I may have a route out.

Arbitrage isn’t really possibly without differentiation between the stock market value and par (or some equivalent). As I’ve no equivalent to par value (or companies in general), this doesn’t look to be possible unless I can do something which will cause a controlled market price rise sometime during a given stock round. With that players would be able to increase a price and then exploit it for arbitrage mid-SR. (More on that score later) Leverage is possible but harder. it really requires a debt structure, or at least a lien structure within the game. That’s not actually that difficult to add though it will be interesting trying to keep it from being an actually interesting decision versus and automatic decision that should be optimised out.

None of which really has to do with the route out. The route out is simpler.

In the conversation and design process to date I’ve been concerned with creating and then manipulating a relatively mature market. Perhaps that’s the wrong goal. Mature markets don’t spring out of the ether whole cloth, they have to be grown. They rely on investment patterns and intentional structures that while they don’t explicitly require history (the ripe situations could be manufactured and simply handed to the players), only really work well after the players have internalised the relationships through the process of experiencing and intentionally growing the history. Which when I thought about it seemed like a deistic clue: Markets are the grown products of history. Well, why not make the game about the growth and formation of the market, not the manipulation of the mature market? As such the game would focus on the creation of the mature market and would effectively end as soon as a viable market was in fact created.

I’m not sure what the measure of a mature market is. I’m sure the economists have some that I should look at. In the meantime perhaps I’ll steal another page from the 18XX and simply time the game via the bank. When the bank breaks the game is over. Figuring out how big the bank should be will be interesting (and will likely have to vary based on player count), but that is a smaller and simpler problem.

Perhaps it is time to retreat to first principles. The core assumption in the game is that it will effectively simulate a market, and that the competitively profitable manipulation and control of that market efficiently describes the player’s activities and interests in the game.

So, what is a market?

Markets have value gradients. Usually only positive value gradients are interesting. A value gradient is defined as any situation in which X is worth more in state X` than the cost to move it to state X’. negative value gradients are usually only interesting when their negative sum effects on other players are larger than the negative sum effects on the current player.

Aside: ‘Systems with value gradients whose state transforms include various time durations are more interesting (X->Xover time T1 for profit P1 vs Y->Y over time T2 for profit P2)Systems which contain multiple competing and interacting value gradients are even more interesting. Especially interesting are less time-profitable transforms which are actually more net valuable due to knock on effects on the dependency graphs. This breeds tactical versus strategic interest in decisions as well as the beginnings of arc for the market. (see: “Special roles and powers: what are they good for?” ) “Roles” and “special actions” are commonly used as shorthand nouns for market state transforms. Common examples enclude the actions in Age of Steam, roles in Puerto Rico, actions KaiVai? etc.’

Interesting markets support arbitrage (almost by definition) and leverage. From Dict.org:

From The Collaborative International Dictionary of English v.0.48 gcide:

Arbitrage \Ar”bi*trage\, n. [F., fr. arbiter to give judgment, L. arbitrari.] … 3. (Finance) the simultaneous or near simultaneous purchase and sale of the same or closely linked securities or commodities in different markets to make a profit on the (often small) differences in price. [PJC]

From WordNet? (r) 2.0 (August 2003) [wn]:

arbitrage n : a kind of hedged investment meant to capture slight differences in price; when there is a difference in the price of something on two different markets the arbitrageur simultaneously buys at the lower price and sells at the higher price v : practice arbitrage, as in the stock market

From WordNet? (r) 2.0 (August 2003) [wn]:

leverage n … 3: investing with borrowed money as a way to amplify potential gains (at the risk of greater losses) [syn: {leveraging}] v 1: supplement with leverage; “leverage the money that is already available” 2: provide with leverage; “We need to leverage this company”

Summary:

0. investment appreciation
1. dividends/profits/income
2. value gradients nee profit opportunities
3. dependency graphs across value gradients
4. time-relative transforms and gradients
5. arbitrage
6. leverage

The current game system fails this definition set, most especially for investment and time-relative transforms. I’ll need to rectify that.

A dry run last night revealed that there is insufficient incentive for players to retain stock. The profits from instant sale are too large to ignore and the marginal gains from appreciation too small. I could steepen the appreciation chart, but that will also glut the mid and late game with money.

Toy idea:

– Award $5 to the plurality holder for each colour at the end of each stock round. $3 to second place, $1 to third, sum and divide for ties.

