search blog tags...
2 Live Crew 6 basic emotions 60 Minutes Achilles Last Stand agile Ai Weiwei Amy Hempel tamp amygdala Anna Karenina Arrested Development art criticism Art Reviews Athena aum B Roll bachelors degrees Backstreet Cultural Museum bacon badass Baxter Black Beevis and Butthead with Billy Dee Williams Bette Midler in a Bathhouse big om Bill Bradley Bill Moyers Bits Body Worlds bomb Bonnie and Clyde Brigitte Bardot Buckingham Forever Stamp bullet proof business management Canada book caparisoned Carl Perkins Carta Marina Cash cash-holding companies Cat On A Hot Tin Roof cayenne characters charcoal drawing Charles Seife Chattanooga Choo Choo Chicago chicken Christina Hendricks Chuck Berry collaboration collard greens colorblindness Columbia Center for the Arts Columbia River Gorge Commodores compromise conservatism Cordobas cow punching Days of Heaven Dead defiance denim desert island songs Detroit's The New Dance Show dinosaurs DRTV Scripts duets Elisabeth Kubler-Ross Elizabeth Taylor Elko National Poetry Gathering emo music entrepreneurship erasers Facts of Life Feynman film sequences film structure Five Easy Pieces flowering time formline art found art Fox Games foxgloves Frances Langford gadfly gambling Game Theory gaslighting George Carlin goddamn Gonzalo Lebrija Good Will Hunting Granito granito de arena Green Porno Bees Growing Up Fast guanxi Guatemala hambone Hank Williams Happy Birthday (the original version) happy families Harrowdown Hill have a coke and a smile hawks & doves Head of Comity Henry Clay High John the Conquerer Hollywood storylines Hottub Time Machine Iceman Gervin ideas versus moments If I Only Had A Brain Independent Film Industrious Poison Snowmen insight and the analytic mind Intern Labor Jack Daniel No. 7 jambalaya Japanese Jascha Kaykas-Wolff Jaws Jed Jo Joseph Campbell Kenny Rogers knight Kraftwerk Led Zepplin lemon Life Is A Highway Louisiana salt domes love story ma cher amio Martin Luther King Jr Maths Matt Taibbi Me So Horny medicine show Memphis Michelangelo mind turf Mississippi mojo mom and dad are fighting again mould Mr. T Muddy Waters murderous drifter Music myth marketing narcissism NCAA Tourney Never Sorry New Orleans Nicaragua Nicholas Brothers Nina Simone No Rain Obama Biden image Ogilvy on Ogilvy oil refining Old Crow Otium Pass That Dutch PDX Window Project Philosophy of Scientific Law Picasso piquance pitching line poem Working For Wages Polish Movie Posters political conservatism as motivated social cognition Prayer Song Pre-Columbian prisoners dilemma punchbowl Radiohead Raphael reach for it reaching out and touching the glory recipe Red White & Blue Dildo Richard Ford ripe fruit Robert Redford Rocky training montage Roger Hagadone Rolling Stones Royal Road r-values Sandy Skoglund Scoville Screenplays Sean Healy Sean Martinez septic tank shaman short film Short Stories Six Easy Pieces Slueth Socrates Socratic method Soldier Mountain somatic Squaw Valley Community of Writers St. Vincent Starvation Wages statistics statues steadicam smoothie Stitches STOCK Act submission cover letter template subplots Sundance Tater Tot Tennessee Songs Tennessee Williams Terrence Malick Texas Two-Step The Brigade The Cambio Man The Economist The Five Stages of Grief The New Yorker Life Coach cartoon The Original Lady Buckjumpers The Parthenon The Pieta the sequence approach The Stooges Brass Band The Unofficial Guide to Submitting Short Prose The Usual Suspects Thin Red Line This American Life this could be the one Thom Yorke Thor: The Dark World Tibetan Book of the Dead Timpanogos tobies Tom Waits Tommy Joseph totem poles Trinity turd turkey basketball Videos vision Werner Herzog when I was a boy back in Tennessee where p is whiskey white dog Whitespace who lit this flame Wilco William Burroughs winner take all economy winning Words Write Around Portland Writerly Issues

Entries in Game Theory (2)


Game Theory II: Hawks & Doves & Others

In game theory, a game called “Hawks & Doves” imagines a showdown between two birds, both of which act on instinct and with a survival tactic to win a resource, say food or a breeding opportunity.

