CARTEL: a board game for teaching game theory

Introduction

This board game follows the theoretical background and principles of Game Theory, one of the most well-known theories in Economics and a method of analyzing and modeling the strategic interaction between Firms in an oligopoly.

The theory includes a set of ideas which looks to strategies that Firms use to make decisions on prices. It also involves dilemmas, particularly the “prisoner’s dilemma”, which can be used to explain the reaction of 2 prisoners lacking trust and pursuing their own interests.

The board game examines the collusive behaviour of Firms in oligopolies, when there are only a few Firms in the market. That leads to cartels in which Firms secretly charge higher prices to Consumers to maximise their profits. Setting up cartels is quite common in such oligopolies.

Since firms recognise that such cartels are illegal because they turn against public interest, they also know that there is a risk to be reported to the regulator. Thus, the regulator should investigate the market, discover cartels and impose fines on those firms which have been involved. Sometimes the fines imposed might be greater than potential gains.

Additionally, because of this reason, there is a possibility of lack of trust between collusive firms: thus the cartel can be broken. Finally, there is chance of the regulator being corrupt, thus bribery restricts fair practice. This is the idea of the board game.

Number of Players: Maximum 7. Minimum 6.
Time: Approx. 45—55 min.

Number of players	Consumers	Firms	Regulator
6	2	3	1
7	3	3	1

The game has been tested with Advanced Level Economics students, aged 17—18.

Equipment

A game board which includes 35 places, banknotes of three different values, £3, £5 and £10, various types of cards (including “CHECK” Cards, “REGULATOR” Cards, “FINE” Cards, “PENALTY” Cards and “PRICE” Cards), 3 tokens and 3 Envelopes for each Consumer player and a dice. The places on the board include the following:

• PAY FINE
• CALL THE REGULATOR
• IS THE REGULATOR CORRUPT?
• EXPOSE THE REGULATOR
• STAY HERE
• FINE RECOVERY

Getting started

Players are divided in two Groups, Firms and Consumers. Preferably there should be 3 players in each group. Another player should take the role of the Regulator.

Each player of the “Firms” group should receive a set of 3 PRICE cards, valuing £5, £10 and £15. They should also receive banknotes of £5 and finally one envelope. This is the water industry and the market is oligopolistic, thus there are only three Firms that provide water services. Therefore, each “Firm” player will undertake one of the following names: “Purified Water Inc.”, “Healthy Water Inc.” and “Special Water Inc.” and receive the respective envelope.

Now we come to “Consumers”. Each player in the “Consumers” group should select their personal token, receive one envelope and banknotes of £10, £5 and £3. Consumers should set up the order in which they will play.

The Regulator must receive the remaining banknotes as well as REGULATOR cards, PENALTY cards, FINE cards and 1 envelope.

Consumers should place the tokens at the start point on the board. Each Consumer has the right to move their own token. The Consumers and the Regulator should sit around the board. Firms should take a place behind them.

Playing the game

At the starting point, the three Firms should secretly set a Cartel. They will agree the starting price which they will charge for their services, i.e. £5, £10 or £15. The lowest price of £5 is legal and not considered a Cartel.

However, as the game progresses any of these Firms has the power to break the Cartel by changing the price, either upwards or downwards without informing their rival Firms.

Every time a Consumer plays, he/she should roll both dice and move their token (piece) the total amount of spaces indicated by the dice. If a Consumer’s token lands on the place “PAY THE BILL” they will have to pay the relevant Firm whose name is indicated on the space. The Firm player must decide what the price will be, select the relevant PRICE card, secretly place it in the special envelope and hand it over to the player. The Firm will decide on the price without informing others. It may take the risk of charging the highest price of £15, or it may decide to break the Cartel and charge the lowest price of £5. The Consumer player should place the appropriate amount of money in the envelope and return it to the Firm. Other players may keep their eyes open during the transaction but without cheating to see the money placed into the envelope. For more fun and as part of strategy and bluffing, Consumers can make comments to deceive other players. During the game, all players, including the Regulator, should keep their money safe in the envelopes.

It is also important that all players should act honestly and always place into the envelope the correct amount of money as instructed.  Players should also make every effort to complete transactions as quickly as possible.

The Regulator’s role

The Regulator’s role is to investigate whether there is a Cartel in the market. They can only interfere only if a Consumer player asks to do so. If any Consumer player’s token lands on the place “Call the Regulator”, they will have the right to report to the Regulator if they reasonably believe that there is a Cartel. A Cartel involves two Firms, not just one.

