# Be Ye Friend Or Be Ye Foe? Part 4

The Story So Far…
Two players are presented with an opportunity.  Each may remain loyal to the other player and betray him. Neither player will interact with the other in any way ever again. There is no out-of-game way to be rewarded and punished.

What could happen?

(1) If both remain loyal, each of them gets the “Cooperation” reward.

(2) If both betray the other, each of them gets the “Betrayal” reward.

(3) If one betrays the other while the other remains loyal, the betrayer gets the “Traitor” reward while the loyal one gets the “Sucker” reward.

This is the prisoner’s dilemma.

In a strict prisoner’s dilemma, the rewards are staggered with the “Traitor” reward best, followed by the “Cooperation” reward, then “Betrayal,” and finally “Sucker” the worst.  In mathematical terms, T > C > B > S.  My instincts as a designer suggest that we should also aim for 2C > T + S > 2B.

Further, We can encourage cooperation or betrayal among our players. Cooperation is more likely when this decision point occurs repeatedly but an uncertain number of times. Betrayal is more likely when this decision point occurs once and without any in-game opportunity for reprisal.

Including The Prisoner’s Dilemma In Game Designs

We have invested three columns to getting very familiar with the prisoner’s dilemma.  We looked at the research surrounding it and the mathematical theories applied to it.  Now let’s look at how this dilemma might be applied to our game designs.  Each of these is presented as a single case study.  You will of course need to adjust them to serve your particular needs.

Retrofitting  Munchkin

One fun way to get a sense of the prisoner’s dilemma in a game is to slip it into the classic back-stabber Munchkin.

A player has drawn a monster to fight.  The other players may play cards to boost the player and boost the monster.  Let’s have each of these other players simultaneously choose who to support–Hero or Monster.  Players that choose Hero are committed to playing cards for the active player.

(1) If the active player defeats the monster, that player gains one level but must give all monster loot away to the Hero players.

(2) If the monster defeats the active player, that player gets all the normal penalties.  The Monster players divvy up the monster’s loot among themselves.

An Area Control Game

There are 20 areas to be scored.  The order in which they are scored is randomized in a deck of cards.  Shuffled among the last 6 cards is an “End of Game” card.  When this card is revealed, the game is instantly over so it is likely that some areas will not score.

Any time two players are tied, they simultaneously select and reveal “Share” or “Steal.”

(1) If both players Share, each receives half (round up) of the victory points + 1 bonus VP.

(2) If both players Steal, each receives 1 victory point.

(3) If one player Shares while the other player Steals, the Stealing player gets all the each victory point and the Sharing player receives none.

A Civilization Game

It is the dawn of civilization.  Two hunting/gathering groups meet in neutral territory.  Each player simultaneously selects and reveals “Peace” or “War.”

(1) If both players choose Peace, each may exchange knowledge and/or goods.

(2) If both players choose War, units damage one another with the victor carrying away a fraction of their combined goods.

(3) If one player chooses Peace while the other player chooses War, the warrior annihilates the opposing player’s group and takes any goods the peaceful group was carrying.

A Political Game

Several players are competing for position in a campaign.  Each player must decide with respect to each opponent whether to run an Upbeat campaign or to run a Smear campaign.

(1) If both candidates are Upbeat, each gains 5 votes.

(2) If both candidates Smear, each candidate gains 2 votes.

(3) If one candidate is Upbeat while the other candidate Smears, the smear candidate gains 6 votes while the upbeat candidate gains 1.

A Racing Game
Two cars are approaching a bottleneck at speed 4.  Both cannot fit through at the same time.  Each will have to decide whether to “Accelerate” or “Brake.”

(1) If both cars Brake, they squeeze through the bottleneck at speed 3.

(2) If both cars Accelerate, they will crash in the bottleneck at speed 5!

(3) If one car Accelerates while the other car Brakes, the accelerating car pulls ahead to speed 5 while the braking car comes through at speed 2.

A Contribution From An Esteemed Reader

Bruno Faidutti mentioned in the comment section of Part 2 of this series that “[his] game Terra is based on the freerider paradox which can be considered a multiplayer generalization of the prisonner’s (sic) dilemma.”  I was only passingly familiar with the freerider paradox and decided to research it further.  The Stanford Encyclopedia of Philosophy offers a solid an overview.

