Author:  Lori Alden

Audience:  High school and college economics students

Time required:  Each game takes about 10 minutes to play and score.  Allow at least one class period to introduce the game.  

NCEE Standards:  scarcity, marginal cost & benefit, allocation of goods & services, gains from trade

Summary:  In this strategic trading game, students assume the role of Vikings who have returned to the medieval outpost of Birka to trade loot from villages they’ve plundered.  Playing cards represent the loot--spades, hearts, diamonds, and clubs.  To play effectively, students must use marginal analysis to determine whether prospective trades will benefit them, probe constantly for mutually beneficial exchanges that remain to be exploited, and bid more for cards that are relatively scarce.  Birka also can be used to conduct several brief experiments about trade, equilibrium, efficiency, and the costs of government regulation.  Birka is also an ideal activity for high school teachers who wish to occupy small groups of students productively for short periods of time, since each game can be played in only ten minutes with as few as four students.

For more information:  Alden, Lori.  2005.  Birka:  A Trading Game for Economics Students.  The Social Studies   96(4):  178-183.

Resources:

  • Two decks of standard playing cards for each group of 4, 5, or 6 students.

  • Copies of the scoring sheet (pdf format), one for each student.

  • Scratch paper and pens for recording scores and conducting experiments.

Overview:

Students play Birka in small trading groups.  Each student is dealt 14 playing cards, and told that the marginal point value of each card depends upon how many cards there are in that card’s suit.  Students then take turns proposing trades in order to improve the total value of their hands, while their opponents compete to take advantage of those trading opportunities.  Each game takes about 10 minutes to play and score. 

  One of the appealing things about Birka is that it’s fun for players of varying abilities.  A beginner can play a passable game simply by trying to accept any trade that results in a marginal gain.  Better players can improve their chances of winning by taking calculated risks in order to get higher prices for their cards.  Since the hands are randomly dealt from two decks of playing cards, each game is different and students can play again and again without losing interest.

I find that players are usually eager to share strategies and advice with their opponents.  Various educators have suggested that engaging students in this sort of collaborative problem-based learning stimulates curiosity, deepens understanding, and enhances critical thinking, social, and communication skills.  Researchers have also found that active learning promotes student achievement and interest.  All of this suggests that a game like Birka might do a better job of presenting economic concepts than the traditional “chalk and talk” lecture method.

While designing Birka, I experimented with several different trading rules with an eye to making the game as fun to play as possible.  I found that a reverse auction, in which one buyer trades with several sellers, best rewards players for skill and speed.  While this type of auction isn’t as familiar as others, it’s being used increasingly by e-commerce websites, like Priceline, Respond, and eWanted.

I recommend introducing Birka after the concepts of marginal analysis and supply and demand have been covered.   I think it’s best to allow students to play two or three games on their own, and to encourage them to discuss strategies with their groups whenever the cards are being shuffled and dealt.  Use the balance of the period for a class discussion of these strategies and the economic principles that lie beneath them.  The experiments can then be performed during one or more subsequent periods.  High school teachers might also want to use the game throughout the rest of the term to fill short time slots or to occupy small groups of students. 

Procedure  

Divide the class into small groups of 4, 5, or 6 students and have each group form a circle around a playing surface, like a table, the floor, or desks joined together.  (Note:  The 4-player game is more strategic and difficult.  Beginners usually do better in groups of five or six.)  Make sure that each student is within arm’s reach of the middle of the playing surface.  Give each student a copy of the scoring sheet (pdf format), and each group two decks of standard playing cards. 

Tell the students that they’re to assume the role of Vikings who have just returned to Birka, a medieval Scandinavian trading outpost, with loot from a village they’ve plundered.  The suits of the playing cards represent the four kinds of goods the Vikings have acquired:  wooden spades, heart-shaped bronze amulets, uncut diamonds, and wooden clubs.  The rank (A-K-Q-J-10-9-8-7-6-5-4-3-2) of the cards is ignored. 

As the scoring sheet shows, the value of any card depends upon the number of cards a player has in its suit.  Players get diminishing points for each additional card in a suit, so that the first club, for example, is worth 150 points, the second 70, the third 25, the fourth 10, the fifth 7, and so forth.   If a player was dealt 2 clubs, 4 diamonds, 5 hearts, and 3 spades, for example, the clubs would be worth 150 + 70 = 220, the diamonds 150 + 70 + 25 + 10 = 255, the hearts 150 + 70 + 25 + 10 + 7 = 262, and the spades 150 + 70 + 25 = 245, and the total value of hand would be 220 + 255 + 262 + 245 = 982.  The object of the game is for a player to end up with the most points by trading cards within the group.    