Thus, the Consumer should openly specify the names of the two Firms he/she believes are behind the Cartel. There is also a possibility that a Firm takes the risk of charging the highest price of £15 on its own and the other two Firms charge the lowest price. Firms will be having a dilemma. If they charge the price of £5, they avoid the risk of being fined, but their earnings will be limited. If they charge higher prices, they earn more money, but risk being reported to the Regulator and having to pay fines.

Paying fines: (Fine Cards)

In case two Firms are found guilty by the Regulator for setting up a Cartel, they have to pay fines. The fine depends on the level of price set as follows:

Price set by two Firms	Fine to pay
£15 from both Firms	£20 for each
£10 from both Firms	£15 for each
£15 from one Firm and £10 from the other	£18 for each
£5 from both Firms	NO FINE

If the Firm is unable to pay the fine, it will have to declare bankruptcy and quit the game. The Regulator should inform Firms about the fine to be paid by using FINE Cards.

Only two Firms should be fined at a time. Once a Firm has paid a fine cannot be fined twice for the same Cartel. It will pay another fine if found guilty in another Cartel.

Even though the Regulator can never win, their role is critical and can significantly influence the progress of the game. They cannot win because otherwise there will always be a motive to be corrupt in order to collect more and more money from Firms.

Why would Firms wish to break a Cartel?

Although a Cartel frequently increases the possibility of higher profits, this might not always be the case. Firms may break the Cartel for several reasons:

• Danger to be reported to the Regulator, to be found guilty and pay fines.
• Lack of trust between rival Firms. That means if a rival Firm breaks the Cartel first, it can gain an immunity benefit, whereas the other two remain exposed to the Consumers and the Regulator.
• In practice, lower prices sometimes may attract more Consumers.

Dominant strategy

This is a situation in Game Theory where a Firm’s best strategy is independent of those chosen by others. Based on that, Firms cannot communicate, so each Firm does not know what the other two Firms intend to do regarding price policy. Therefore, it seems that any of the above three Firms in the game can be better off by charging the highest price of £15. John Nash referred to such situation as a dominant strategy.

The dilemma is symmetric, so the dominant strategy for all three Firms involved is to charge the highest price, increasing their chances to make higher profits. However, this could be risky for all Firms to adopt. The risk implies fines to be paid if caught by the Regulator.

Penalty cards

In case a Consumer calls the Regulator but the Regulator believes there is NO evidence that a Cartel exists in the market, the Consumer shall receive 1 PENALTY Card from the Regulator. The Regulator must also present the card “NO FINES” to all players.

Regulator’s decisions to impose fines are final and are NOT subject to any negotiations. The Regulator should judge as fairly as possible whether a Cartel exists in the market and make every effort to provide justice to the market in order to protect Consumers’ interest from being overcharged. However, justice may NOT prevail if the Regulator is corrupt.

How the Regulator investigates the market: CHECK Cards

Every time a Consumer pays the bill to a Firm by using the envelope, the Regulator will pick up a “CHECK” Card. If the card states: “OPEN THE ENVELOPE” he/she will have to open the envelope and see the content. It must NOT be revealed to other players. Thus, the Regulator will keep information to judge later on whether a Cartel exists in the market. Accordingly, if the “CHECK” Card states: “DO NOT CHECK” they must not open the envelope. The Regulator must express an opinion and impose fines, if necessary, only if called by a Consumer to investigate.

Reward a Firm which did not take part in the Cartel

When the Regulator imposes fines on two Firms because of a Cartel, the 3rd Firm must be rewarded by the Regulator provided that up to this point it has not been observed, through CHECK cards, charging a price above £5.

In case where all 3 Firms charge the lowest price of £5, the Regulator will have to announce if the recent investigation through CHECK Cards showed that all 3 Firms have charged the lowest price.

The danger of having a corrupt Regulator

In case the Regulator is corrupt, he/she will not take-up the duties properly and has no good reason to fine Firms which set a Cartel.

If the player’s token lands on the place “Is the Regulator corrupt?”, then the Regulator must secretly place in the envelope one of the two “REGULATOR’s cards” and give it back to a Firm of his/her choice. All other players may keep their eyes open during the transaction.  One card writes: “I am a Corrupt Person and I follow BRIBERY” and the other “I am an Honest Person full of Integrity”.

