Today in the United States we are celebrating Martin Luther King Jr. Day, a holiday marking the birthday of Martin Luther King Jr. He was, of course, the chief spokesman for nonviolent activism in the Civil Rights Movement, which successfully protested racial discrimination in U.S. federal and state law. Yet though we celebrate the work and words of this civil rights leader, a half century has passed since his death and still race relations are more tense than ever. It a dilemma that seems impossibly difficult to solve.

As frustrating as dilemmas are in real-life, situations with difficult solutions can be entertaining in games. After all, one of the reasons we play games is to overcome hard challenges.  Dilemmas especially occur in situation in which the difficult choice has to be made between two or more alternatives, especially equally undesirable ones.

Perhaps the first dilemma that you experienced was on your own birthday.  Your parents bring in the birthday cake, and kids being kids, everyone wants their fair share but is afraid the another kid will claim the bigger piece. How do we cut the cake so that everyone thinks they got their fair share?

The cake cutting scenario is an example of a zero-sum game, a situation in which each participant’s gain or is exactly balanced by the losses or gains of the other participants.  If one kid gets a bigger piece, then another kid will necessarily get a smaller piece of the cake.

Let’s simply the situation by saying that there are only two kids, each of whom is suspicious that the other one will take the larger of the two slices when the cake is cut.  Fortunately, Mom comes up with the obvious solution to this dilemma: have one kid cut the cake into two slices, and have the other kid pick a piece first.  Naturally, the kid cutting the cake will try to cut the cake as evenly as possible, knowing that the other kid will try to take the larger piece.

So, what does cake slicing have to do with games?  Well, for every two-person, zero-sum game with a finite number of strategies, there exists a value V and a mixed strategy for each player, such that

• Given player 2’s strategy, the best payoff possible for player 1 is V,
• Given player 1’s strategy, the best payoff possible for player 2 is −V.

Player 1’s strategy guarantees him a payoff of V regardless of Player 2’s strategy, and similarly Player 2 can guarantee himself a payoff of −V. This solution is called “minimax” because each player minimizes the maximum payoff possible for the other—since the game is zero-sum, players also minimizes their own maximum loss. The solutions to these type of zero-sum games are so obvious that these are scenarios game designers need to avoid.

Now, let’s take a look at another dilemma scenario. Two criminals, Mario and Luigi, are arrested and imprisoned. Each criminal is placed in a separate interrogation room with no means of communicating with the other. The police lack sufficient evidence to convict the pair. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a bargain:

• If Mario and Luigi each betray the other, each of them serves 2 years in prison
• If Mario betrays Luigi but the Luigi remains silent, Mario will be set free and Luigi will serve 3 years in prison (and vice versa)
• If Mario and Luigi both remain silent, both of them will only serve 1 year in prison on a lesser charge

This scenario is called the Prisoner’s Dilemma. Is it better to betray my partner in crime or stay loyal? Well, because betraying a partner offers a greater reward than cooperating with him, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other. Pursuing individual reward logically leads both of the prisoners to betray, when they would get a better reward if they both kept silent.

This scenario presupposes that the two prisoners cannot communicate with each other, but what if they could? In reality, people have a bias towards cooperative behavior in this and similar games, much more so than predicted by simple models of “rational” self-interested action. So games in which players can communicate and negotiate for resolving dilemmas can make for compelling strategic gameplay.

Here’s another scenario with a social dilemma.  A group of farmers share a field on which their cows can graze.  They all agree to each only have two cows graze on the field so that the field won’t be destroyed from too many cows grazing on it.  Of course, cooperation is best for all concerned, but what if one of the farmer decided to break the agreement bring five cows on to the field, to the detriment of everyone else, so that he can profit by having more cows to milk?

Some players will compete against the others even when cooperation is best for everyone, and this risk can bring some exciting tension to a game. For the game designer to set up such a scenario, a game requires individual rewards (in this case, well-fed cows that can be milked) with shared penalties (over-exploiting the field), with the rewards outweighing the penalties.

Dilemmas like these force the player into making risk/reward decisions that can bring about very strong emotional immersion in games.  The dilemma of determining when it is better to cooperate or compete can bring about exciting gameplay.

Just remember that life is not a game, so when away from the board or video screen, let’s all work a bit harder to get along with each other.