The first dealer in each group is randomly selected.  He or she shuffles the two decks together, deals 14 cards face down to each player, and sets the remaining cards aside face down.  The players sort their cards by suit.   

The dealer is the first to serve as a “buyer.”  At the beginning of a turn, a buyer can either pass or initiate a trade.  To initiate a trade, the buyer first requests one or more specific cards.  For example, the buyer might say, “I want to buy a club,” or “I want to buy two spades,” or “I want to buy a club and a spade.”  A request may not change during the buyer’s turn.  After making a request, the buyer must lay one or more cards that he or she is willing to offer in exchange (a “bid”) face up in the middle of the table. 

Once the bid is laid on the table, any of the opposing players (the “sellers”) can accept it by being the first to place the requested card or cards on top of the offer.  Once a bid is accepted, both the buyer and seller are committed to the trade and must immediately exchange cards.  If no seller accepts the bid, the buyer may either withdraw it or increase it by adding one or more additional cards.  A buyer may not subtract any cards when altering a bid.  A buyer’s turn is over when he or she passes or withdraws the bid, or when a bid has been accepted.

The role of buyer then rotates clockwise to the next player.  The game ends when the opportunity to be a buyer has gone twice around the table.  The players then calculate their scores by summing the value of each of their cards.  For example, if a player has four cards in each of two suits and three cards in each of two suits, the total value of the hand is 255 + 255 + 245 + 245 = 1,000.  If several games are played, the role of dealer rotates clockwise around the table.  The overall winner in each group is the player with the highest average score.

South is the first to serve as buyer.  She has a 6-4-2-2 hand (6 spades, 4 diamonds, 2 hearts, and 2 clubs) which is worth 961 points.  She wants to trade a spade for a club or heart.  

South says, "I want a club."  She then bids a spade by putting it in the middle of the table.

West quickly accepts the trade by throwing the requested club on the spade.  West gives up a fourth club (worth 10 points) but gains a third spade (worth 25 points).  South gives up a sixth spade (worth 4 points) but gains a third club (worth 25 points).

The role of buyer rotates to West, who has a strong 4-4-3-3 hand.  

West says "I want a club and a spade" and bids a heart by putting it in the middle of the table.  None of the other players would benefit from the trade, so nobody accepts the bid.  West withdraws his bid and the role of buyer moves to North.

North would benefit by trading a fifth spade (worth 7 points) for a third heart (worth 25 points).

So North says "I want a heart" and bids a spade by putting it in the middle of the table.  East would benefit from the trade since he would give up a sixth heart (worth 4 points) and gain a fourth spade (worth 10 points).  

But East doesn't accept the bid, gambling that North will sweeten it with another card.  When nobody accepts the spade bid, North adds a diamond to it.  

East quickly responds by slapping a heart on the bid.  Notice that West also would have benefited from the trade, but he responded too slowly.

It's East's turn to serve as buyer.  He desperately needs a club since he's short in that suit.

East says "I want a club," and bids a heart.  None of the others respond to the bid.

East therefore adds a diamond to his bid.  South would benefit slightly from the trade, but doesn't respond in hopes that East will add another card to his bid.

East adds another heart to the bid and South accepts the trade by putting a club on top of the cards.  East gained a second club (worth 70) but gave up a fourth and fifth heart (worth 10 and 7 points) and a fifth diamond (worth 7 points).  South gave up a third club (worth 25 points) but gained a third and fourth heart (worth 25 and 10 points) and a fifth diamond (worth 7 points).

The role of buyer now goes back to South, who will try to trade away a spade and a diamond for a club.  None of the other players gain from the trade, so it's rejected.  West, North, and East will also fail in their attempts to trade.  After East passes, the hand is over.   South has a 5-5-4-2 hand, worth 999 points.  West has a 4-4-3-3 hand, worth 1,000.  North has a 4-3-3-3 hand, worth 990 points, and East has a 4-4-3-2 hand, worth 975.  The total value of the four hands after trade is 999 + 1,000 + 990 + 975 = 3964.  Recall that before trading began, South had a 6-4-2-2 hand worth 961, West had a 4-4-4-2 hand worth 985, North had a 5-4-3-2 hand worth 982, and East had a 6-4-3-1 hand worth 916.  The total value of the hands before trade was therefore 961 + 985 + 982 + 916 = 3844.  By trading, the Vikings increased their wealth by 3964 - 3844 = 120.

