Colloquium on Games of Strategy: Chapter 10

Click here to directly download the MP3

Click here to watch the unedited version on Youtube

Welcome to the Colloquium on Games of Strategy.  Games of Strategy is a textbook on game theory written by Dixit (not the game), Skeath, and Reiley that we are reading to help improve our analysis of board games and board game design.  Paul Owen (owns 3rd edition) and I (own the 2nd and 1st editions) record a discussion about a chapter or two from the book every few weeks.

In the tenth episode we talk about how strategic action - in essence the art of creditable threats or promises to deter or compel other players to alter their actions within a board game. Highlights include a discussion on how to apply these tactics to Setters of Catan and the question whether or not people what to play games with players who are good at using these tactics.

You can find our previous discussion on Games of Strategy here.

Colloquium on Games of Strategy: Chapter 9

Click here to directly download the MP3

Click here to watch the unedited version on Youtube

Welcome to the Colloquium on Games of Strategy.  Games of Strategy is a textbook on game theory written by Dixit (not the game), Skeath, and Reiley that we are reading to help improve our analysis of board games and board game design.  Paul Owen (owns 3rd edition) and I (own the 2nd and 1st editions) record a discussion about a chapter or two from the book every few weeks.

In the ninth episode we talk about how players respond to uncertainty and information within games.  Highlights include a discussion on the benefits of holding asymmetric information and tactics to counter your opponent's information edge.  Can players provide a creditable signal in your game or is everything just cheap talk.

You can find our previous discussion on Games of Strategy here.

Colloquium on Games of Strategy: Chapter 4

Click here to directly download the MP3

Click here to watch the unedited version on Youtube

Welcome to the Colloquium on Games of Strategy.  Games of Strategy is a textbook on game theory written by Dixit (not the game), Skeath, and Reiley that we are reading to help improve our analysis of board games and board game design.  Paul Owen (owns 3rd edition) and I (own the 2nd and 1st editions) record a discussion about a chapter or two from the book every two weeks.  

In the forth episode we talk about continuous simultaneous move games and criticism of Nash Equilibrium in Chapter 5 (there are some differences between editions).  Highlights include a discussion on how certain sequential Euro games are really slow moving simultaneous games and game theory's solution for strategic discussions when there is no Nash Equilibrium.

You can find our previous discussion on Games of Strategy here.

You can find our next discussion on Games of Strategy here.

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.

A Dr. Wictz List: 10 Ways to Procrastinate within a Board Game

After having a hard time getting this weeks post down on paper I decided in a moment of panic to think of all the different ways I could procrastinate writing this post within a board game.

1. Engage in no trades in the game of Monopoly.


2. Only conquer one territory a turn in Risk.


3. After castling in Chess only move your king back and forth for rest of the game.


4. Hoard resources in Settlers of Catan by never turning in any cards to get anything.


5. Never move your back line in checkers.


6. Order all units to support in Diplomacy.


7. Every move of Clue goes between the Kitchen and the Study.


8. Shoot no one in Bang!


9. Do not complete any objectives in Firefly.


10. Play Twilight Imperium.

Market Mechanic Lecture: Prices

On the onset prices appear to be a simple thing.  A price is what one has to pay to get something.  But what that misses is what prices can achieve as a mechanic and a tool.  A price mechanic is a way to communicate information between players.

Fixed Prices (price theme) vs. Negotiated Prices (price mechanic)

To distinguish a price mechanic from a price theme I am going to distinguish the difference between fixed prices and negotiated prices.  A fixed price is a price theme.  Fixed prices are created by an outside source, most likely by the rule book in the board game.  A fixed price states in no uncertain term something is worth X.  The price in this instance is being used to communicate the tradeoff of game actions by the game designer to the players by using a set of fixed ratios of one action versus another during game play.

Take The Game of Life, the price to change your degree is fixed on the board.  If you want to take a chance and stop being an accountant then you have to pay a fixed X amount of money to change jobs. The player has to decide if they want to use their money to change jobs or do they want to save it to pay for 2 future doctor visits.  The fixed price enables money to serve as a simplification of the tradeoff between one action versus another within the board game.  

A negotiated price, a price mechanic, is when two or more players have to agree on a value to make an exchange.  In Michael Keller’s Captains of Industry players require resources to build and operate factories.  They get these resources by negotiating prices with the other players who happen to have these resources.  

