneous, but we can decide to be the first to choose, we can try to choose Continue. When choosing the first aggressive strategy, the other is forced to choose the passive strategy, otherwise it would cause its own destruction … or not?

Using Chicken to model a situation such as the Cuban missile crisis is problematic not only because the compromise outcome is unstable but also because, in real life, the two sides did not choose their strategies simultaneously, or independently of each other, as assumed in the game of Chicken described above. The Soviets responded specifically to the blockade after it was imposed by the United States. Moreover, the fact that the United States held out the possibility of escalating the conflict to at least an air strike indicates that the initial blockade decision was not considered final – that is, the United States considered its strategy choices still open after imposing the blockade.

As a consequence, this game is better modelled as one of sequential bargaining, in which neither side made an all-or-nothing choice but rather both considered alternatives, especially should the other side fail to respond in a manner deemed appropriate. In the most serious breakdown in the nuclear deterrence relationship between the superpowers that had persisted from World War II until that point, each side was gingerly feeling its way, step by ominous step.

Before the crisis, the Soviets, fearing an invasion of Cuba by the United States and also the need to bolster their international strategic position, concluded that installing the missiles was worth the risk. They thought that the United States, confronted by a fait accompli, would be deterred from invading Cuba and would not attempt any other severe reprisals. Even if the installation of the missiles precipitated a crisis, the Soviets did not reckon the probability of war to be high (President Kennedy estimated the chances of war to be between 1/3 and 1/2 during the crisis), thereby making it rational for them to risk provoking the United States.

There are good reasons to believe that U.S. policymakers did not view the confrontation to be Chicken-like, at least as far as they interpreted and ranked the possible outcomes. I offer an alternative representation of the Cuban missile crisis in the form of a game I will call Alternative, retaining the same strategies for both players as given in Chicken but presuming a different ranking and interpretation of outcomes by the United States. These rankings and interpretations fit the historical record better than those of “Chicken”, as far as can be told by examining the statements made at the time by President Kennedy and the U.S. Air Force.

Princess Bride Movie

Our hero Westley, in the guise of the Dread Pirate Roberts, confronts his foe-for-the-moment, the Sicilian, Vizzini. Westley challenges him to a Battle of Wits. Two glasses are placed on the table, each containing wine and one purportedly containing poison. The challenge, simply, is to select the glass that does not lead to immediate death.

Roberts: All right: where is the poison? The battle of wits has begun. It ends when you decide and we both drink, and find out who is right and who is dead.
Vizzini: But it’s so simple. All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet, or his enemy’s? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I’m not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool; you would have counted on it, so I can clearly not choose the wine in front of me.
Roberts: You’ve made your decision then7
Vizzini: Not remotely. Because iocane comes from Australia, as everyone knows. And Australia is entirely peopled with criminals. And criminals are used to having people not trust them, as you are not trusted by me. So I can clearly not choose the wine in front of you.
Roberts: Truly, you have a dizzying intellect.

The scene, beyond providing some comic relief on the theme of common knowledge, also has an important lesson on strategic moves; if the rules of the game may be changed, then the game can be rigged to one player’s advantage:

Vizzini: let’s drink — me from my glass, and you from yours.
[allowing Roberts to drink first, he swallows his wine]
Roberts: You guessed wrong.
Vizzini (roaring with laughter): You only think I guessed wrong — that’s what’s so funny! I switched glasses when your back was turned. You fool. You fell victim to one of the classic blunders. The most famous is “Never get involved in a land war in Asia.” But only slightly less well known is this: “Never go in against a Sicilian when death is on the line.”
[He laughs and roars and cackles and whoops until he falls over dead.]
[Roberts begins to rescue Buttercup, the girl over whom this battle was staged in the firstplace]

Buttercup: To think — all that time it was your cup that was poisoned.
Roberts: They were both poisoned. I spent the last few years building up an immunity to iocane powder.

The movie contains several other scenes with game-theoretic themes, including many on bluffing.

The Good, the Bad, and the Ugly- Clint Eastwood Movie

I think that the final scene in this Clint Eastwood movie is the most outstanding example of game theory. Three men in a triangle — each with a gun, a rock at the center of the three. It is up to each man to evaluate his situation. All are excellent shots. Who do they shoot?

Clint has supposedly put a message on a rock that holds the key to everything, but do the other two trust Clint to have actually written the correct answer? As the other two evaluate the situation, they realize they can’t trust Clint to have written the answer on the rock — therefore they can’t shoot Clint who likely still has the answer. That means the other two can only shoot each other, but only one will likely hit before the other.

What they don’t know is that Clint has given one an unloaded gun… Clint can ignore this one. The one Clint has to worry about with the loaded gun will try to kill the one with the unloaded gun. Neither will fire at Clint. Clint will fire at the one with the loaded gun. As the camera passes from one face to the other the audience is meant to figure out what each would do.

The guy with the loaded gun shoots at the guy with the unloaded gun — Clint shoots the guy with the loaded gun. Game over. As with the hangings in the movie, he has dangled Duco out as bait while Clint takes the money.

The game is decided before it starts.

Clint sets up a situation where each evaluates their possible moves, but in reality, Clint has already won the game. Its a brilliant example of people making the best decisions based on the information available to them…and somebody manipulating the information available to them.

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