Bilateral anarchy with uneven strength

• There are two players: a giant \(J\) and a dwarf \(D\). \(J\) is much stronger than \(D\).
• If \(J\) attacks, \(D\) has no defense against it and cannot respond. The payoffs are \([x-c, 0]\) if \(J\) attacks, where c is the cost of using violence and \([0, x]\) if he does not.

The cursing game

• Assume now \(D\) has the ability to curse in response to an attack
• If \(J\) does not attack, the payoff remains the same as before. If \(J\) attacks and \(D\) does not curse, the payoff is \([x-c, 0]\). If \(J\) does attack and \(D\) does curse back, the payoffs are \([x-c-p(z), 0]\), where \(p(z)\in[0, 1]\) is the probability assigned by \(J\) to the possibility the the curse is effective.