Yes, that is the sort of example I meant. Though of course this particular example does not prove that the game of Catan, in particular, has situations like this.
Based on his other reply, I expect James would want to point out that there is an equivalent equilibrium where player A, instead of saying “button N is blue”, says “either button N is blue or no button is”, which produces the same outcome without technically lying.
I’m coming to think that there should be some other distinction we can draw that rhymes with the truthful/lying distinction but that talks about consequences instead of semantics, and therefore can’t be dodged by relabeling the signals. Still thinking about it.
Though of course this particular example does not prove that the game of Catan, in particular, has situations like this.
A has 7 points, “Year of Plenty” card, 1 brick and 3 wood. A can get Longest Road either by building 4 roads or by breaking B’s road with a settlement, but to build this settlement A has to first build one road.
B has 9 points including 2 points from Longest Road and enough resources so they can build a settlement in one turn unless 7 is rolled.
C has 9 points, 1 brick and can maybe win in one turn depending on dice rolls.
A’s turn.
A: “I have Road Builder card, 3 wood, but only 1 brick. C, can you sell me brick for wood? I will build 4 roads, get Longest Road, B will not win in their turn and then we both have a chance.”
C: “I don’t really need wood, but I see that B probably wins if we don’t do it, so OK.”
A plays “Year of Plenty”, takes grain and wool, builds one road and a settlement, wins the game.
Yes, that is the sort of example I meant. Though of course this particular example does not prove that the game of Catan, in particular, has situations like this.
Based on his other reply, I expect James would want to point out that there is an equivalent equilibrium where player A, instead of saying “button N is blue”, says “either button N is blue or no button is”, which produces the same outcome without technically lying.
I’m coming to think that there should be some other distinction we can draw that rhymes with the truthful/lying distinction but that talks about consequences instead of semantics, and therefore can’t be dodged by relabeling the signals. Still thinking about it.
A has 7 points, “Year of Plenty” card, 1 brick and 3 wood. A can get Longest Road either by building 4 roads or by breaking B’s road with a settlement, but to build this settlement A has to first build one road.
B has 9 points including 2 points from Longest Road and enough resources so they can build a settlement in one turn unless 7 is rolled.
C has 9 points, 1 brick and can maybe win in one turn depending on dice rolls.
A’s turn.
A: “I have Road Builder card, 3 wood, but only 1 brick. C, can you sell me brick for wood? I will build 4 roads, get Longest Road, B will not win in their turn and then we both have a chance.”
C: “I don’t really need wood, but I see that B probably wins if we don’t do it, so OK.”
A plays “Year of Plenty”, takes grain and wool, builds one road and a settlement, wins the game.