Even though the Firm is not in Cartel, it will still have the obligation to pay and to not expose the Regulator. If the Firm is called to pay, it must refrain from any comments which can help other players to understand. From that point and on, the Regulator should not impose any fines on that particular Firm. In case the Firm has not enough money to pay, it will have to expose the Regulator and the game comes to an end. (See the “Conclusion” section). Thus, the corrupt Regulator should give the card to a Firm he/she believes keeps enough money to pay.

Expose the Regulator if you believe he/she is corrupt

If the Consumer’s token lands on the place “Is the Regulator corrupt?” and believes that the Regulator is corrupt, he/she may openly expose him/her by announcing that claim. The Consumer must select ONE Firm which has received a “REGULATOR’S card” in the past to verify this. The Firm may confirm that it had previously received the card: “I am a Corrupt Person”. If the Regulator is corrupt he/she will have to pay a fine to the player who exposed him/her.

The player must be very cautious before exposure. In case the Regulator is NOT corrupt, the Consumer must quit the game.

For example, a Consumer has already paid a bill of £15 to a Firm and another bill of £15 or even £10 to another Firm. This provides reasonable grounds to assume that there is a Cartel. But the player has to wait until the token lands on the place “Call the Regulator”, to report the Cartel. When this happens, the Consumer should openly specify the names of the two Firms involved.

The following table presents the possible outcomes regarding price policy set by two Firms at a time and the fine to be imposed by the Regulator, if they are found guilty:

Table A. Collusion Between Firm A and Firm B

		Firm A
		Lowest Price:€5		Mid-Price: €10		Highest Price:€15
Firm B	Lowest Price: €5	NO FINE	NO FINE	NO FINE	FINE €15 *	NO FINE	FINE €20 **
	Mid-Price:€10	FINE €15 *	NO FINE	FINE €15	FINE €15	FINE €18	FINE €18
	Highest Price: €15	FINE €20 **	NO FINE	FINE €18	FINE €18	FINE €20	FINE €20

* Provided that the 3^rd Firm has charged the Price of €10
** Provided that the 3^rd Firm has charged the Price of €15

Ending the game

In case any two Consumers are out of the game, because they run out of money or because of two penalty cards or false exposure to the Regulator, then “Firms” will be the winners. Among them, the Firm with the highest value of money is the top winner.

Otherwise, if any two Firms are out because they run out of money, the Consumers will be the winners. Again, the one with the highest value of money will be the top winner.

Alternatively, the game may end if a Consumer exposes the corrupt Regulator. This particular Consumer will be the winner together with the Firm with the highest value of money.

In case the Regulator is left without money, the game will again come to an end. The player, from both Firms & Consumers, with the highest value of money will be the winner.

The Nash equilibrium

This is the situation in Game Theory where each Firm’s chosen strategy maximizes pay-offs given the other Firm’s choice, so that no Firm has an incentive to alter behavior in any future period. This model can be used to investigate a wide range of strategic decisions that Firms need to take.

Where is the Nash equilibrium in this board game?

If we assume that 2 out of the 3 Firms choose to charge the lowest price of €5 in order to avoid the risk of being reported to the Regulator and receive fines, the 3^rd Firm of the game could maximize pay-offs by charging the higher price of €15. This is under the assumption that the 3^rd Firm is informed about the choice of its rivals. In this way, the 3^rd Firm would have no risk to be fined, since there is no Cartel in the market, thus it has no incentive to alter its behavior. 

However, if we assume that 2 out of the 3 Firms choose to charge the highest price of €15 in order to maximize profits, the 3rd Firm of the game perhaps could maximize pay-offs by charging the lowest price of €5, then again in this way, the 3^rd Firm has no risk to be fined, since it has decided not to participate in the Cartel. In the long run this Firm might gain an advantage over its rivals by gaining a higher market share. Therefore, it would have no incentive to alter its behavior.

Feedback

The AL Economics students from the school helped in the construction of ideas and suggestions as to how to improve it and to minimise the problems which were encountered. Below are some examples of student comments after testing the game:

“Handing over the envelopes is a lot of fun. Playing the role of “Firm” is exciting to decide whether to charge the lowest price of £5 or to gamble and charge the higher price of £15. Playing the role of “Consumer” is also exciting to claim that there is a cartel and hope not to receive a penalty card”

“I love playing board games and I have played many. Cartel is quite exceptional for a board game”

“Books could never give a better understanding on what can possibly happen in an oligopoly behind the scenes as this board game has given me”

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