– Possibly ramp these set plurality awards as the game progresses.

The 18XX manage the below problem through the minimum investment needed to float companies. The first stock round of the game is entirely concerned with establishing the early companies. By the second or third round the cash strapped are still tied to the efficiency wheel of getting their companies deployed correctly (which usually sucks up every dollar). However those with a little free cash, even just one share’s worth, will go on a stock rampage, cycling across all other player’s companies buying what they can and then dumping it. This pattern isn’t a so much of a problem because companies pay dividends and the stock will ultimately appreciate (and is why the stock chart is wedge-shaped). In some games this pattern is even helpful as the pool shares then pay dividends into the company.

In contrast to this game there is no guaranteed long term appreciation. There’s no safety net that simply continuing to run the company and pay dividends will result in market appreciation. The primary dividends are the free money off ships with your pilot at your wharf, and those are tactical and not tied to future prospects.

Gahh. Methinks a core assumption will be rethought.

The next problem is that the incentive for cube trashing is too high in the early game (possibly in the whole game). There’s too little cost or risk to the trasher, especially in a sell-buy-sell game. I could drop to a sell-buy/buy-sell but that merely puts the phasing off by one without removing the problem. Ditto for sell-or-buy. The optimal path remains to simply buy in one’s own goods, sell them, and then rotate through the goods in the bank pool trashing them until you can’t any more. While there are risks to doing this if other players are still active in the Stock Round, it is easy enough to wait until only one player is still in and then go on a rampage. The last two held goods will still provide between $10 and $5 in bonus income, same as before. What’s lost is the appreciation and investment value. The resulting end-pattern of goods values is a direct implication of initial configuration of goods on ships versus turn order, and it isn’t even hard to calculate what the end-state will be at the start of the first stock round.

Possible address: Make purchases cost $market+1. This slows open market purchases.

Hurm. The game is losing coherency. Time to clean up and simplify. Bring out the Holy Reducing Crucible!

There’s not enough money in the game to viably support regularly dropping money out of the economy in auction payments so I’m going to lose the auction cards and auction typing. In replacement (and it really isn’t replacement) will be the semi-standard rule that the first to pass in the previous round is the first player in the current round. As the early passers (generally) have laess to do and are therefore somewhat resource starved, this would seem to make some sense and help partially balance out the first mover advantage of wharf buyers.

One of the interesting things about 18XX shares is that they have two values and thus two sources of profit: dividends and market value. I’ve attempted to remove the dividend consideration by making goods on ships at your wharf a free money fountain (modulo pilots?) but I’m not yet convinced it in fact works in terms of investment balance, leverage and creating arbitrage situations.

The market is too simple. The choices are binary too often and that removes both the tension and the interest.. They need to be at least trinary and preferably well salted with quadratic or better.

Possible addresses:

– Train rush in the wharves. Implement the wharves as an ordered card deck. Only the top wharf may be bought. Some are upgrades/extensions to the current wharf, some are replacements. Periodically the purchase of a bigger wharf will result in knock on effects:

a) More goods enter the supply.

b) More goods are added to all approaching ships.

c) Sufficiently small wharves either rust instantly (are discarded from play) or last only to the end of the current stock round. (I like rusting better but it may provide too much of a run-away leader)

d) If a wharf rusts while it contains a ship with goods, the goods are discarded to the bank (or supply?) and the market price moved down as if they were sold(?)

– Ship capacity now affects the wharves they may dock at. If a ship’s contents are too large for the wharf a player brings it to, then ship must discard trade goods until it fits (this can be explained in terms of draught). Such discarded goods are dumped in the bank (or back in supply?) and the market prices are reduced as if they were sold(?)

– Players start with a pilot marker. During stock rounds they place the pilot marker on any ship which will arrive in the next operating round, or may move it among approaching ships (once). In this way players may place a partial claim on approaching ships.

– Some larger wharves come with additional pilot markers. Some are constrained to the next turn, two turns out etc.

– Players may bring ships with other’s pilots to their wharves.

– When a player buys a good from a ship with another player’s pilot or moves from their warf to their warehouse, half the value of the good must be paid to the owner of the pilot.

– When a ship empties during a stock round any pilot marker on it is returned to the owning player, who may then place it on an approaching ship instead of buying goods/wharves/warehouses etc.

