Breaking the Chains of Analysis Paralysis – The Prisoner's Dilemma (Part 3 of 7)

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If you’re here, reading a game designer blog discussing analysis paralysis, then I’m pretty sure you probably have some idea of what I mean by the words “Analysis Paralysis” (hereafter referred to as AP). If you don’t, don’t fret! Jump back to Part 1 and read the “What is AP?” section for a primer on the subject.

This is the third article in a series of 7, each article in this series will go into depth on one potential cause of AP, examples of situations where it can be problematic, and present some solutions that can improve the situation.

  1. The Black Box
  2. The Paradox of Choice
  3. The Prisoner’s Dilemma – this article
  4. The Maze to Victory – Jan 3
  5. Relationship Status: It’s Complicated – Jan 10
  6. Sophie’s Choice – Jan 17
  7. Bigger vs Better – Jan 24

If you have any suggestions, examples, questions, or want to point out something I’ve missed, please do so in the comments. This is not a scientifically rigorous examination of AP, and I would be happy to include any contributions you have!

The Prisoner's Dilemma

The problem of risk outweighing reward.

Category: Quality

Player Symptoms:

  1. Repeated examination of the same game elements/components.

  2. Long pauses of intense consideration.

  3. Verbally or manually tracing out options for an extended period of time.

  4. False-starts, repeatedly starting play and stopping again before any action is taken.

  5. Keeping a hand on a piece while continuing to consider options if “hand comes off, move is final” rules are in effect.

  6. Examining other players for clues or cues for extended periods of time.

Many of the symptoms of AP induced by the Prisoner’s Dilemma are the same as those induced by the Paradox of Choice, but with a key difference. The decision paralyzing the player is a very simple one, typically a single choice from a limited set of options – sometimes as simple as a ‘yes’ or ‘no’. Often the information available to be considered by the player is equally simple.

Cause of Problem:

The classic game theory thought experiment of the Prisoner’s Dilemma hinges on two key factors that can cause AP: when risk outweighs reward, and when success depends on anticipation or prediction of another’s action.

Problem 1: Risk Outweighs Reward

A common way to add fun decision making into a game is to introduce the concept of Risk vs Reward. This idea works best by applying variations of the idea that a player must choose either to take a Risk which can grant a big reward (or gain nothing) or to play it Safe by taking a small but reliable reward. The core of the decision revolves around which risks to take, when to take them, and whether the potential reward outweighs the chance of achieving it.

The Prisoner’s Dilemma takes this reward structure, and flips it – a situation that can have all the stress of taking chances while leeching away the satisfaction of getting something for your trouble.

If you are not familiar with the Prisoner’s Dilemma, it’s a very simple thought experiment.

You and your friend have been busted and have been placed in separate rooms. You are both given a choice: stay silent or snitch. If you both stay silent, you each get 1 year. If you both snitch, you each get 2 years. But if one of you stays silent and the other snitches… the snitch gets off scott free, and the one who stays silent gets 3 years.

The math on this works out that overall the best solution for both of you is to stay silent – you both get 1 year, but overall together you have the smallest penalty. From a selfish perspective if you snitch you’ll either do 0 or 2 years (averaging out to 1), and if you stay silent you’ll either do 1 or 3 years (averaging out to 2). But… if you both automatically snitch, altogether you have the worse possible outcome.

The problem with the Prisoner’s Dilemma as a source of AP is that the fear of failure is more paralyzing than the motivation to obtain the best possible result. Most people have at least a basic understanding of the fear of failure – the motivation to avoid the worst-possible outcome. It is a core survival instinct, and transcends rationality. But the drive to obtain the best possible outcome is not quite so common. We would like to get the best result, but in general we are not driven to obtain it at any cost.

Security has a value all its own, in general we are satisfied with a result that meets a minimum standard if we are secure in the knowledge that we can obtain it. We take risks if the potential reward is greater than the cost of failing to obtain it adjusted for our perceived likelihood of doing so.

Simply put – is the reward worth the risk?

Safe Options

So why does the Prisoner’s Dilemma cause Paralysis? Part of the answer is there is no safe option. There is no fallback, there is no way to effectively hedge your bets, it’s all in and regardless of the choice you make – there is a high probability you will fail.

Back in the early 2000’s there was a huge uptake of Poker as a competitive and even spectator sport. Texas Hold’em was everywhere. It was tense, it was dramatic, and with the right editing it could even be exciting. But what you saw while watching it was a half-dozen people sitting around a table in the throes of some form of paralysis.

Each hand plays the same way, 2 secret cards, flop of 3 visible, then 4, then 5, best combination of 5 cards wins. Each round the decision faced by each player was simple, bet or fold. And players would spend long minutes at a time considering what to do. The available information isn’t changing, the odds aren’t changing, bet or fold.

This is common in almost any bluffing or wagering game. To bet is to risk losing what you bet for the chance of winning whatever anyone else bets. To fold is to sacrifice what you’ve already bet and risk that the next hand will present better odds to win it back. But every choice is a risk.

This is a source of paralysis.

Strategy

In the Prisoner’s Dilemma the concept is the same but the calculation is a bit different.

If you assume that a conservative strategy is the best approach (always snitch) because the average (-1) is better than the average of the co-operative strategy (always stay silent, -2), then you must also consider that your opponent is making the same choice. If that is the case, you will always end up with the worst possible outcome (-2).

Now if you always co-operate, you can hope that your opponent will do the same… however the selfish approach for your opponent to snitch will always give you the worst possible personal outcome (-3).

