トップPDF Game11 最近の更新履歴 yyasuda's website

A game-theory model illustrates how reputation is traded.5 The follow­ ing game-theoretic example is completely abstract-it is not a model of a irm per se-but it clearly demonstrates how reputation is traded. Consider the two­ period repeated game analyzed at the beginning of Chapter 22; the stage game is reproduced in Figure 23.1. Here I add a new twist. Suppose there are three players, called player 1, player 21, and player 22. In the irst period, players 1 and 21 play the stage game (with player 21 playing the role of player 2 in the stage game). Then player 2' retires, so he cannot play the stage game with player 1 again in period 2. However, player 2' holds the right to play in pe­ riod 2, even though he cannot exercise this right himself. Player 2' can sell this right to player 22, in which case players 1 and 22 play the stage game in the second period.

  This  is  an  introductory  course  in  game  theory,  which  will  provide  you  with  mathematical  tools  for  analyzing  strategically  interdependent  situations,  i.e.,  the  situations  in  which  your  optimal  decision  depends  on  what  other  people  will  do.  In  particular,  we  will  study  central  solution  concepts  in  game  theory  such  as  Nash  equilibrium,  subgame  perfect  equilibrium,  and Bayesian equilibrium.  To  illustrate  the  analytical value of these tools, we will cover a variety of applications, e.g., international  relations,  business  competition,  auctions,  marriage  market,  and  so  forth.  There  is  no  prerequisite  for  this  course,  although  some  background  on  microeconomics  and  familiarity of probabilistic thinking would be helpful. 

  Exist exactly one for ANY exchange problem.   Always Pareto efficient and individually rational[r]

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

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]

  Paul Romer (1955-, 内生的成長理論) → 学界から消えた！？   Ben Bernanke (1953-, マクロ、金融) → FRB議長を辞めたのは好材料？   Douglas Diamond (1953-, 銀行取付) → 金融は無い？   清滝信宏 (1955-, マクロ、金融) → まだ早い

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

Consider a consumer problem. Suppose that a choice function x(p; !) satis…es Walras’s law and WA. Then, show that x(p; !) is homogeneous of degree zero. 6. Lagrange’s Method You have two …nal exams upcoming, Mathematics (M) and Japanese (J), and have to decide how to allocate your time to study each subject. After eating, sleeping, exercising, and maintaining some human contact, you will have T hours each day in which to study for your exams. You have …gured out that your grade point average (G) from your two courses takes the form

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

(5) Suppose that this game is played finitely many times, say T (≥ 2) times. De- rive the subgame perfect Nash equilibrium of such a finitely repeated game. Assume that payoff of each player is sum of each period payoff. (6) Now suppose that the game is played infinitely many times: payoff of each player is discounted sum of each period payoff with some discount factor δ ∈ (0, 1). Assume specifically that A = 16, c = 8. Then, derive the condition under which the trigger strategy sustains the joint-profit maximizing prices you derived in (3) (as a subgame perfect Nash equilibrium).

Strategy and Outcome
   Strategy in dynamic game = Complete plan of actions   What each player will do in every possible chance of move.   Even if some actions will not be taken in the actual play, players specify all contingent action plan.

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.

   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]

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

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