Every bird’s tactic is one of two options: he either fights (hawk) or fakes like he will fight and flees if the other bird doesn’t back down (dove).

If two birds in conflict both be Hawks, they fight to the point of injury, and ceteris paribus each has a 50% chance of winning and a 50% chance of losing. It’s a probability coin toss.

Being nearly fatally injured is worse for the loser than winning is beneficial for the winner. You may win the fight and eat or breed, which is good, but that guy almost died, which is really bad.

We might score the fight +50 for the winner and –80 for the loser. Because all fights according to the conditions of the game are always 50/50 odds, the average payout for the fight is (50 minus 80) divided by 2 = –15, which means over the long run and after enough fights, all hawks average a loss.

If two birds in conflict both be Doves, then they both pretend to want to fight until one or the other eventually backs down. This could take a second, or it could last for days, but neither of them ever intend to fight, only display as though they will.

As with two hawk fights, the winner in a dove standoff gets a resource, which we valued at +50. The losing dove gets no resources, but he also doesn’t get injured, so that’s a zero payoff rather than a big negative.

However, both doves spend energy pretending they are going to fight, so that must count for something negative. Say they both spend the same energy posing like fighters and expend –10 of energy each, which means the winning dove nets +40 and the losing dove, –10.

Unlike with the hawks, the average payout for a two-dove showdown is a gain, (40 – 10)/2 which equals +15, which means over the long run and after enough chest-bump standoffs, every dove averages a win.

So why isn’t everyone a non-fighter for a positive average gain? Because when you’re a hawk, the payoff is risk-free when you encounter a dove. You take it all, +50, and, at the first little peck in the head the dove backs down and gets a zero.

In the game, the dove doesn’t even waste standoff energy when he sees he’s against a hawk. Hawks beat doves. Every time. In the game. It’s a more complex version of the game "Chicken."

Music break:

In "Hawks & Doves," there are NOT two kinds of birds. There is one species of bird with different tendencies to express either hawk or dove behavior. The species expresses hawk and dove behavior in proportion to how the payoffs for survival condition that behavior.

If most everyone expresses dove behavior, then a hawk can make a killing with little risk.

If most everyone expresses hawk behavior, then it’s going to get bloody with a lot of injured losers. And though he wins against doves, every hawk’s going to lose half the time when he fights another hawk.

If you crunch the numbers for payouts of +50 for winning, –80 for losing fights, and –10 for bluffing, then the average payouts for hawks and doves look like this:

Hawks: –15p + 50(1 – p) = 50 – 65p
Doves: 0p + 15(1 – p) = 15 – 15p

where p is the proportion of the population playing hawk, and (1 – p), the proportion playing dove.

In stable populations, the average payoffs between hawks and doves are equal, which makes p = 0.7 in the example: a world with 70% hawks and 30% doves.

  • If that world started far from stability, say with 1 hawk and 99 doves, it would many generations later have 70% hawks and 30% doves (The world would “approach” that proportion).
  • If that world started with 99 hawks and 1 dove, it would also generations later have 70% hawks and 30% doves.
  • If that world started with 50 hawks and 50 doves, it would still, generations later, have 70% hawks and 30% doves.

This all assumes the average payoffs stay the same through the generations. This also assumes the behavior stays the same: a species of bird exhibiting hawk and dove behavior, stuck in a timeless struggle against one another for an evolutionary stable strategy.

But that’s not what happens. Mutation happens. New behaviors begin to show hawk and dove behavior blended in the same strategy. Perhaps there's a new kind of bird that beats up on doves, but won’t fight any hawks. Bully!

Perhaps it's a bird that will sometimes fight hawks and win, but knows when to be a dove and take a dive rather than lose. Perhaps it's a hawk all its life and then, one day, switches, out of the blue.

In game theory, the hawk and dove behavior isn't choosen. The birds play out probabilities of possible phenotypes and successful mutations arise to either live or not live. They are automatons.

In the human world, we’d like to think we can choose. Suppose the birds choose, too?

Cooperation is the best choice for maximizing resources. Guaranteed. It's been proven mathematically and morally. If the Hawks & Doves and the crafty Mutations amongst them would all share, then we wouldn't have so much conflict. Perhaps that's true, depending upon how much of the resource was available and for how long.

