Friday, January 16, 2015

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.


  1. Despite the variable availability of resources in Settlers of Catan, another factor that suppresses trade near the end of the game is the "zero sum" nature of winning vs losing. If you have nine points, no trade that benefits me outweighs the possibility that you will build the thing you need to get your tenth point and win the game. (I feel as though you wrote about the fact that trade depends on a "non-zero-sum" economy in an earlier post, but I'm not strongly motivated enough to go look it up.)

    Like the Monopoly end-game, the Settlers end-game gets uninteresting when it boils down to rolling dice to see who randomly benefits enough to win the game after no one is motivated to trade.

    1. You are absolutely correct, both on the problem and the fact I previously wrote on it in my Market Mechanic Lecture: Trade post.

      (For those of you who have not read it you can find the post at the following link

      If you were a student in one of my economic classes Paul, you would be earning major brownie/participation points for making that connection.

      What I hope is I am building on that earlier insight by showing a trade game can be broken by achieving an equilibrium long before it hits the zero-sum constraint that halts all trades that also breaks down a trade mechanic based game.

    2. I must add that at the zero-sum part of a game, you are also achieving an equilibrium. Paul correctly points out that your preference to win the game overrides any other incentive to trade and that if you are in that situation you need to either end the game, or change the situation where both parties might benefit from trade.

      For example, using Settlers of Catan, if I have 9 VP, Paul would not trade with me unless something could happen to reduce me to 8 VP. That said, I think Paul creates an interesting challenge...what modification could we make to Settlers of Catan that would get rid of the dice chucking at the end of the game?

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