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7.5. Welfare Effects of Picking Orders and Targets. The flexible deferred accep- tance algorithm follows a certain picking order of hospitals in each region when there are some doctors remaining to be tentatively matched after hospitals have kept doctors up to their target capacities. One issue is how to decide the picking order. One natural conjec- ture may be that choosing earlier (that is, having an earlier order in the flexible deferred acceptance algorithm) benefits a hospital. As we have mentioned earlier, this would be a problematic property: If choosing earlier benefits a hospital, then how to order hospitals will be a sensitive policy issue to cope with because each hospital would have incentives to be granted an early picking order. Fortunately, the conjecture is not true, as shown in the following example. The example also shows that the different choices of orders result in different stable matchings, thus the choice of an order does matter for the algorithm’s outcome.

Prisoners’ Dilemma: Analysis (3)
  (Silent, Silent) looks mutually beneficial outcomes, though    Playing Confess is optimal regardless of other player’s choice!   Acting optimally ( Confess , Confess ) rends up realizing!!

Prisoners’ Dilemma: Analysis
   ( Silent , Silent ) looks mutually beneficial outcomes, though    Playing Confess is optimal regardless of other player’s choice!    Acting optimally ( Confess , Confess ) rends up realizing!!

3(a - e)/4, is greater than aggregate quantity in the Nash equilib- rium of the Cournot game, 2(a - e)/3, so the market-clearing price is lower in the Stackelberg game.. Thus, i[r]

   If the stage game has a unique NE, then for any T , the finitely repeated game has a unique SPNE: the NE of the stage game is played in every stage irrespective of the histor[r]

(a) If an agent is risk averse, her risk premium is ALWAYS positive. (b) When every player has a (strictly) dominant strategy, the strategy profile that consists of each player’s dominant strategy MUST be a Nash equilibrium. (c) If there are two Nash equilibria in pure-strategy, they can ALWAYS be Pareto

(c) Solve for the total saving S by all types who save and the total borrowing B.. by all types who borrow.[r]

    5. Bayesian Nash Equilibrium (12 points)  There are three different bills, $5, $10, and $20. Two individuals randomly receive one  bill each. The (ex ante) probability of an individual receiving each bill is therefore 1/3.  Each  individual  knows  only  her  own  bill,  and  is  simultaneously  given  the  option  of  exchanging her bill for the other individual’s bill. The bills will be exchanged if and only  if  both  individuals  wish  to  do  so;  otherwise  no  exchange  occurs.  That  is,  each  individuals can choose either exchange (E) or not (N), and exchange occurs only when  both  choose  E.  We  assume  that  individuals’  objective  is  to  maximize  their  expected  monetary payoff ($). 

Find (all) pure‐strategy Nash equilibrium if it exists.  iii.[r]

e z . The prices of the three goods are given by (p, q, 1) and the consumer’s wealth is given by ω. (a) Formulate the utility maximization problem of this consumer. (b) Note that this consumer’s preference can be expressed in the form of U (x, y, z) = V (x, y) + z. Derive V (x, y).

elimination of strictly dominated strategies can never be selected (with positive probability) in a mixed-strategy Nash equilibrium.[r]

Prove that if a firm exhibits increasing returns to scale then average cost must strictly decrease with output. 4.[r]

Combination of dominant strategies is Nash equilibrium. There are many games where no dominant strategy exists[r]

(a) The intersection of any pair of open sets is an open set. (b) The union of any (possibly infinite) collection of open sets is open. (c) The intersection of any (possibly infinite) collection of closed sets is closed. (You can use (b) and De Morgan’s Law without proofs.)

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

  A tree starts with the initial node and ends at2. terminal nodes where payoffs are specified..[r]

  A strategy in dynamic games is a complete action plan which prescribes how the player will act in each possible.. contingencies in future..[r]

  4. Incomplete Information (16 points, think carefully)  There are four different bills, $1, $5, $10, and $20. Two individuals randomly receive  one bill each. The (ex ante) probability of an individual receiving each bill is therefore  1/4.  An individual knows only her own bill, and  is  simultaneously given the option of  exchanging her bill for the other individual’s bill. The bills will be exchanged if and only  if  both  individuals  wish  to  do  so;  otherwise  no  exchange  occurs.  That  is,  each  individuals can choose either exchange (E) or not (N), and exchange occurs only when  both  choose  E.  We  assume  that  individuals’  objective  is  to  maximize  their  expected  monetary payoff ($).