Answer whether each of the following statements is true or false. You DON’T need to explain the reason. a) If a game has finite number of players and strategies, there always exists at[r]

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(b) Consider the two-period repeated game in which this stage game is played twice. Suppose the repeated game payo¤**s** are simply the sum of the payo¤**s** in each of the two periods. Then, is there a subgame perfect Nash equilibrium of this repeated game in which (A,X) is played in the …rst period? If so, fully describe the equi- librium. If not, explain why.

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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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A tree starts with the initial node and ends at.. 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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elimination of strictly dominated strategies can never be selected (with positive probability) in a mixed-strategy Nash equilibrium.[r]

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Both the Bertrand and Cournot models are particular cases of a more general model of oligopoly competition where firms choose prices and quantities (or capacities.). Ber[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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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!!

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

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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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