The Game of Gotcha

by Win Wenger, Ph.D.
Winsights No. 37 (January 2000)

One simple thing could make ours a hugely better world—If more people had the basic concepts which would allow them to recognize and use the opportunities around them for cooperative gain, while developing a sense which allowed them to better avoid being destructively exploited or “conned.”

The relevant concepts have, in fact, been around for a half century or longer, in the branch of game theory known as “non-zero-sum games.” They are usually associated with discussions of something called “The Prisoner’s Dilemma,” a very negative context which most people don’t identify with (I hope!), or pay it much attention. Thus relatively few of even those few people who encounter the concept are likely to transfer the relevant understandings into their own, hopefully more positive, lives and circumstance. And yet …

The basis of “non-zero-sum games” is one of the utterly vital truths of human society which ought to be one of the major cornerstones of the educational curriculum from pre-K and Head Start on through college.

As yet this should-be educational cornerstone has not made it even into American high schools, much less elementary and pre-schools. A few have encountered it in specialized college courses or in independent reading, including some who are presently reading these lines now. But certainly not even a majority of college students and graduates, or the reading public, has even an inkling.

Most of the rest of this particular Winsights article is a set of instructions or “lesson plan” for teaching this cornerstone concept to a class in social studies, economics, political science, history, civics, behavioral science….or even to a Sunday school class!

What is a “non-zero-sum game” situation?

A non-zero-sum game situation is very different from— and also a lot more frequent in occurrence than—the zero-sum game that the unthinking public reflexively considers most situations to be. And that difference is critical, crucial indeed throughout most areas of life. To understand non-zero-sum games both positive and negative, first consider the zero-sum, which is where the sum together of all wins and losses = 0. If someone wins, someone else has to lose. Most people still believe you can’t really get ahead without beating someone else down in the process.

Yet most economic transactions (and most other transactions as well), especially between partners of relatively equal bargaining position, are in fact positive-sum games. The (voluntary) sale would not occur if both buyer and seller didn’t each stand to gain from that trade. The cash from a sale of bread is worth more to the store owner than is that bread; the bread is worth more to the buyer than is that amount of cash. In fact, human organizations and institutions exist mainly to actualize some of the opportunities people have to benefit from working together in some form of cooperation.

The inefficiencies and unproductivity of coercive command structures have long since consigned both slavery and the communist “dictatorship of the proletariat” to history’s dustbin. (Such rescue services as the police or military are specialized for fast-response situations and—in civilized countries at least—are careful to defer to civilian policy which has somewhat better checks on the decisions arrived at.)

Even such games as football, basketball and chess, which officially have one winner and one loser, actually have strong non-zero-sum components. If the object of the game were only to determine who won and who lost, a flip of the coin would suffice. How exciting—band on the sidelines, 70,000 screaming fans, 11 players on each team—just to decide the whole outcome with but the flip of a coin! The non-zero-sum elements include the excitement of the contest itself; the opportunities to hone one’s own skills against an opponent; the opportunity to learn from a skilled opponent; the opportunity to capture imagination and admiration; the adrenaline rush….. And why would schools form cooperative athletic leagues with “their most hated and bitterest rivals” except for both these non-zero-sum elements and the added revenues such long-standing rivalries generate in attendance?

So it is possible, in most real-life situations and most games, to have win-win instead of merely win-loss, and also to have loss-loss, as the late Cold War for so long threatened to become. (What would you call a nuclear war which only ten Americans survived but only one Russian survived? A stunning victory?)

And what difference does it make in your dealings with other people, in how you treat other people, and the kinds of situation you can move effectively in, if you understand most situations to be win-win opportunities instead of assuming that to win you must make someone else lose?

