Ijime , which is the Japanese term closest in meaning to the word **bullying**, has been a pressing social issue in Japan for the last 30 years. 29 Although **bullying** is generally characterized by direct
forms of aggression which often occurs in the playground (Craig et al. 2000), a major type of ijime is “characterized by more indirect forms of aggressions, often conducted by a group of pupils who were a victim’**s** classmates or even “friends” to the victim, mainly in the classroom” (Kanetsuna et al. 2006). Verbal forms (e.g., teasing, verbal threats) are more frequent than physical forms such as hitting and kicking (Morita et al. 1999). Hence, a major type of ijime causes mental rather than physical suffering to victims. Taki (2001) argues that personal factors (i.e., rearing conditions) do not meaningfully characterize bullies and victims in Japan. Thus ijime “can happen at any time, at any school and among any children” (p.2). His empirical data also suggests that from 1997 to 2000, over 30 percent of primary and junior high school students had bullied others and also experienced being bullied.

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

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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!!

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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]

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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]

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(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

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

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

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

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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).

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

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(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.)

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

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payoff) while M gives 1 irrespective of player 1’**s** strategy.
Therefore, M is eliminated by mixing L and R .
After eliminating M , we can further eliminate D (step 2) and L
(step 3), eventually picks up ( U , R ) as a unique outcome.

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

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

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

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

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

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

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