Regarding the second problem, there’s a nash equilibrium where two agents bomb box 1 while betting on box 2 and two other agents bomb box 2 while betting on box 1. No agent can unilaterally change its strategy to score more.
They can though? Bomb box 5, incentivise box 1 or 2, bet on box 3 or 4. Since FDT’s strategy puts rewarding cooperative hosts above money or grenades, she picks the box that rewards the defector and thus incentivises all 4 to defect from that equilibrium. (I thought over her strategy for quite a bit and there are probably still problems with it but this isn’t one of them)
Regarding the second problem, there’s a nash equilibrium where two agents bomb box 1 while betting on box 2 and two other agents bomb box 2 while betting on box 1. No agent can unilaterally change its strategy to score more.
They can though? Bomb box 5, incentivise box 1 or 2, bet on box 3 or 4. Since FDT’s strategy puts rewarding cooperative hosts above money or grenades, she picks the box that rewards the defector and thus incentivises all 4 to defect from that equilibrium. (I thought over her strategy for quite a bit and there are probably still problems with it but this isn’t one of them)
Ah sorry, I somehow forgot you could put your money in one box and bet on another box.