Question 1: Two hunters, players 1 and 2, can each choose to hunt a stag, which provides a rather large and tasty meal, or hunt a hare-also tasty, but much less filling. Hunting stags is challenging and requires mutual cooperation. If either hunts a stag alone, then the stag will get away, while hunting the stag together guarantees that the stag will be caught. Hunting hares is an individualistic enterprise that is not done in pairs, and whoever chooses to hunt a hare will catch one. The payoff from hunting a hare is 1, while the payoff to each from hunting a stag together in 3. The payoff from an unsuccessful stag hunt is 0. Represent this game using a game table and find all pure pure-stategy Nash equilibria of this game.
Question 2: An item is up for auction. Player 1 values the item at 3 while player 2 values the item at 5. Each player can bid either 0, 1, 2, or 3. If player i ε {1, 2} bids more than player j ε {1, 2}, j ≠ i, then player i wins the good and pays his bid, while the loser does not pay. If both players bid the same amount, then a fair coin is tossed to determine who the winner is, and the winner gets the good and pays his bid while the loser pays nothing.
a. Write down the game table of this game.
b. Does any player have a strictly or weakly dominated strategy?
c. Is this game dominance solvable using IESDS?
d. Find all pure strategy Nash equilibria of this game?