Dynamic Game (12 points, moderate) Consider a dynamic game depicted by Figure 1. a) Express this game into normal-form (strategic-form) by drawing the payoff matrix. b) Find all Nash eq[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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Two neighboring homeowners, 1 and 2, simultaneously choose how many hours to spend maintaining a beautiful lawn (denoted by l 1 and l 2 ). Since the appearance of one’**s** property depends in part on the beauty of the surrounding neighborhood, homeowner’**s** benefit is increasing in the hours that neighbor spends on his own lawn. Suppose that 1’**s** payoff is expressed by

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Introduction to Market Design and its Applications to School Choice.. Yosuke YASUDA.[r]

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2 units of the firm 1’**s** good and A − p 2 + p 1
2 units of the firm 2’**s** good. Assume that the firms have identical (and constant) marginal costs c(< A), and the payoff for each firm is equal to the firm’**s** profit, denoted by π 1 and π 2 .

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Q = K 1 =4
L 1 =8 Then, answer the following questions.
(a) In the short run, the …rm is committed to hire a …xed amount of capital K(+1), and can vary its output Q only by employing an appropriate amount of labor L . Derive the …rm’**s** short-run total, average, and marginal cost functions. (b) In the long run, the …rm can vary both capital and labor. Derive the …rm’**s**

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(b) If consumer’**s** choice satis…es the weak axiom of revealed preferences, we can always construct a utility function which is consistent with such choice behav- iour.
(c) If a consumer problem has a solution, then it must be unique whenever the consumer’**s** preference relation is convex.

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安田予想で未受賞**の**候補者たち
Robert Barro (1944-, マクロ、成長理論) → イチオシ！
Elhanan Helpman (1946-, 国際貿易、成長) → 誰ともらう**の**か？
Paul Milgrom (1948-, 組織**の**経済学、オークション) → 今年は厳しい… Ariel Rubinstein (1951-, ゲーム理論) → 今年は厳しそう…

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Exist exactly one for ANY exchange problem. Always Pareto efficient and individually rational[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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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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A tree starts with the initial node and ends at.. terminal nodes where payoffs are specified..[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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Substituting into p+q = 3=4, we achieve q = 1=2. Since the game is symmetric, we can derive exactly the same result for Player 1’**s** mixed action as well. Therefore, we get the mixed-strategy Nash equilibrium: both players choose Rock, Paper and Scissors with probabilities 1=4; 1=2; 1=4 respectively.

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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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