Trade Mechanic Equilibrium in Board Games

Ever reach a point in a trading game when players no longer trade?  That dreadful part of Monopoly where all the properties are traded into monopolies and all there is left to do is to chuck dice until someone wins the game.

Why do trade games freeze?  Trade games freeze because players no longer have any trades that make both parties better off.  When I engage in a trade both the person I trade with and myself are better off from the trade.  But, it is possible that there are a limited number of transactions within a game where that is true.  

If there is a fixed amount of resources in the world, trade makes people better off by sorting the resources to the people who value them the most.  Imagine we are splitting two bags of M&M’s in a room full of board game players.  Initially, we randomly distribute the M&M’s to the players. Then we assign each player a different color they should collect.  If a person who only wants green M&M’s trades 3 brown M&M’s to a person who wants as many M&M’s as possible in exchange for one green M&M, both are better off.  In this world, their trade does not create new M&M’s, their trade only redistributes the M&M’s, but the players are richer as a result.  

As long as no new additional M&M’s are created, and assuming people maintain the same preference for particular types of M&M’s, eventually there will be a point where no one can make a trade that will make someone better off.  If I only want yellow M&M’s and I have, through trade, gotten ahold of all the yellow M&M’s, then there are no more trades that exist that will benefit me.  At some point, every person trading M&M’s will hit this constraint, be it from the lack of having something to trade for what you want or from collecting all of the M&M's you desire.

Economists consider this point when there are no longer any possible trades that make people better off to be an equilibrium.  When equilibriums occur, trading ends.  If trade is a phase in your game, then equilibrium is when players should move onto the next phase of your game, if you do not move on then basically your players are sitting around doing nothing.  

But what if you don’t want to move on?  What if trade is not a phase, but the main mechanic of the game?  What can board game designers do to keep players trading?

Designers options can be broken into two broad categories.  Category one - change the preferences of the players playing the game.  Category two - change the amount of resources available to trade.  

Changing Players Preferences

Players reach an equilibrium because their current set of preferences have been fulfilled.  If I can only earn victory points by collecting sets of five bricks and two wheat then I no longer have any motivation to trade for anything else (unless it helps me get three stones and two wheat).  Furthermore, if I successfully have traded for all the possible sets of 5 brick and 2 wheat, I no longer have any motivation to engage in trade whatsoever.

But what if something happened that changed my preferences?  Say I also have the ability to exchange 3 wheat and 2 stones for victory points.  This changes what sets of resources I want in my hand and pushes me back into the trading market to attempt to acquire the goods I need.

Variability in players trade preferences can also come from varying the payouts of preexisting actions.  Lets say a player always was able to exchange 3 wheat and 2 stones or 5 brick and 2 wheat for victory points, but what changes is how much victory points each sets earns relative to the other.  This change in relative value changes the value of cards in a players hand and potentially stimulates more trade.

How a game shifts players preferences can vary.  Some games may give players exogenously varying goals where the game instructs the players what is the change in the payout for particular actions. This can be done with dice, cards, etc.  Take the game of Compounded.  Each player has the opportunity to trade elements with other players.  The value of having a particular element will change because the compounds available to be created to earn victory points vary throughout gameplay.  New compounds, dictating the value of each element, become randomly available as they are drawn from the deck.

Other games, like Post Position, alter goals with an endogenous mechanics.  An endogenous mechanic is when players actions empower them to manipulate the victory point value of certain actions/positions/holdings through gameplay.  

Players in Post Position engage in trade by making bets for or against a horse.  For one player to bet a horse is going to do well, they have to entice another player to make a trade with them by betting a horse is going to do poorly.  These bets are based on each player’s expectations (aka preferences) on how they think the race is going to play out.  

The expected outcome of the race comes from inputs by the players.  Before each betting round players secretly submit 2 or 3 horses they wish to move up in the race.  The ability of players to endogenously manipulate the position of the horses alters players preferences for which horses they wish to bet for or against and keeps players trading with each other until the end of the game.

Altering Resource Availability

Another, more settle way, to stimulate trade is to alter the availability of resources within the game.  Altering resources has the benefit of changing the value of actions without explicitly changing the price for said action.  The price for upgrading to a city in Settlers of Catan may remain at 3 stones and 2 wheat, but the cost to players of achieving that goal and acquiring the 1 VP that goes with it, will vary due to the availability of stones and wheat for them to trade.

Altering resources can occur both from mechanics that increase the number of resources in the game as well as mechanics that reduce the number of resources within the game.  When the robber removes cards from a players hand, say brick, it increases the cost to that player of constructing roads and alters the value that player places on brick.

You might have noticed that altering resource availability motivates trade in two different ways.  First, it changes the overall cost of acquiring a resource.  When there are more or less places where I can acquire the resource, the cost of earning victory points through collecting different sets also changes.  Second, it changes the preferences of players of what resources they desire.  If I lost all of my wood to the robber and I need to build one more road to guarantee the victory points from having the longest road, then my value for wood will dramatically increase because the resource is now scarce within my hand.  These two effects combined potentially changes what combination of goods in players hands where they do or do not benefit from trade.  This variability provides an opportunity to move from a point in the game where player no longer benefit from trade back to a point where they do benefit from trade.

