Two operations-research games for more than one person at one screen. Pass the device, and find out what the mathematics says about how you actually decide.
Both are hot-seat: one device, passed between players, with a screen between turns so nobody sees anyone else’s private numbers. Bots can fill any seat. Everything runs in your browser and nothing is sent anywhere.
Online rooms are not offered: they need the site’s hosted database, which is not switched on. When it is, the same games will get rooms; until then this page does not pretend.
Each round every bidder is dealt a private value from 0 to 100 and writes down one bid. The highest bid wins. In a first-price auction the winner pays their own bid; in a second-price auction they pay the highest losing bid. The question the game puts to you: how much of your value do you bid, and does it change with the rules?
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Four stages move one product: retailer, wholesaler, distributor, factory. Each week you see only what you were ordered, what you received and what you hold, and you place one order. Customers want 4 a week and, in week 5, 8 a week from then on. That one change is the whole experiment.
This game needs JavaScript.
tools/verify_ormulti.mjs tests the engines against independent calculations. For the auction: a second-price bidder can never gain by deviating from the truth (checked exactly, for every value and every alternative bid), the first-price equilibrium bid is within a unit or two of the best reply, and expected revenue is the same under both formats to within the rounding of whole-number bids. For the Beer Game: a chain ordering 4 a week stays at exactly 12 units everywhere, units are conserved every week, and the order swings of the “chase the stock target” policy grow at each step up the chain while pass-through stays close to the customers’ own.
What the pages print to you at the end is measured from your own play, next to the theory. The theory holds under stated assumptions (private uniform values, risk-neutral bidders, no collusion). Real auctions and real supply chains break them, which is why the field exists.
Mechanism design and auctions in the course Inventory and the bullwhip in the course