Lesson Plan for “The Game of Gotcha”

  1. However many students you have for the occasion, prepare at least 3 times as many “Gotcha” cards. A “Gotcha” card is an index card with Gotcha printed in large letters on one side, Meetcha printed in large letters on the other.
  2. Have each of your students also fold a sheet of notebook paper, which they are to use to conceal which side of the card is uppermost until after it has been played and their partner’s card also played.
  3. Obtain, presumably from a bank, approximately a dollar in pennies for each student. Keep two-thirds of the pennies in a ready box, distribute the other third evenly among your students.
  4. Say to your students, “These pennies, and however many more you happen to win in this little game, are yours to keep. This is reward and/or tuition for something invaluable and positive we are to discover together, so it is not any form of the usual win-lose gambling. Nor does this exploratory lesson in any way countenance such gambling. But you do have a chance to win some money, and you do have a chance in this game to lose the pennies distributed to you and have to sit out the remainder of the game as a loser.” (It is your option whether or not to permit losing students to add their own pennies to stay in play, but it would be somewhat difficult to enforce a ban on their doing so.)
  5. “Your Gotcha card has the word Gotcha on one side, and Meetcha on the other side. You and your partner play your respective cards at the same time, inside your folded sheets so that neither of you can see what the other has played until both your cards are sitting there. If you’ve played the card Meetcha side up, you’ve played a Meetcha. If you’ve played the card Gotcha side up, you’ve played a Gotcha. I will come around to each desk (or table) at the end of each round of play, open your folded sheets to reveal your play, and give you pennies accordingly or take pennies away accordingly. Listen carefully — scoring is as follows:”

    Scoring chart for the game of Gotcha
  6. (You might also draw a chart as per the above matrix and post it up on the board for all to see.)
  7. “If you have played a Meetcha card and your partner has also played a Meetcha card, I will give you each three pennies for that round. If you have played a Meetcha card and your partner has played a Gotcha card, I will give your partner five pennies, but I’ll take away six pennies from you. If you have played Gotcha and your partner has played Meetcha, I will give you five pennies but take away six cents from your partner. If you have both played a Gotcha card, I will take away three cents from each of you.”
  8. Play one round, somewhat theatrically. After reactions settle, have the paired students pull into groups of four or so to “buzz” on what happened, what was going through their minds when they made their play, and what they think it all may mean. The rules of Dynamic Format can be useful for keeping this a well-focused, orderly activity. Get some consensus of observations/opinions also from the class as a whole, starting with a report from the groups.
  9. Reconvene and announce a series of five consecutive rounds, each played like the one above, same partners or different, you coming around at the end of each round to reveal the play and to pay and collect accordingly. Each pair also keeps score on the outcome of each play in the series. Indicate but don’t actually state that the game, for better or worse, will be over after that fifth round.
  10. Again after reactions settle, have the pairs pull back together into groups of four or so to “buzz” on what happened, what was going through their minds when they made their play, and what they think it all may mean. As these groups report, work toward consensus of observations/opinions from the class as a whole.

Further options

  • You can go on from there into teaching whatever points you find appropriate for this context.
  • You can let yourself be “persuaded” into allowing one more round of five plays (or three) next class meeting if, meanwhile, your students develop further insights on what has happened and why, and what it may mean in other contexts. That will result in your students’ arguing over the matter up and down halls to the next class and making you the envy of the other teachers.
  • You can pick two appropriate students to play a series of ten rounds in front of the rest of the class, and have them report back on what was going through their minds at various points of the game, and answering questions from the rest of the class.
  • Run some form of this game with three players or four or five, provided basically the same non-zero-sum payoff structure is kept. Make comparisons with the situation in which only one other person has to be trusted to get mutual benefits realized.

Points you want to make sure get understood

  • That most real-life situations are in fact like a game in that your “play” affects the outcomes of others and vice-versa.
  • That most such situations are in fact non-zero-sum.
  • That in most situations you can “win” by helping someone else also to “win.”
  • That it’s possible also for everyone to lose. Examples: nuclear war; starving nations conducting an arms race; prolonged strikes and lockouts; mutual bad-mouthing. The original “Prisoner’s Dilemma” when, if one prisoner snitched on his partner in crime, he’d go free or get a much reduced sentence but the other guy’d get the book thrown at him and vice versa, while if each “turned state’s evidence” on the other, both would get stiff sentences.
  • What kind of a situation is a chain-letter? A pyramid scheme? What kinds of situations instead are you likelier to come from with a win?
  • What are some of the things one needs to do to engender trust so that “win-wins” can be achieved?
  • In what kinds of situation is it easier, and what kinds harder, even when clearly non-zero-sum, to build the kind of relationship which will allow win-wins to be won?