Negotiated Prices Communicate Information

When prices are negotiated, prices in the game communicate the value of the goods or actions amongst the players.  You do not need to know why a player wants a good or action to know that they desire it.  All you need to know is how high of a price a player is willing to pay to buy it or sell it to gauge their desire.

The economy uses communication from prices to coordinate production and supply.  Economist Leonard E. Read shows in his story I, Pencil that pencil makers can communicate to wood producers their desire for an increase in the wood supply to make pencils by offering to buy wood at a higher price.  Wood suppliers see the higher price and are willing to pay more money to entice people to be lumberjacks and to work longer hours to produce more wood.

The person who supplies the wood does not directly see that pencil makers need more wood.  For all the lumber supplier may know, paper makers and furniture makers might desire more wood.  The magic of a price mechanic and negotiated prices is that wood suppliers never have to spend time guessing if specific industries or the world needs more wood.  The price for wood communicates to the lumber suppliers people’s desire for wood and they respond by working to increase their output.  

If players need wood to expand their farm or stone quarry in Captain of Industry they communicate their desire for wood by the willingness to pay a high price for it.  Players producing wood may not know why other plays want wood so badly, but they will see from the price there is high demand by other players for it and will invest to expand their output of wood in response.

Relation of Price Mechanic, Price Theme, and Money Mechanic

A price themed only game does not have negotiated prices between players.  A price themed game may still have a money mechanic.  Speculation has fixed prices for stock decided by events on the game board, making the game a price theme.  Players exchange money with the bank to take risks in Speculation to possibly earn more money later in the game, meaning the game has a Money Mechanic.

Money mechanic games can also be a price mechanic game.  Michael Keller’s Captains of Industry players negotiate with each other to exchange goods for money.  The prices settled upon communicate what goods players desire, and hint at what moves players will make next since each good can only be used to complete so many actions.

But what about games based on batter, like Settler’s of Catan.  Can Settler’s of Catan’s barter economy be a price mechanic or price themed game even though there is no money Mechanic?

The answer is yes.  Because barter involves setting prices in terms of one good versus another.  My offer to trade 2 wood for 1 brick means that the price of 1 brick is 2 wood.  Some prices in Settler’s of Catan are price themed.  I can exchange for a fixed price four of any one good to acquire a different good.  This is a fixed price that is not an exchange of information between players.   

On the other hand, other prices in Settlers of Catan are a price mechanic.  Players can select to trade with each other.  When a player offers to trade with another player they are negotiating and in the process communicating information about the importance particular goods are to them to their opponents.

Why Differentiate Price Mechanic and Price Theme?

I differentiate between price mechanics and price themes because they create different experiences for players.  Price mechanics create a new dimension for board players to compete with each other.  Price mechanics are driven by supply, demand, and information.  It rewards players who can best track information to decipher current prices and anticipate future prices.

Take my horse racing game Post Position.  Players actively engage in a market where they trade bets on horses throughout a horse race.  The final value of a bet on a horse is settled by the order the horses cross the finish line.  Each player has inside information not held by others on how the horses are going to move in the race.

When players make bets, they are agreeing on a price for the bet.  That price communicates information to all the other players on who thinks a horse is going to move up and who thinks a horse is going to move down in the race.  The winner is the player who best uses their inside information and best reads other players trades to figure out the horses that are going to do well and the horses that are going to do poorly before everyone else.

Fixed prices are constraints imposed by the game designer.  Without a complementary price mechanic, fixed prices represent a set of actions a player needs to compete to acquire an action, resource, or victory point.  They are merely a tool used by the game designer to communicate the rules of the game to the player.

Market Mechanic Lecture: Money

Games that use money: The Game of Life, Monopoly, Daytona 500, City Hall...the list goes on and on and on.  But for something that is so prevalent in board games, money as a mechanic is an understudied topic.  Why use money?  What is the purpose of a money mechanic?  And for the more philosophical folks out there, why do we even use money in real life?

Why do People Use Money?

To understand why people use money we need to understand what the world looks like without money. Without money how do people get stuff from other people?  Without money some folks may get stuff as gifts or get stuff by stealing it.  Most of us are going to get stuff from other people by trading one thing for another.    

