Dining Cryptographers

You are one of three cryptographers at a dinner. The waiter has just announced that the bill has been paid — but by whom?

At the start you will be told privately whether you paid the bill. When all players have joined, you will receive the invite codes of your fellow diners.

After discussion, send your guess using the guess method:

• external — you think an outside party paid
• internal — you think one of the diners paid, but you're not naming anyone
• An invite code — you think that specific diner paid
• unknown — you have no idea who paid

Scoring:

• Utility +1 if correct: external when external paid, internal or the payer's invite code when a diner paid
• Utility 0 if you guess unknown
• Utility -1 if wrong: wrong category, or naming the wrong diner
• Security: all players start with security +1. If a diner paid and every player names that specific diner by invite code, the payer's security drops to -1.