However, if you decide to choose randomly and assume that your opponent will do the same, the average improves to -1.5 because of the distribution of choice combinations. There are other strategies that can do better – but by the very nature of the problem, consistency will produce a worse outcome for you than inconsistency.

Thus there is no safe option that will give you a reasonable, or even average, result. Every time you choose to stay silent or snitch, you are gambling just like each hand of poker.

This is AP induced by risk outweighing the reward, where every decision carries the fear of failure – because there is no safe option, and outcome of every decision is ultimately not within your ability to control.

This form of paralysis is commonly compounded by:

Problem 2: Anticipation

As humans we are hard-wired to search for patterns in randomness. Being able to extrapolate from incomplete information to identify a threat hiding in a forest or the tall grass is essential to survival. And so there is a constant underlying sub-conscious thought that anything that seems random can be understood, controlled, identified, and most importantly… predicted. If only we think about it enough.

This applies directly to the problem of AP caused by the risk/reward circumstances of games like Poker and the Prisoner’s Dilemma. There is an innate belief that if we can understand the randomness, we can reduce the risk and improve the likelihood of avoiding failure by choosing the correct option.

In Poker, if we read the unconscious signals another player is giving us, if we analyze their pattern of betting, we can outfox them by getting an idea of what cards they are hiding and gain an edge.

In the Prisoner’s Dilemma if we analyze the pattern of choices being made by the other player carefully enough we can figure out a way to co-operate, or punish them, in order to improve our overall result.

Games that are built on bluffing or intersect bluffing and wagering are ripe for this kind of AP. This combination of avoiding failure and predicting a random result hits at a weak point in the human psyche – the survival instinct.

Solutions:

This is a hard one to resolve because oftentimes players who choose to play games that include bluffing and wagering are choosing them because they involve bluffing and wagering. It’s a thrill, an adrenaline rush, to gamble and win, to outthink your opponent. That is the very source of enjoyment for these games.

The times that these problems are good candidates for resolving are when they are not core to the experience of the game. If these are secondary or tertiary mechanics and players are showing signs of excessive consideration and delay as a result, there are some simple ways to speed things along.

Drafting:

In a circumstance where players are wagering or bidding to obtain a certain option or effect, drafting may be an alternative to consider. By taking turns selecting an option from a pool, rather than bidding on it, you eliminate the penalty for failure and allow a more even distribution of options for players with different or more risk-averse playstyles. By rotating which players gets first choice, you can also produce a fairer distribution of options and reduce focus on this aspect of the game.

A way to enhance a drafting system by incurring selection costs is to add a pricing mechanism. More valuable options can be priced higher which is a system commonly used by many deck-building games. Or, a queued pricing system such as race selection in Smallworld where the first in the queue is free, but if there is a more valuable option in the queue a player must place a payment token on each skipped option to obtain it – a payment that can then be acquired by another player who may choose a lesser option.

Blind Bidding:

Another method to reduce AP caused by rounds of interactive bidding, is a blind bidding system. Players place a single bid in secret, and the highest bid wins. Although this can cause its own form of AP, a single round combined with simultaneous decision making can reduce the overall time and cost of any AP that does take place.

A variation on this is priority bidding. Players place a blind bid on selection order instead of bidding on a resource. The player who places the highest bid gets first selection, then the next highest gets seconds, etc. This has the added bonus of reducing the fear of failure by removing the all-or-nothing approach to bidding on a resource. By bidding on positioning, a player may end up not getting the best option available – but they will still be able to get something and this also adds another dimension to selection strategy by allowing players to place value on how much selecting first is worth to them.

Consolation Rewards:

This typically applies to a many-participant situation where an ante (or participation cost) is present and a winner-takes-all result. A lottery, for example. The risk-reward calculation for winner-takes-all is very stark, you either win it all (odds dependent on the number of participants) or you fail. But by offering lesser, secondary rewards, overall participation can be increased and overcome resistance or paralysis in choosing to do so. I’m going to turn it over to an excerpt from Shortstack (based on a report from the Journal of the Academy of Marketing Science) to give more information about why.

Offering more than one prize might seem like an effective way to attract more entrants to a contest. However, giving away multiple prizes can actually have the opposite effect. According to a report in the Journal of the Academy of Marketing Science, offering more than one of the same prize doesn’t cause participants to perceive their odds of winning as better. The researchers attributed this to consumers being unable to evaluate the value of prizes when there are more than one available. There is a subconscious assumption that offering more than one of the same prize diminishes the value of it, and there’s less of that nail-biting excitement to participate. However, there is a benefit to offering more than one prize if the prizes are all different. When you offer different prizes at different levels, users feel like they have a higher chance of winning something.

Safe Options:

Lastly, providing a ‘safe’ option as a fallback can empower players who may be having difficulty selecting from multiple high-risk options by providing a default choice. A well designed safe option can be tricky, it can’t be too valuable to negate the potential benefits of taking a risk, but it also cannot be so poor that it is never selected.

In the Prisoner’s Dilemma, suppose we add in a third option, a “plead guilty” choice that automatically (regardless of the other player’s choice) gives each player 1.5 years. This option is precisely as valuable as a strategy of pure randomization. It allows a mechanism by which two players who are in an always-snitch cycle to break that pattern and establish a trust level for co-operation and a release valve that can negate the stress of selecting between two high-risk options.

Next Week

If you have any comments, suggestions, or examples that you would like to share about this week’s topic, please tell us about them in the comments.

Next week we will be looking at the The Maze to Victory.