What usually develops during cooperation is the simple game theory game, Prisoner's Dilemma, where the hawk may agree not to fight, but he's afraid the other bird is a hawk, too, and won't live up to his promise not to fight. So the cooperative hawk feels like he's going to get taken. He's afraid violence will disturb the peace.

In the 1950s, a contest was held to solve the problem of the Prisoner's Dilemma. What's the best strategy for hawks willing to be cooperative but distrustful of other bird's commitment to peace? Computer scientists, philosophers, mathematicians: answers came from all around. Organizers pitted strategies against one another. Some strategies involved extremely complicated math and decision matrices.

The winningest strategy was simple: Tit-for-Tat, "do unto others" until they do you wrong, then do to them as they did to you. Over enough games played, Tit-for-Tat won.

What a boring way to win.


Game Theory

This photo taken for free (minus the guard's scowling from across the room) at Portland Art Museum's exhibit "Disquieted."

Coordination, Battle of the Sexes, Chicken, Prisoners' Dilemma: These are the four basic games in game theory. They compare how two players make a choice.

In game theory, payoffs for one player depend on the choices of the other player. Numbers represent the payoffs one player receives for himself relative to what the other player receives for himself; the numbers have no meaning beyond that relative comparison.

Players are assumed to be self-interested, meaning they want to get the highest payoff for any given decision. Also, the players make choices at the same time, so they can't conspire and work out what they plan on doing beforehand. 

1. Coordination Game
You just met Jo. You are taking Jo to Fancy’s on a first date. You and Jo both prefer to dress up formally, but either of you is willing to dress casually if that means you will match each other.

Neither of you wants to go formal if the other is going casual. Neither of you wants to go casual if the other is going formal.

The payoffs for each situation are assigned values in the table as two relative numbers: (You, Jo). Higher is better.



2. Battle of the Sexes Game
After a few dates, you both decide your favorite place is Mellow’s. Now, you want to start dressing casually, but Jo still wants to dress formally. Again, you’d rather match than not match, either way.

Battle of the Sexes


3. Chicken Game
You and Jo break up. (Stupid clothing arguments!) You want to go have a drink at your favorite place, Mellow’s, but you don’t want to go there if Jo is going to be there. That’s the worst thing that could happen. (Jo thinks so, too!)

Neither wants to be the one to go someplace else and have the other get to keep going to Mellow’s. Both of you would like to keep going to Mellow’s, and have the other find a new place.



4. Prisoners’ Dilemma Game
You can’t stand it. Why won’t Jo find a new place? That’s still what you want.

But you’d rather go to Mellow’s and scowl across the bar at Jo than go someplace else knowing Jo gets to enjoy Mellow’s free and clear.

And Jo feels exactly the same. (You two are made for each other.)

Prisoners' Dilemma

Why The Dilemma?
The prisoners’ dilemma is the most interesting case of the four. It’s the only situation where you both lose as a result of following your own self-interest. Both you and Jo are destined to lose when things get to prisoners’ dilemma stage. The decisions could play out like this:

In Coordination, times are good, and you and Jo both want the same thing. So if you think Jo will dress formally, you dress formally (because 2>0, and 0 is what you get if Jo goes formal and you go casual). If you think Jo will dress casually, you dress casually (1>0). Jo’s decisions and payoffs are the same.


In fact, there’s no reason Jo wouldn’t choose to dress formally and get a 2, unless she thinks you don’t want to, in which case you are not in Coordination at all, but rather …

Battle of the Sexes, which is the same as Coordination, except one of you is going to lose slightly when the other gets what he or she wants.

If you think Jo will dress formally, you still dress formally (1>0), though Jo will enjoy it more (2>1). Likewise, if you think Jo will dress casually, you still dress casually (2>0), and you enjoy it more than Jo does (2>1).

Battle of the Sexes

Either way, you both want to match, because not matching means zeros. If you didn’t care about matching anymore, you and Jo’s relationship would result in a breakup and become a game of …

Chicken, which takes a different turn. Think of two cars headed toward one another on a one-lane road. If both do not swerve, they both crash and get zeros. In Chicken, no one wants to crash.

So if you think Jo will go to your old favorite place Mellow’s, you go someplace else (1>0). If you think Jo will go someplace else, you go to Mellow’s (3>2). In fact, if you want to be sure you avoid a zero, your best choice is to always go someplace else, because you will at least get a 1 and you might get a 2.