-Thank you to Kevin Kulp and T.C. Petty III for motivating me to write on this topic with our conversations at Congress of Gamers.

Market Mechanic Lecture: Trade

To understand why trade mechanics are important in board games you have to first understand why trade is important outside of board games.  When I say trade I mean someone actually trading something with someone else.

People can trade physical objects--I trade a banana for a coconut.  People can trade actions--I will rub your shoulders if you rub my feet.  People can trade actions for objects--I will babysit your kids and in exchange you will give me a shrubbery.

Why do People Trade?

The reason I trade a rubber ducky for a golf ball is because I value the golf ball more than the rubber ducky.  If you gave me a golf ball for a rubber ducky then you value the rubber ducky more than the golf ball.

Why can I say with confidence that I value the golf ball more than the rubber ducky and you value the rubber ducky more than the golf ball.  Because we each voluntarily made an exchange with each other, and by exchanging we revealed our preferences.  If I thought the golf ball was worth less than the rubber ducky then I would not have exchange the golf ball for the rubber ducky.  

Since we both value the goods we received in trade more than the good we exchange, we are both better off by making the trade.  This is true even if someone complains about the price of the exchange prior to trading.  If I spend the whole time arguing that the rubber duck is really worth two golf balls and not one, but I still exchange the rubber ducky for one golf ball, guess what, my reveal preference from the trade shows that I really value one golf ball more than a rubber ducky.

People complain about prices for a variety of reasons.  Much of the time they are just wishing they were able to get more bang for their buck.  If I was willing to accept one golf ball for a rubber ducky there is no question I would happily also accept two golf balls for a rubber ducky.

Notice we end up trading not only because we have things we value differently, but we each have something the other person wants.  If I had a rubber ducky and you a ripped t-shirt covered in horse poo, there is nothing I am willing to give you for your ripped t-shirt covered in horse poo.  I just do not want it and in a world of volunteer trading, I am not going to give you something to take it.

Trade in Board Games

Like real life, people make trades in board games because each person values what they are receiving in the trade more than what they are giving up in the trade.  When I trade two wood for a stone with another player in Settlers of Catan that means I value the stone more than the wood and my trade partner values the wood more than the stone.

If you are designing a game that utilizes a trade mechanic it needs to motivate players to value different goods differently.  When everything is worth exactly the same there is no need for player trades.  If a green cube is worth one victory point, and a red cube is worth one victory point,  players have no incentive within the game to exchange cubes.  Neither player gains any edge in gameplay by making an exchange.  They are in fact the same good that happen to be different colors.

Game designers desiring trade in their game need to also make sure trades exist where the players trading can benefit from the exchange.  I am not going to make an exchange with another player unless I think it helps me win the game.  The same goes with the person making the exchange with me.  A player is not going to trade me three stones in Settlers of Catan if it will enable me to upgrade a settlement to a city and provide me with the last victory point I need to win the game.  

Creating an environment conducive to trading is challenging in board games since many board games, unlike the real world, are zero-sum games.  A zero-sum game means that for one person to succeed everyone else must lose.  When I win the game of Monopoly everyone else playing the game lost the game.  

In the real world, when I trade maple syrup I made with the butcher for a pound of beef, neither one of us is worried that the trade is going to give the other person an edge to defeat the other.  I am excited because I now have some delicious beef to grill and the butcher is excited because he is going to use the maple syrup to glaze a ham.  The butcher making a glaze ham has no negative effects on me.  And me grilling some beef to eat has no negative effects on the butcher.

But in board games, every trade I make has the risk of hurting me by giving my competitor a new resource he can use to beat me.  That makes people guarded about the trades they make within a board game and makes it harder to construct a game where trading is a relevant mechanic to game play.  

Trade Theme vs. Trade Mechanic

A game with a trading theme is a game where gameplay is centered on a story where a player makes a trade with a real person or some defined other to get a good.  In Acquire, people trade stock with a stock market.  In Monopoly, players trade property with each other as part of the theme on making real estate deals.  Settlers of Catan, players exchange goods with each other to represent trade between different colonists on an island.

A trade mechanic is when players voluntarily exchange with other players.  When I voluntarily exchange wood for stone with another player we are utilizing a trade mechanic in Settlers of Catan.  Not all games with a trade mechanic have a trade theme.  Compounded is a game centered on making compounds in a chemistry lab.  Players can exchange elements with each other to help them construct their compounds.  The game is not marketed as a trading game.  The story does not centered on who makes the best exchanges.  But players can utilize a trade mechanic to help them win.     

Acquire is a trade themed game without a trade mechanic.  Players are not making trades with each other.  Stock buying in Acquired is just the theme for making strategic bets.  The bank does not benefit when players buy stocks.  It merely converts money from one value to the next based on a formula that calculates a number based on laying of tiles on the game board.

Paying rent on property in Monopoly is not a trade mechanic either.  Players are forced to pay rent by the rules of the game.  Players do not negotiate with different property owners over which property to rent and enter into a voluntary agreement.  They are told by dice rolls that you must rent this property and pay this fixed rent.  Otherwise, you are not playing the game.

In short, to prevent confusion over whether a game has a game mechanic or not you can always rely on answering a simple question.  Do players voluntarily exchange with each other?   For the game to contain a trade mechanic then players must engage in exchange voluntarily.