I’ve a wee wish to have goods which are entirely stored in warehouses (none in supply or on ships) have their price move up on the market, but also to have an additional one or two goods of that type added to the supply, thus diluting the monopoly. There are obvious problems with this, primary is perhaps that it limits vertical growth to a maximum of five steps per game in a 4 player game. 4 player games would have 16 turns with one step up on turns 3, 6, 9, 12, and 15 in the optimal case. Of course the odds against hitting that pessimal case are large. One to two steps per game would be more typical.

Hurm. Maybe that’s enough if I also have vertical rises on no goods of a given type being transacted on the turn. Yeesh. If I do that that’s going to make the probability math for the goods type distribution rather interesting if the trading game isn’t to be degenerate.

Gahh. I would like to reward monopolies. They should be difficult anyway.

Other problems:

–The race condition between warehouses and wharves. Warehouses offer same measure of market control by putting latency into transactions but also disproportionately rewards those early in the turn order after the next auction (they’ll get the modulo ships). Wharves offer supply chain control through volum. plus the income from cross player purchases.. I like that it isn’t quite clear without defining the current stock price context and holdings which should be bought first. Nice screwage opportunities around the turn order too.

– I’m a little worried that the screwage opportunities may be too large, making investing more than trivially in a colour another player holds too risky. The only address I see for that is to make the gains from continued holding via increasingly large steps in market value large enough to offset the slam opportunity. Touchy that. Too large and the game is a fast rich-get-richer. To low and each player will self-selct themselves into a primary colour and thus isolate.

– I suspect that I’ll have to grow the size of the supply with each wharf bought. Otherwise the early turn probabilities will be too low in setting up the 4th row of ships to be interesting. Players should be making decisions as to what goods to dump early in order to affect the goods distribution likely for turn 4 after the bank cubes are moved into the supply and the turn 4 ships put out and stocked. The growth can’t be linear or the nice asymmetric distribution will tend to skew badly (the numbers should be small). Gahh!

– I wonder if I can just increase the number of colours as wharves are bought, thus helping to preserve the initial asymmetry and offering a tempting monopoly target.

Figure an asymmetric collection of trade goods; some fairly linear set of distributions, not a lot of variance but enough to be significant. A few more of some than others. The total number of goods cubes would approximate ((2N)+M) where M isn’t large and N is the number of players.

Trade goods are cubes. Simpler that way.

A grid of cards 2N+1 wide and 3 deep is laid out. Two cubes are placed on each card. A card represents a ship arriving in the harbour. Each row of cards represents a full turn of the game. The remaining goods form the supply from which future row/sets will be drawn.

First turn turn order is determined randomly?

Each player has an identical set of cards, each card identifies an auction type (Vickrey, Dutch, English etc). each player also has one warf card.

The first player from the last turn selects an auction type and discards their card for that auction type. if the first player has no more auction cards then they select an auction type from the first player in turn order who has an auction card left. An auction is held in accordance with the card to determine turn order. (Dollar auction bad) In turn order each player moves one of the bottom row of ship cards to an empty wharf card in front of them (possibly to another player’s wharf?). This continues in rotation until each player has one ship per wharf. This represents a ship docked at that player’s wharf. The ship which wasn’t selected is emptied into the bank and the prices for those goods moved down as if they were sold.

In rotation each player:

a) optionally sells one or more cubes from their warehouse to the bank and instantly moves the market value down one row per cube sold

b) buys a cube from a ship in front of another player for the current market cost of the cube (cash paid to other player)

OR

simply moves a cube from the ship at their warf into their warehouse for free (if there’s room)

OR

buys a cube from the bank for market price and moves it into their warehouse (if there’s room, cash paid to bank)

OR

buys a warehouse (stores additional cubes)

OR

buys an additional wharf (limit on total number of warfs per player, possibly with a limited upgrade path, possibly with a rusting mechanism)

c) optionally sells one or more cubes from their warehouse and instantly moves the market value down one row per cube sold

The player may not buy a cube of a colour they have sold in that (larger) turn. They may sell cubes from their warehouse. This repeats until all players pass. Once a player passes they may not perform further actions. Any cubes on a player’s wharf when they pass are dumped to the bank for no money, but the market value is reduced as if they were sold. Market prices are then adjusted according to the market activity and any cubes in the bank are returned to the supply. A new row of cards/ships (number of warfs in play plus 1) is then laid above the other two rows and filled with two cubes each per card, thus setting the ships for 3 turns hence.

Repeat for N times the number of players turns.