Bribes: Two players discover themselves in the legal battle over the patent. Patent is worth 20 to every player, so winner would receive 20 and loser 0. Given norms of country, it is common to bribe judge hearing the case. Every player can offer the bribe secretly, and one whose bribe is highest will be awarded patent. If both select not to bribe, or if bribes are same amount, then every has the equal chance of being awarded patent. If the player does bribe, then bribe can be valued at either 9 or 20. Any other number is regarded very unlucky, and judge would surely rule against the party who offered the different number.
i) Determine unique pure-strategy Nash equilibrium for the game.
ii) If norm were different, so that the bribe of 15 were also acceptable, is there pure-strategy Nash equilibrium?
iii) Determine symmetric mixed-strategy Nash equilibrium for game with possible bribes of 9, 15, and 20.