 

To summarize:
  • Each student gets 14 cards.
  • Only the suit matters, not the rank (A-K-Q, etc.)
  • The object of the game is to trade to get the highest total points.
  • The scoring sheets tell how much each card is worth.  The first card of each suit is worth more than the second, the second is worth more than the third, etc.
  • The role of "buyer" rotates twice around the table in a game.
  • The buyer begins by making a request for one or more specific cards (e.g., "One heart.")  Requests can't change during the buyer's turn.
  • After making a request, the buyer lays one or more cards (a bid) on the table.
  • The buyer must trade with the first player to lay the requested card or cards on the bid.
  • If no players accept the bid, the buyer may add more cards to it.
  • A buyer’s turn is over when he or she passes or withdraws the bid, or when a bid has been accepted.

Discussion

I recommend beginning a class discussion of the game by having students share any strategies that they’ve discovered.  Write their ideas on the board, and then discuss the economic principles that underlie each strategy.  Here are some examples of what you might talk about:

Strategy:  Try to achieve a balanced hand with roughly the same number of cards in each suit. For example, if you have six spades and one club, it’s advantageous to trade a spade for a club.  You sacrifice only 4 points when you give up the sixth spade, but you gain 70 points when you acquire the second club.  Teaching points:   Point out that the scoring sheets are consistent with the law of diminishing marginal benefits, in that Viking traders are assumed to value the first unit of a good more than the second, the second more than the third, and so on.  Make sure that all students understand how to “think at the margin,” and how to compare the marginal benefit with the marginal cost of a proposed trade.  Remind students that marginalism solves “how much” or “how many” problems by breaking them down into many small problems.  For example, the problem of how many hamburgers to buy can be expressed as several problems:  Should you buy the first one?  The second?  The third?  Marginalism suggests you should keep buying hamburgers only as long as the marginal benefit covers the marginal cost. 

Explain that marginalism teaches us not to overdo things.  Just as it doesn’t make sense for a Viking trader to acquire a lot of spades, it usually doesn’t make sense for people to buy five hamburgers at a time, or listen to a song ten times in a row, or brush their teeth for twenty minutes every morning.  For most of us, the marginal benefit of, say, a third hamburger doesn’t cover its marginal cost.  Nor does the marginal benefit of listening to a song for the sixth time.  And even dentists don’t expect us to brush our teeth for more than two minutes straight—the marginal benefit of brushing for a third minute doesn’t cover the marginal opportunity cost of that time. 

Strategy:  If you’re a seller, plan ahead so that you can accept bids quickly.  When a buyer makes a request, immediately think about what bids you’d be willing to accept in exchange for it.  Hold the requested card or cards in your hand so that you can quickly accept an advantageous bid.  Teaching points:   Sellers in competitive markets must worry constantly about losing business to competitors.  This gives them an incentive to keep prices low for buyers.

Strategy:  Pay attention to what cards your opponents are bidding, accepting, and rejecting.  If you want to sell a club, for example, and you suspect that the other players don’t have very many, then you may be able to get two or more cards for it.  Teaching points:   Since the marginal benefit schedule for cards in each of the suits is identical, the demand for cards in each suit is the same.  This is because the marginal benefit curve for any individual is identical to that person’s demand curve, and the market demand curve is simply the horizontal sum of all of the individual demand curves in the market.  What changes from game to game is the total supply of cards in each suit.  Suppose that 17 hearts are dealt, but only 9 clubs, as shown in this figure.   According to the supply and demand model, the equilibrium price of hearts will be lower than that of clubs.  Astute players try to deduce whether cards in any suit are relatively scarce or abundant so that they can make more advantageous trades. 

Strategy:  Take risks from time to time.   It sometimes pays to refuse a buyer’s bid even though accepting it would make you slightly better off.  If you hold off, you might be able to get a better deal later on.  Teaching points:   Once you’ve decided that a trade is advantageous, you often face another kind of tradeoff:  whether to trade now for a certain marginal gain or to reject the trade in hopes of getting a larger marginal gain in the future.  Suppose that Sarah can get a fourth heart (worth 10 points) by giving up a fifth club (worth 7 points), and achieve a marginal gain of 3 points.  If she waits, though, she believes that there’s a fifty-fifty chance that she can get a third diamond (worth 25 points) for her club, for a marginal gain of 18 points.  The tradeoff, then, is between a 100% chance of getting 3 points now or a 50% chance of getting 18 points later.  Neither choice is wrong—Sarah’s decision will depend largely on her taste for risk. 

Experiments

After students have played a couple of games and discussed their strategies, Birka can be used to conduct several experiments. 