Although I haven’t personally played Terra, it is clear how the freerider paradox could be quite an interesting basis for a game.  My first thought was how it might interact with the Peace War Game we discussed in part 2 of this series.  The freerider paradox will definitely get a full treatment from this blog sometime soon.  In the meantime, be sure to read the article at Stanford and try your hand at integrating it into one of your games.

Closing Thoughts

The prisoner’s dilemma mechanism can bring interplayer tension into a variety of settings.  It can be used to encourage collaboration.  It can be used to encourage competition.  It is a versatile device in your designer toolbox.

Have you played a game with a Friend and Foe mechanism? What did you think of it? Have you written one? How did your players respond to it?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  You keep reading. I’ll keep writing.

# Be Ye Friend Or Be Ye Foe? Part 3

The Story So Far…
Two players are presented with an opportunity.  Each may remain loyal to the other player and betray her. Neither player will interact with the other in any way ever again. There be no out-of-game way to be rewarded and punished.

What could happen?

(1) If both remain loyal, each of them gets the “Cooperation” reward.

(2) If both betray the other, each of them gets the “Betrayal” reward.

(3) If one betrays the other while the other remains loyal, the betrayer gets the “Traitor” reward while the loyal one gets the “Sucker” reward.

This is the prisoner’s dilemma.

In a strict prisoner’s dilemma, the rewards are staggered with the “Traitor” reward best, followed by the “Cooperation” reward, then “Betrayal,” and finally “Sucker” the worst.  In mathematical terms, T > C > B > S.

Further, cooperation is much more likely if this decision point occurs repeatedly but obscures the exact number of times it will occur.

Correctly Staggering Rewards

In a strict prisoner’s dilemma, the rewards are staggered with the “Traitor” reward best, followed by the “Cooperation” reward, then “Betrayal,” and finally “Sucker” the worst.  In mathematical terms, T > C > B > S.

We discussed the Friend or Foe game show in detail in our last column.  Notice that this game deviated from this structure a bit–the “Betrayal” reward and the “Sucker” reward were identical; going home with no money.  Returning to mathematical terms, T > C > B = S.  If you opt to have two identical outcomes, this is the place to do it–at the bottom.  Notice also that in their scheme, T + S = C + C = total prize money.  Considering the demands of a of a game show–the need for clear rules that are easily parsed by the audience viewing at home–I can certainly see why they made this decision.

Personally, I would go a bit further than the standard T > C > B > S. I would also aim for 2C > T + S > 2B.  This was the reward structure of the peace war game and it suits my general design style.  Let’s go back to our Friend or Foe game show for an illustration.

Two players are going into the final showdown.  They have amassed \$1000 in prize money.  Here are the possible outcomes under the standard game rules:

A) If both vote friend, they each get \$500.

B) If both vote foe, they each get \$0.

C) If one votes friend and the other votes foe, the foe gets \$1000 and the friend gets \$0.

Now imagine that we make a small tweak to the rules.  If both players choose “Friend,” we’ll throw in an extra 10%.  Now the decisions are:

A) If both choose friend, they each get \$550.

B) If both choose foe, they each get \$0.

C) If one chooses friend and the other chooses foe, the foe gets \$1000 and the friend gets \$0.

This is a small change but it has broad implications for the players.  If the players consistently choose friend, they end up collectively further ahead on repeated plays–\$550 + \$550 = \$1100–than any other case–\$1000 + \$0 = \$1000 in case (B) and \$0 + \$0 = \$0 in case (C).  Of course, this game show doesn’t have repeated plays.  This decision is the last one of the game. But these players are conscientious, not amoral.  And that makes it all the more challenging for our players.

To Be Continued…

Our next column addresses ways to put Friend or Foe mechanisms into our own designs. See you Tuesday!

Have you played a game with a Friend and Foe mechanism? What did you think of it? Have you written one? How did your players respond to it?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  You keep reading. I’ll keep writing.

# Be Ye Friend Or Be Ye Foe? Part 2

The Story So Far…
Two players are presented with an opportunity.  Each may remain loyal to the other player or betray him. Neither player will interact with the other in any way ever again. There is no out-of-game way to be rewarded or punished.

