Understanding strictly dominated strategies, and 3 ways this can save you money

The trouble with the world is that the stupid are cocksure and the intelligent are full of doubt–Bertrand Russell

A few months ago I was trying to catch a cab in San Francisco on a busy Saturday night. It is quite a game to pick the right spot. The popular spots have more cabs but there are also more people competing for the cabs.

To minimize my wait time, I decided it best to go near a popular intersection but stay away from the crowd. I was lucky and soon a cab came quickly towards me. As it was approaching, a lady from half a block away began yelling at me that she had been outside first and that I was “stealing” her cab. I politely replied that I had not seen her, but since another cab was coming after mine, she should hail that cab instead of yelling at me. She scowled before taking my advice.

I recounted the incident from the cab and decided that yelling at me was the dumbest thing she could do. If she really wanted to catch a cab, she definitely would not have yelled at me.

Game theory explains why this is the case. Since I was closer to the approaching cab, I had full control of taking the cab. Knowing this, she had a range of choices to increase her own chances of getting a cab. She could ask me politely to give up the cab. She could ignore me and keep looking for cabs. She could try calling for a cab on her phone. She could go to another corner.

All of these other choices would have improved her chances of getting a cab. And if she also needed to tell me she was there first, she could have spoken politely. I would have given her the cab if I believed her. By yelling instead, she gave me a bad impression and was not helping her cause.

In game theory, when a player’s action (her yelling) is worse than another action (say, her asking politely), regardless of how other players decide to act (whether I give her the cab or not), the action is said to be dominated.

Game theory has obvious advice: never choose a dominated action. If you learn one thing from my blog, let this be the lesson: please, never play dominated strategies.

Dominated strategies are not just bad decisions; they are the dumbest possible decisions. Buying lottery tickets is a losing bet and dumb, but even then you have a chance to win–hence it is not as bad as being dominated. So you can think of dominated decisions as being worse than buying lottery tickets.

And surprisingly people still make dominated decisions! Here are a few that I can think of:

1. Paying an annual fee for a credit card without rewards

There are tons of no fee credit cards offering rewards. If you are have such a bad credit score that you cannot qualify for any of these, it is not worth getting a credit card. Use a debit card, cash, or money transfers. These cards are a disaster; check out the terms for yourself on one of the worst credit card ever.

2. Overpaying for some thing you want

If you value some thing at $100, don’t spend more for it! In Ebay auctions, people tend to overbid an item if they get caught up in winning the auction. More on this topic when I discuss auction theory…

3. Not asking for fees to be waived on your accounts

When you ask for a fee to be removed, the worst than can happen is the company will say no. Many companies pay hundreds of dollars to acquire customers so they are willing to forgive some mistakes if they can keep you.

When I called my cell phone company about roaming charges, I first told them “I have roaming charges I need to be taken care of.” The representative saw I was a good customer and was immediately willing to refund 75% of the charges. This was before I even explained the details of my situation. I was later credited 100% when they agreed it was a billing mistake. But I learned that it helps to ask even if you are at fault.

Oh yeah, and don’t forget the cab example: it often helps if you ask politely.



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  • Avnish

    Hey, sorry for my long absence, residency applications got in the way!

    You should do more articles like this which relate economic theory not only to personal finance but also to regular events in life. I liked it.

    However, one response. In your taxi cab example, people attempt to yell at someone else in order to intimidate and it often works (I’m not proud but I’ve done it a few times during moments of extreme inebriation on the streets of NYC). You just happen to be someone on whom such action does NOT work. So my question is as follows:

    If we assume there exists a case where it is equally likely that one could get a cab through either badgering or asking politely, can we say then that the action of badgering is “dominated”? (Assuming, of course, that in all other instances one interacts with people like you where badgering would not work)

    Keep up the good work man.

    -A

  • http://www.mindyourdecisions.com Presh

    Hey Avnish,

    Glad to see you commenting again and thanks for the positive reaction. Good luck on residency apps.

    You raise a good point that yelling may be beneficial; I did not consider that but I now see how that might work. Especially when alcohol is involved.

    To answer your question, if badgering works equally well as asking politely for one person, but it is worse than asking politely for every one else, then the formal term is that badgering is “weakly” dominated. It is “weak” since that one case has badgering <= polite asking instead of a <.

    In this case, it is better as a general rule to ask politely since it does you at least as good as yelling and some times it is strictly better.

  • Joon

    This sentence makes little sense to me:

    “In game theory, when a player’s action…is worse than another action…, for every action other players…the action is said to be dominated.”

    The “for every action other players” part is confusing.

    I’ve summed up your advice to “don’t make bad decisions.”

    Thanks for the advice.

  • http://www.mindyourdecisions.com Presh

    @Joon: Thanks for the comment; I’ve revised the sentence to make it slightly clearer.

    What I’m trying to capture is that your payoff depends on what other players do. So, let’s say your action is to run a red light. It’s a bad idea, but it’s not “dominated.” If there are no cars around and no cops around, then it is quicker for you to run the red than to stop. So your action depends on what others are doing.

    A dominated action is NEVER a good idea regardless of what other people are doing. If I impale myself, that sucks regardless of what any one else is doing.

  • Joon

    excellent clarification

  • Glenn

    Don’t forget the utility derived from yelling at a white boy, and the steep discount rate that comes with it. Yelling in the heat of the moment can bring extreme pleasure. Yelling in a few minutes is less enjoyable. I’ll give you weakly dominated at best.

  • http://www.mindyourdecisions.com Presh

    @Glenn: Fair enough.

  • Pingback: The Price is Right Lucky Seven game – a good example of dominated strategies - Mind Your Decisions

  • Pingback: Winning a “Beauty Contest,” Or How My Professor Gambled $250 Teaching a Lesson in Game Theory - Mind Your Decisions





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