The Game Theory of Risky Chicken
Sitting in my Game Theory class at Kenyon College, I found the “Repeated Prisoner's Dilemma” to be a compelling concept, and I was struck with a board game idea. This game would put our greed for immediate satisfaction at odds with our need to make prudent choices. It would necessitate making, and sometimes breaking, promises. It would require players to weigh their cold, strategic calculations against the social pressure to be honest. This game would become Risky Chicken.
Of course, Risky Chicken is not the first game to utilize the Repeated Prisoner’s Dilemma, and it will not be the last. But no other game is quite like Risky Chicken, between its simple gameplay, funny concept, and the blunt, direct way that it brings Repeated Prisoner’s Dilemma dynamics to the forefront.
The Prisoner’s Dilemma
If you’re unfamiliar with the Prisoner’s Dilemma, I suggest watching our video blog about tacos below. The Prisoner’s Dilemma is a specific situation in which two rational actors can choose either to cooperate with each other or “defect”; if both actors cooperate, they are each better off than if both defect. However, if one actor defects while the other cooperates, the defector’s outcome is best of all, and the cooperator’s outcome is worst (or tied for worst.)
The normal Prisoner’s Dilemma only has one “rational” outcome: for both players to defect, and therefore for each player to be worse off than if both had cooperated. As I mentioned in the video, this doesn’t always happen in practice. For various reasons, one or both players in real-life Prisoner’s Dilemma situations often choose to cooperate. These reasons might include genuine altruism, social pressure, and moral beliefs.
It’s not that a player who cooperates in a one-time Prisoner’s Dilemma game is wrong, per se. It’s just that, when we’re talking about quantifiable utility, as economists often do, the decision to cooperate appears irrational. This is an important distinction to make. There might be other, immeasurable forces compelling us to act in certain ways. For example, someone might keep their promise to cooperate to avoid feelings of guilt or shame, and this decision is perfectly legitimate. But if we reduce human desires down to strictly the payout at stake in the game, cooperating is not a rational decision. A purely rational actor will always defect in a one-time Prisoner’s Dilemma game.
The Repeated Prisoner’s Dilemma
Defecting is no longer automatically rational when we introduce the Repeated Prisoner’s Dilemma. The Repeated Prisoner’s Dilemma is what it sounds like: the Prisoner’s Dilemma game played multiple times between two players.
Repeated Prisoner’s Dilemma games give each player a certain ability that they lack in the one-time version. Essentially, the repeated nature of the game gives each player the tool of enforcement. In the one-time game, all I can say is “I’m going to cooperate, and I hope you’ll cooperate too! If you defect, I'll be dissapointed.” Sure, this tactic might convince some to cooperate, but it’s missing tangible incentives. In a repeated game, however, I can say “I’m going to cooperate, and if you defect, I will defect next time to punish you. If you cooperate, I’ll continue to cooperate for as long as you do.”
What’s crucial about this dynamic is that cooperation goes from an irrational choice to a potentially rational one. Choosing to cooperate and giving the other player the chance to cooperate could be hugely beneficial for both in the long run. If both players prove trustworthy, both can continue to cooperate and reap the rewards of the mutually beneficial outcome every time. If one player chooses to defect in order to capture extra short term benefit, the other player can choose how to respond. Perhaps they will defect until the other player cooperates for a round, or perhaps they’ll simply resolve to defect indefinitely.
A surprising, fragile equilibrium can arise between two players in the Repeated Prisoner’s Dilemma. While each player could be better off by defecting each individual time that the game is played, each resists the desire to defect in favor of the long-term benefits of cooperation.
What this all means for Risky Chicken
Risky Chicken is a Repeated Prisoner’s Dilemma game, but with a couple unique characteristics. One is that Risky Chicken eventually ends. Nobody knows exactly when the game will end, but as scores increase, players know that the end is nigh, and alliances can often fall apart as everyone scrambles to help themselves.
Another unique trait of Risky Chicken is that there are more than two players in each game. While two players are actively playing at a time, there are at least three in a game, giving each player the discretion to choose a partner at their turn. This means that a player’s way to enforce cooperation is stronger than “If you lie, I’ll never trust you again.” It’s “If you lie, I’ll never choose you again,” thus diminishing your opportunities to get ahead. This can be an effective threat, but it doesn’t always work. The temptation to defect and get extra immediate utility (in our case, “gold coins”), remains strong.
What makes Risky Chicken so special is the fact that there is no optimal strategy. Even the most sophisticated supercomputer in the world could not “beat” Risky Chicken by developing some fancy code. It’s a game of real people and interactions, of emotional pleas for honesty and the pain of being betrayed. Yes, there are clearly wise and unwise strategic decisions. But, the best players are the ones who successfully read the room and understand their fellow players. You have to know when to keep your promises but also when to break them, and this is as much of an art as it is a science.
Written by Ben Reingold