What could happen?

(1) If both remain loyal, each of them gets the “Cooperation” reward.

(2) If both betray the other, each of them gets the “Betrayal” reward.

(3) If one betrays the other while the other remains loyal, the betrayer gets the “Traitor” reward while the loyal one gets the “Sucker” reward.

This is the prisoner’s dilemma.

In a strict prisoner’s dilemma, the rewards are staggered with the “Traitor” reward best, followed by the “Cooperation” reward, then “Betrayal,” and finally “Sucker” the worst.  In mathematical terms, T > C > B > S.

The Prisoner’s Dilemma In Mathematics

the Nash equilibrium for this game is for each to betray the other.  The logic is an extension of the amoral player presented in my last post and looks like this:

(1) If you remain loyal, I am better off betraying you.  In this way, I get the “Traitor” reward which is the best of the rewards I can get when you remain loyal.

(2) If you betray me, I am better off betraying you.  In this way, I get the “Betrayal” reward which is the best of the rewards I can get when you betray me.

(3) Therefore, I should betray you.

(4) Since you also know this, you should also betray me.

(5) Therefore we betray each other.

This logic is well-illustrated at by this video from Kahn Academy.

The Prisoner’s Dilemma In The Social Sciences

Avinash Dixit and Barry Nalebuff present a classic arms race as an immediate example of the prisoner’s dilemma in their article at The Concise Encyclopedia of Economics.  Two nations could Cooperatively prosper if neither invested in weapons and instead devote their resources to more positive objectives.  Instead, the two nations both choose Betrayal and the arms race continues.

Dixit and Nalebuff go on to assert “On a superficial level the prisoners’ dilemma appears to run counter to Adam Smith’s idea of the invisible hand. When each person in the game pursues his private interest, he does not promote the collective interest of the group. But often a group’s cooperation is not in the interests of society as a whole…One must understand the mechanism of cooperation before one can either promote or defeat it in the pursuit of larger policy interests…The most common path to cooperation arises from repetitions of the game.”

In game designer terms: We must understand when and why our players cooperate before we can either encourage and discourage in the pursuit of engaging decisions.  A path for us is to have this decision point occur repeatedly throughout our game.

The Mathematical View of Multiple Iterations

Game theory sticks to its amoral guns, even in the face of iterative play.  Its argument looks like this:

(1) We know that I am best off betraying you in a single iteration because you have no opportunity to retaliate.

(2) You know this too.

(3) Therefore, we should betray one another in the final round.

(4) Therefore, I should betray you in the second-to-last round.

(5) Therefore, you should betray me in the second-to-last round.

(6) Iteratively, we betray one another in every round.

This issue is fixable.  Key to this logic is based is the assumption that the players know which iteration will be the last iteration.  When players are denied this knowledge, the starting point assumed in step (3) of the logic above is invalidated.

In game designer terms: Players should be presented with this decision point repeatedly but our game should obscure the number of times it will do so.

Peace War Games

Even in a group that doesn’t play the same game repeatedly, there exists a metagame memory of previous behavior which is carried into future games. I would suggest that designers can expect players to therefore gravitate toward Peace War Game behavior.

Peace War Games are iterated versions of the prisoner’s dilemma, extended out to larger numbers of players.  Players are cast as nations, with each turn’s decision being whether to choose “peace” or “war” with each neighbor.  According to Wikipedia, peace makers became richer over time, falling behind only the “Genghis Khan” strategy of constant aggression in which war supplied a steady stream of resources.  The player response to Genghis Khan is an interesting one–the “Provocable Nice Guy.”  This player selects peace always until attacked.  When several Provocable Nice Guys work in consort, they promote one another while reigning Genghis Khan in.

Because they are iterative and because they involve groups of players, peace war games give us the most insight into how players are likely to act when faced with prisoner’s dilemmas in our games.

To Be Continued…

Our next column looks at the design of Friend or Foe rewards.  Which types of rewards incentivize what types of behavior? See you Friday!

For those of you interested in further reading, Homo Ludditus makes several interesting arguments in its Nobody Understands “Prisoner’s Dilemma” article.  While it contains several points I cannot agree with, it does make some solid ones as well.  Certainly worth the time it will take you to read and digest it.