Experiment #1:  Is trade a positive sum game?   At the beginning of a game, have your students measure the total value of the cards they were dealt and record those values on slips of paper.  Collect the slips and, while the students play the game, add the values and record the sum on the board under the heading “The Vikings’ wealth before trade.”  After each group has completed the game, have students submit new slips of paper giving the value of their hands after trade.  Record the sum of these values on the board under the heading “The Vikings’ wealth after trade.”  Your students should discover that trade has greatly increased the Vikings’ wealth.  Have them discuss how this could happen if the total number of spades, hearts, diamonds, and clubs held by each group didn’t change.  They should observe that they were able to increase the value of the cards simply by changing the way they were allocated.        

Experiment #2:  Does unrestricted trade result in an efficient allocation?   A market is said to be in equilibrium when there’s no tendency to change.  This occurs when each participant is doing the best he or she possibly can.  After a game is over and scored, ask your students to lay their cards face up on the table.  Have each group examine the cards to see if its market is in equilibrium.  Explain that a market is not in equilibrium if any mutually beneficial exchanges can still be made, since that implies that some of the participants aren’t doing the best they can.  If students identify any opportunities for mutually beneficial exchanges, have them make those trades so that their group’s market is in equilibrium.     

An allocation is efficient when it’s impossible to make someone better off without making someone else worse off.  Have each group check to see if its allocation of cards is efficient.  Some groups will find that their allocations are indeed efficient.  Others won’t, since some players may have declined trading opportunities that would have made others better off, but would have left them neither better off nor worse off.  

Experiment #3:  Do trade restrictions entail economic costs?  Suppose that the village of Birka imposes this trading rule:  It’s forbidden to trade spades.  Ask students to play a game with this new rule.  When they’re done, have the students put their cards face up in front of themselves,  check the cards and, if necessary, make additional trades in order to reach equilibrium under the trade restriction.  After the groups have achieved equilibrium, have each student write his or her score on a slip of paper.  Collect these slips, and tell the students that you’ve decided to lift the trading rule and that all suits can now be traded.  Have them continue playing the game until the role of buyer has rotated once more around the table.  As they play, add their scores and write the sum on the board under the heading “The Vikings’ wealth with trade restrictions.”  When the students have finished their games, have them again display their cards and, if necessary, make additional trades to put their markets into equilibrium.  Have students write their new scores on slips of paper, and write the sum of these values on the board under the heading “The Vikings’ wealth without trade restrictions.”  The Vikings’ wealth, of course, should be higher without the trade restrictions.  Ask your students to explain why.  Also ask them to give examples of trade restrictions that are imposed by our society (e.g., prohibitions against prostitution and gambling, and restrictions on the sale of certain drugs, Cuban cigars, and human organs).  Discuss with them whether lifting these trade restrictions would make us better off.  [Note:  Scores from the game played in this experiment should not be included when determining a student’s overall average score.]

Experiment #4:  Do price controls entail economic costs?  Suppose that the village of Birka imposes a different trading rule:  Only one card can be traded for another card.  As in Experiment #3, have students play a game under this rule, display their cards, and then, if necessary, make additional trades in order to reach equilibrium under the restriction.  Write the sum of their scores on the board under the heading “Vikings’ wealth under price controls.”  Then lift the price controls and allow the students to continue playing the game until the role of buyer has rotated once more around the table.  Have them again put their markets into equilibrium, then write the sum of their new scores on the board under the heading “Vikings’ wealth without price controls.”  As before, the Vikings’ wealth should be greater without the restriction.  Ask your students to explain why.   Also ask them to give examples of price controls in our economy (e.g., minimum wage, rent control, and usury laws).  Discuss with your students whether eliminating these price controls would make us better off.  [Note:  Scores from the game played in this experiment should not be included when determining a student’s overall average score.]

Classroom Tournaments

As with most card games, success at Birka depends on both skill and luck, and several games must be played in order to identify the most skillful players.  One way to do this is to have a round-robin classroom tournament that can be played over the course of several days, weeks, or months.  To win a round-robin Birka tournament, a student must (1) play complete rounds in three different trading groups and (2) have the highest average score.

It’s best to start a tournament after the students have mastered the basic rules of the game and completed all of the experiments.   Start by counting the number of students who will be playing and deciding on the size and number of the trading groups.  Try to keep the sizes of the groups roughly equal.  Randomly assign the students to the groups and appoint a scorekeeper for each.  Have the groups play until each student has had one chance to deal.  When they’re done, use a spreadsheet program to record each student’s scores after the first round and post the spreadsheet in the classroom.  Have the students play rounds in two more randomly assigned groups, and continue to collect and post scores.   After the third round of play, determine the winner by calculating each student’s average score.

 

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