The problem with going someplace else is that you really want to go to Mellow's. And Jo can win big if she knows you will always go someplace else, because she can go to Mellow's free and clear. That starts to bother you, making you jealous of her always getting a 3 to your 1. When you can’t get over it, the situation becomes a …

Prisoners’ Dilemma, where you are both trapped with a low payoff. If you think Jo will go to Mellow’s, you go to Mellow’s (1>0). If you think Jo will go someplace else, you still go to Mellow’s (3>2). And Jo’s payoffs are exactly the same to her.

Prisoners' Dilemma

So what happens is you both go to Mellow’s, scowl at each other all night, and get a 1—even though you both would get a 2 and be better off if you just went someplace else. (Ain’t it always the way?!)


"Facts of Life" image from Hulu

If You Play The Record Backwards
Maybe that's being too cynical. If we could run the story with Jo backwards, it might go like this instead:

Say you are in a prisoners' dilemma when you first see Jo at Mellow's: You're both in relationships with other people, and you both know going to Mellow's could tempt you to cheat, because you have seen each other several times and know you are attracted to one another.

After enough nights of winking (instead of "scowling") across the bar at Mellow's, you play a game of chicken and talk to one another. Both of you swerve, and you start a relationship at "a different place." (It's qismat! You both simultaneously picked the same different place. "Fancy seeing you here.")

At first, it's a battle of the sexes, where you're trying to decide who wants what and who likes what. But then you fall in love, and you both realize you want the same things. You're now coordinated, like the matching Adidas sweatsuits your aunt and uncle used to wear at family dinners.

Music break ...

Self-Interested Behavior is Inefficient
Unless you and Jo can stay together in your desire to match—or if you can’t cooperate after you no longer want to match—the prisoners’ dilemma seems inevitable. And it’s most inefficient, because the lowest possible combined payoff is guaranteed: 1+1 = 2, which is less than the other two possibilities, 3+0 = 3 or 2+2 = 4. (Again, the actual numbers are irrelevant, beyond a relative comparison.)

Why can’t you both go someplace else and leave Mellow's behind? Because neither of you can get past the mindset that says you must always do what gives you the most satisfaction: When you always act in your own self-interest, you are doomed to always go to Mellow’s and scowl (as long as it remains your favorite).

To the other player, it appears you've deliberately chosen lower satisfaction in order to inflict extra low satisfaction on them. Jo says, “Why would you come here and ruin both our nights, instead of going someplace else and both of us having a good time?” She can’t recognize the reverse schadenfreude: Each of you gets the most displeasure (0) when the other is most fortunate (3).

This reverse schadenfreude occurs in money-sharing experiments, too, where people are generally happy to receive $1 for nothing, unless they know the person giving them $1 was given $100, had to give at least $1 of it away (based on the rules of the experiment), and kept the maximum amount ($99) for himself.

When experimenters allow the recipient the option of killing the entire deal—where no one gets any money—the recipient will do so, and receive nothing in exchange for the other player receiving a “bigger” nothing. The receiver will continue to kill the deal until his portion gets above $20, or so.

This behavior is an evolutionary survival strategy—a concept of “fairness” in the face of unearned gains that seems to be common to all human beings.

Photo "Direction of Time" by the author

Without Fairness, The Best Choice is “I Don’t Care”
If a recipient does not have the option to kill the deal, then his only choice is to be happy with $1 (or whatever he is given). Period.

But don’t be too cynical about it, because some few people will choose to split the money $50/$50, and even some tiny number of people will opt for a $99/$1 split in your favor. Experiment proves this does happen. (Thank you, Mother Teresa!)

More likely, the only escape from a prisoners’ dilemma is not to give a damn about payoffs at all. Because if you are truly powerless to cooperate and fairness is entirely out the window, you can argue and protest as much as you like, but changing the game is outside your control.

It is in your control to give the other person Mellow’s and the 100 bucks and wipe your hands of the situation. Your new price is zero. Your new game is freedom. Imagination. You swerve out of the way every time. You walk away happy … as long as you never, ever, never look back. And as long as you don’t mind being a “chicken.” BwooOOOooock, booock, booock, booock, boock, bock.

Playground tactics still keep us in the game.


Source for game basics: "Games People Play," Scott Stevens