Have you played a game with a Friend and Foe mechanism? What did you think of it? Have you written one? How did your players respond to it?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  You keep reading. I’ll keep writing.

# Be Ye Friend Or Be Ye Foe? Part 1

Two of the designers in my group recently became entranced by the friend or foe mechanism.  John and Luther have attempted to throw this mechanism into exploration games, war games, and economic games.  In their own words, they have been “throwing it at every wall, hoping it will eventually stick.”

There’s something to be said for that kind of devotion.

With their campaign underway, there have naturally been a number of conversations abound the veritable water cooler.  What are its features?  Its weaknesses?  Where does it succeed?  Where does it fail?  This is of course exactly the kind of thing this blog exists to share.

What is Friend or Foe?

The eponymous game show was played in rounds.  Three teams of two players each competed to amass prize money.  The best overall team went into a culminating final showdown.

In the showdown, these two teammates secretly voted “Friend” or “Foe.”

A) If both choose friend, they split the contest money evenly.

B) If both choose foe, they each get nothing.

C) If one chooses friend and the other chooses foe, the foe gets all the money and the friend gets nothing.

What if you were an amoral decision-making machine?

If you are amoral, you should always choose foe:

(A) If your partner chooses friend, you get everything.

(B) If your partner chooses foe, you get nothing but succeed in preventing him from taking everything.

Most of us are not amoral.  Our actions are how we identify who we are.  This identification is not only how we identify who we are to the outside world.  Our actions are also how we identify who we are to ourselves.  Most of us wish to believe that we are good people and that we do good things.
What if you are absolutely trusting?

If you are absolutely trusting, you should always choose friend:

(A) If your partner chooses friend, you get an equal share.

(B) If partner chooses foe, you get nothing but know that you still did the right thing.

Most of us are not absolutely trusting either.  We want to see good things happen to good people and bad things happen to bad people.  We wish to be conscientious as Wikipedia defines it: “the personality trait that is defined as being thorough, careful, or vigilant;…exhibit a tendency to show self-discipline, act dutifully, and aim for achievement” as opposed to “People who score low on conscientiousness…are more likely to engage in antisocial and criminal behavior.”

Now a tricky decision has appeared.  If you are to be conscientious, your choice must be based on your assessment of your opponent:

(A) If you believe your partner will choose friend, you should also choose friend and thereby share equally.

(B) If you believe your partner will choose foe, you should also choose foe and thereby deny him from making off with all the cash.

The Prisoner’s Dilemma

The Friend or Foe showdown is a form of the Prisoner’s Dilemma game theory concept, which was originally posed by by Merrill Flood and Melvin Dresher in 1950.  Also in 1950, Albert W. Tucker introduced the prison sentence theme.  It breaks down in the following way:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police offer each prisoner a plea bargain in exchange for testifying against the other. Here’s how it goes:

A) If both remain silent, each of them will only serve 1 year in prison.

B) If both betray the other, each of them serves 2 years in prison.

C) If one betrays the other while the other remains silent, remains silent, the betrayer will be set free and the silent one serves 3 years in prison.

Notice right off that this situation is framed in terms of punishment rather than reward so the decision space has different implications.

Notice also that this unlike the Friend or Foe game show, this is not a zero-sum game.  2 total years are meted out in case (A).  The total years in case (B) are 4.  The total is 3 years in case (C).  This difference gives the original prisoner’s dilemma a rather more interesting decision space than its game show incarnation.  The Friend or Foe game show, by contrast, was closer to zero sum.  I would suggest that this staggering of the rewards/penalties makes the prisoner’s dilemma more interesting for our players.  We’ll talk more about that in our next installment.

Has Anyone Researched This?

Yes they have!  There is a great deal of research into Friend or Foe decisions.  Game theorist mathematicians have studied it from a standpoint of pure logic.  Social scientists have studied it from a standpoint of human behavior.  Both perspectives will give us insight into the kind of behavior we can expect from our players.  See you Tuesday!

Have you played a game with a Friend or Foe mechanism? What did you think of it?  Have you written one? How did your players respond to it?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  You keep reading. I’ll keep writing.