The choice function C does not need to be observable.. 3.[r]

4 さらに読み込む

Consider the case that M ≻ m. By I and C, there must be a single number v(**s**) ∈ [0, **1**] such that
v(**s**) ◦ M ⊕ (**1** − v(**s**)) ◦ m ∼ [**s**]
where [**s**] is a certain lottery with prize **s**, i.e., [**s**] = **1** ◦ **s**. In particular, v(M ) = **1** and v(m) = 0. I implies that

15 さらに読み込む

To understand how to work with the concept of subgame perfection, con sider the game pictured in Figure 15.4. Note irst that this game has one proper subgame, which starts at the node reached when player **1** plays V at the initial node. Thus, there are two subgames to evaluate: the proper sub game as well as the entire game. Because strategy proiles tell us what the players do at every information set, each strategy proile speciies behavior in the proper subgame even if this sub game would not be reached. For example, consider strategy proile (DA, X). If this profile is played, then play never enters the proper sub game. But (DA, X) does include a speciication of what the players would do conditional on reaching the proper subgame; in particular, it prescribes action A for player **1** and action X for player 2.

さらに見せる
6 さらに読み込む

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!!

27 さらに読み込む

Preferences
To construct a model of individual choice, the notion of
preferences plays a central role in economic theory, which specifies the form of consistency or inconsistency in the person’**s** choices. We view preferences as the mental attitude of an individual toward alternatives independent of any actual choice.

16 さらに読み込む

“Soon after Nash ’s work, game-theoretic models began to be used in economic theory and political science,. and psychologists began studying how human subjects behave in experimental [r]

26 さらに読み込む

囚人**の**ジレンマ：注意点
このゲームでは個々**の**プレーヤーが最適戦略を持つ
【最適戦略（支配戦略）】 他**の**プレーヤーたちがどのような行 動を選択しても、自分がある特定**の**行動Aを選ぶことによって 利得が最大化されるとき、行動Aを「支配戦略」と呼ぶ。

22 さらに読み込む

Cournot Game with Unknown Cost | コストが不明**の**クールノーゲーム (2)
Assuming a linear (inverse) demand, p = a − (q **1** + q 2 ), the profit function
becomes
π i (q **1** , q 2 ) = [a − (q **1** + q 2 ) − c i ]q i for i = **1**, 2, i 6= j.

15 さらに読み込む

2. if ω ′ = p ′ x(p, ω), then either x(p ′ , ω ′ ) = x(p, ω) or
(p ′ − p)(x(p ′ , ω ′ ) − x(p, ω)) < 0.
Proof The proof for **1** is left for the assignment. Assume that
x(p ′ , ω ′ ) 6= x(p, ω). By Walras’**s** Law and the assumption that

16 さらに読み込む

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

23 さらに読み込む

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

23 さらに読み込む

Zermelo’**s** Theorem
Thm For any finite perfect information games, there exist at least one backward induction solution in pure strategies.
Furthermore, if payoffs differ between any two different strategy profiles, there is exactly one backward induction solution. It establishes the following claim originated by Zermelo (1913).

13 さらに読み込む

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**

3 さらに読み込む

St Petersburg Paradox (**1**)
The most primitive way to evaluate a lottery is to calculate its
mathematical expectation, i.e., E[p] = P **s**∈S p(**s**)**s**.
Daniel Bernoulli first doubt this approach in the 18th century when he examined the famous St. Pertersburg paradox.

15 さらに読み込む

(b) Let p be a probability that player 2 would choose Rock, and q be a probability that she chooses Paper. Note that her probability of choosing Scissors is written as **1** p q. Under mixed strategy Nash equilibrium, player **1** must be indi¤erent amongst choosing Rock, Paper and Scissors, which implies that these three actions must give him the same expected payo¤**s**. Let u R ; u P ; u S be his expected payo¤**s** by selecting

2 さらに読み込む

(c) Formulate the cost minimization problem (you may denote a target output level by y). Then, solve it and derive the (minimum) cost function, c(w **1** , w 2 , y).
5. Risk Aversion (15 points)
Suppose that a division maker has the vNM utility function, u(x) = ln x.

2 さらに読み込む

where x is a vector of choice variables, and a := (a **1** , ..., a m ) is a vector of
parameters ( パラメータ ) that may enter the objective function and constraint.
Suppose that for each vector a, the solution is unique and denoted by x(a).
◮ A maximum-value function, denoted by M (a), is defined as follows:

34 さらに読み込む

(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).

さらに見せる
2 さらに読み込む

i (p, u) denote the Hicksian demand function of good i and e(p, u) denote
the expenditure function. Then, state the Shephard’**s** lemma.
(c) Using envelope theorem, derive either (a) Roy’**s** identity, or (b) Shephard’**s** lemma. You can assume that the first order conditions guarantee the optimal solution, i.e., ignore the second order conditions.

2 さらに読み込む

(b) Does this production function display increasing, constant, or decreasing re- turns to scale? Explain why.
(c) Formulate the cost minimization problem (you may denote a target output level by y). Then, solve it and derive the (minimum) cost function, c(w **1** , w 2 , y).

2 さらに読み込む