Trading envelopes (harder) Julie flips a fair coin. If the coin lands head-up, she puts $10 in envelope one and $100 in envelope two. If the coin lands tails-up she puts $100 in envelope one and $1,000 in envelope two. She then mixes up the envelopes and gives them to Alice and Berta. Alice and Berta look in their own envelopes, but not each other's. Simultaneously, they each choose whether to trade (T) or not (NT). The trade only occurs if they both choose trade. 1. What is the type space for Alice? 2. What is the strategy set for Alice? 3. Find all of the pure strategy Bayesian Nash equilibria.

Amir and Beatrice play the following game. Amir offers an amount of money z € [0, 1] to Beatrice. Beatrice can either accept or reject. If Beatrice accepts, then Amir receives 1 - z dollars and Beatrice receives a dollars. If Beatrice rejects, then both receive no money. As in the Ultimatum Game, Amir cares only about maximizing the amount of money he receives. Beatrice, on the other hand, detests Amir, and therefore cares about the amount of money that both receive: if Amir receives y dollars and Beatrice receives a dollars, then Beatrice's payoff is a-ay where a > 0. (a) Find all pure strategy Nash equilibria of the game in which the two players choose simultaneously (thus Beatrice accepts or rejects without seeing Amir's offer). Solution: The NE are the strategy profiles in which Beatrice rejects and Amir's offer a satisfies 2-a(1-x) ≤0, i.e. r ≤a/(1+a). (b) Find all subgame perfect equilibria of the sequential game in which Amir first makes the offer and Beatrice observes the offer…

Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C.   Max prefers A to B to C. Sally prefers B to A to C.   To decide which restaurant to go to, the friends adopt the following procedure:               First, Max eliminates one of three choices.   Then, Sally decides among the two remaining choices.   Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining).   a.Write down the extensive form (game tree) to represent this game.   b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be?   c.What is the subgame-perfect equilibrium of the above game?   d. Does your answer in b. differ from your answer in c.? Explain why or why not.   Only typed Answer

Theo and Addy are deciding what toys to pick out at the toy store.  Depending on what toys they pick, they can play different games together, but they can’t coordinate their choices.  They can’t talk to one another at all until after that make their choice. Below is their payout matrix which shows their utility for each choice.  All the bold figures are for Theo and all the non bold figures are for Addy.       Addy       Strategies Theo Strategies   Toy Gas Pump Jump Rope Toy food                        20 10         10 3   Ball                         7 3           9 4   a) If Theo chooses Toy Food, what would be the possible outcomes for Addy? What would be best for Addy? b) If Addy chose a Toy Gas Pump, what are the possible outcomes for Theo? What would be best for Theo? c) Does Addy have a dominant strategy? If yes, what is her strategy? If not how can you tell?   d) Does Theo have a dominant strategy? If yes, what is her strategy? If not how…