# Combinatorium playtest complete

Six players agreed to participate in my playtest of a game using a combinatorial auction mechanic. We completed all but the final round (when the first, second, and third place finishers were all clinched).

### Gameplay History

Here are links to the rules, inventory/contracts, and bids for the complete game.

Game rules

Winning bids in each round are highlighted, with the cost identified next to the player name, in bold. (Many costs are zero.)

Round 1: Contracts Bids
Round 2: Contracts Bids
Round 3: Contracts Bids
Round 4: Contracts Bids
Round 5: Contracts Bids
Round 6: Contracts Bids
Round 7: Contracts Bids
Round 8: Contracts Bids
Round 9: Contracts Bids
Round 10: Contracts

Dual values of relaxed Winner-Determination Problem, i.e., price estimates. (If partial bid fulfillment had been allowed, how much more value would there be from adding one extra VP or good?) As expected, the price of a victory point increases on each round (except for round 8). There was not any difference I could see in price between low-value and high-value goods, though.

### Lessons learned

Nate, the winner, posted some ideas and thoughts about strategy in an earlier post on the game.

I found that having other people play the game (and not just strategies I'd made up) gave me a much stronger sense about what the game is actually about--- it's building coalitions. Your bid is going to win only if it's compatible with high-value bids from other players. Worse, you can't even increase the cost to a winning player unless your bid makes part of a "second-best" coalition. So effective bidding requires not just naming an appropriate price, but also considering what goods are likely to be contended and what other players will bid on. (A known problem with VCG auctions is that the addition of a losing bid can actually *decrease* the prices paid by the winner. There might be a tweak to the mechanism to work around that, by examining all subsets of players.)

Because that's where the real competition is, I have a different picture of the game than when I first started. I was thinking in terms of large pools in a multi-day game, similar to social "building" games or email poker. But with a large pool there are just too many combinations to engage in speculative or exploitive bids. Also there would have to be adjustments as players dropped out (as happened here.) It probably makes more sense to think of an online game on the same timescale as, say, Ticket to Ride, with a smaller number of players and quick turnaround.

Because the game is about coalition-building, a dominant strategy may be to collude with other players and reach an agreement ahead of time. This could be less of an issue in a shorter-term pickup game rather than "league" play. (Ticket To Ride could have the same "spoiler" problem, in theory.) I am not aware of any of my test-players communicating offline to engage in bid-rigging. :) The difficulty of implicit coalition-building meant that players could afford to bid high values with little concern that they would actually have to pay full price.

Only Nate and Tyler tried to adopt a strategy of bidding speculatively for goods they didn't yet need. This is very effective if only one (or maybe two) players do so, otherwise costs should go up quickly. But it paid off well for Nate. The mechanism of getting your new contracts before deciding which ones to cash in (and not requiring mandatory cashes) was meant to encourage this. It might be worthwhile limiting inventory size, or imposing a cost on it--- but it's not clear if this is necessary, or whether the strategy is self-limiting if more players pursue it.

The mechanism for generating contract values produced more variability than seemed "fair". There were a couple good suggestions for this. One was to make contract value increase with every good required; as I implemented it, an additional low-value good would instead decrease value. It might also make sense to ensure everybody gets a 3-good contract on each round or at least to start--- or have a 3-good, 6-good, and random-good contract as the three per round. I also thought about the possibility of generating a "deck" of contracts that was the same for each player but shuffled differently, so that only the order you received contracts would differ.

A way to scale the game to larger player sets (more like my original concept) would be to introduce alternate victory paths, so that the game was more about "building" and less about "bidding".

Thanks again to Nate, Tyler, Bruce, Jerrod, Andrew, and Kevin for their time.
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