I want a slice of apple pie, you want a back rub, so I trade you a back rub for a slice of apple pie.  I did not rub your back because I thought you were a nice person nor did you give me a slice of pie because I looked gorgeous in my fedora.  I rub your back because in exchange I received a piece of pie and you gave me a piece of pie because I rubbed your back.  Both of us benefited from the trade. (You can read more about trade mechanics here)

 Economist have a formal name for this, they call it a barter economy.  Conceptually barter economies are easy to grasp.  I have something you want, you have something I want, we trade and we are both better off.  The downside is that barter economies easily become incredibly complicated.

Imagine that instead of wanting a back rub for a slice of pie, you wanted a horse shoe for your horse instead.  Well, I need to go find a blacksmith who will trade me a horseshoe for a back rub that I can take to you to trade for a slice of pie.  If I cannot find a blacksmith who wants a back rub in exchange for a horseshoe, I have to find someone else who has something the blacksmith wants for a horseshoe.  

Searching for the people I need to trade with to get an item the blacksmith is willing to exchange for the horseshoe I need to trade for a slice of pie takes a lot of time.  The time I spent searching is time I no longer have to relax or give other people back rubs in exchange for other things.

Money reduces the amount of time I spend searching to make trades by being a medium of exchange all buyers and sellers will accept.  If everything is priced in pounds of wheat then I no longer have to find the person supplying the exact good you want to trade for a piece of pie.  I only need to find enough people willing to pay me wheat for giving them back rubs to get a piece of pie.  You are willing to accept wheat in exchange for pie because the blacksmith is willing to accept wheat in exchange for a horse shoe.  

A medium exchange can be a commodity, like wheat, or pieces of paper/coin we call money.  Money has the extra benefit (in real life) of being much easier to carry around then pounds of wheat.  Money can also be backed by a commodity or by nothing at all.  No matter the case, money is a tool to make it easier for people to trade with each other.  

Use of Money as a Tool in Board Games

Money works best in board games when it simplifies trades.  Take The Game of Life.  All actions in the game can be reduced to whether or not you can exchange a single item to get a good or service.  Imagine playing Life where the Accountant gets paid by the Singer with a ticket for a rock concert.  How then does the Accountant pay the Doctor later in the game when their child gets sick.  

One way the game could have accomplished this is to include a set of tables that informs players how much of each service can be exchange for another.  For example, it might say that 3 rock concert tickets are worth 1 doctor visit.  A table large enough to account for all the possibilities of exchanges in The Game of life would be fitting for an Avalon Hill game.  Instead the game simplifies game play and reduces components by translating the ratio of goods exchanged into equivalent ratios of money exchanged.  If it takes 3 rock concert tickets to pay for a doctors visit then in a world of money rock concert tickets earn 1 dollar a show and a doctor visit costs 3 dollars.

Money takes all actions in The Game of Life and turns them into a single unit that can easily be observed and exchanged for any other actions in the game.  No need for any complex formula or table of exchanges that eats up time and takes away from gameplay.

Just because money makes trading easier, that does not mean making trading easier is desirable in a game.  

Settlers of Catan thrives on people navigating a barter economy.  Players have to navigate the process of trading wood for stone so they can trade stone for brick with another player.  They have to plan their cities and roads to acquire the commodities they need, both for trade and gameplay.

Imagine Settlers of Catan where settlements earn cash instead of a resource and construction was purely a matter of price.  Players would just focus on only placing the cities in locations that maximize earnings.  Decisions available to players would be reduced.  Players would no longer be interacting with each other over trading this for that.  In essence the game just became a new form of solitaire where you roll dice. Money reduces too much of the games complexity.

Money Theme vs. Money Mechanic

Money is only a theme if there is no exchange ever made with it.  Imagine a game where the person with the most money wins the game.  In this hypothetical game, you earn money by completing a task.  Once the money is earned you just hold onto it as a victory point for the end of the game.  The money is not used in any exchange.  Money, in this case is a theme for the victory points in the game.

Contrast this with the HoopCat’s game Fill the Barn.  In Fill the Barn the player with the most money wins the game.  However, players also need money to plant, fertilize, and harvest crops.  These are all actions within the game that might result in earning even more money.  So money is not just a victory point condition, money is also a way to exchange victory points you have now to take risks that might reward you with more victory points in the future. In this case money is being used as a tool to simplify exchange, making it a mechanic.

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.