Price posting model: Sellers post (and commit) price before search activity.
← Straightforward way of endogenous value distribution
• Let start from a simple labor market model where 2 firms (j=A,B) and L workers. • Fi ’s pa off is � = � − � , where y is the marginal revenue (exogenous),
variable is less than or equal to a particular value. e.g., ) The cumulative probability distribution of the high of the next new person. you meet. Cumulative probability : Continuous ra[r]
Binary case: � is the estimator of of y between t=1 and t=0 groups when the effect of other factors (u) is totally equal between groups.3. Heteroskedasticity and Homoskedasticity[r]
• Outside option (value of unemployed) is determined by market tightness and the wage distribution ← market level variable and sufficient to characterize the match level variable (wag[r]
Wage dispersion: Standard mincer equation (wage is explained by education level and labor market experience) cannot explain almost part of the wage variation5. “tru tural u e plo e t: [r]
⇒ We a argue so if it is a rare e e t that e o ser e our urre t sa ple under the null hypothesis; the population mean is equal to � �,0 .
⇒ It’s easure e t is the pro a ilit that e o ser e sa ples hi h ha e ore e tre e ea s tha our urre t sa ple. ⇒ Called as p-value.
2. Definition: equilibrium
• Fi ’s e t de isio -making can be characterized by threshold strategy: a firm entries the market if and only if � ≥ ത�.
• The market equilibrium is defined over { � , � , ത�} and expected utility and profits, which is satisfied
2. Main finding
• The discussion can be extend more general cases; the number of alternative is more than 3 (but still finite number), and/or risk averse agent.
→ The job-acceptance (stopping) probability is generally increasing according to period because the option value is decreasing. (Experimental Evidence)
f (x, a) s.t. g(x, a) = 0.
where x is a vector of choice variables, and a := (a 1 , ..., a m ) is a
vector of parameters that may enter the objective function, the constraint, or both. Suppose that for each vector a, the solution is unique and denoted by x(a).
(c) Derive the competitive equilibrium (both price w ∗ and allocation x ∗ ).
(d) Now consider an exchange economy with n consumers and k goods. We de- note the bundle of total endowments by ω = (ω 1 , . . . , ω k ). Suppose that all
consumers have identical (strictly) convex preferences. Then, show that equal division of total endowments, i.e., x i = ω/n for all consumer i, is always a
j + x j − x i x j , where x i is i’s effort and x j is the effort of the other player. Assume
x 1 , x 2 ≥ 0.
(a) Find the Nash equilibrium of this game. Is it Pareto efficient?
(b) Suppose that the players interact over time, which we model with the infinitely repeated version of the game. Let δ denote the (common) discount factor of the players. Under what conditions can the players sustain some positive effort level k = x 1 = x 2 > 0 over time?
M P 1 : max
q≥0 p(q)q − c(q).
where p(q)q is a revenue and c(q) is a cost when the output is fixed to q. Let π(q) = p(q)q − c(q) denote the revenue function. Assume that the firm’s objective function π(q) is convex and differentiable. Then, the first order condition is:
Decision under Uncertainty | 不確実性下の意思決定
We have so far not distinguished between individual’s actions and consequences, but many choices made by agents take place under conditions of uncertainty. This lecture discusses such a decision under uncertainty, i.e., an environment in which the correspondence between actions and consequences is not
j + x j − x i x j , where x i is i’s effort and x j is the effort of the other player. Assume
x 1 , x 2 ≥ 0.
(a) Find the Nash equilibrium of this game. Is it Pareto efficient?
(b) Suppose that the players interact over time, which we model with the infinitely repeated version of the game. Let δ denote the (common) discount factor of the players. Under what conditions can the players sustain some positive effort level k = x 1 = x 2 > 0 over time?
M P 1 : max
q≥0 p(q)q − c(q).
where p(q)q is a revenue and c(q) is a cost when the output is fixed to q. Let π(q) = p(q)q − c(q) denote the revenue function. Assume that the firm’s objective function π(q) is convex and differentiable. Then, the first order condition is:
Bibliography II
Michal N´ an´ asi, Tom´ aˇs Vinaˇr, and Broˇ na Brejov´ a. The highest expected reward decoding for hmms with application to recombination detection. In Proc. of CPM’10, pages 164–176, 2010.
I. Holmes and R. Durbin. Dynamic programming alignment accuracy. J. Comput. Biol., 5:493–504, 1998.
(c) There are two pure-strategy Nash equilibria: (A; X) and (B; Y ).
(d) Let p be a probability that player 2 chooses X and q be a probability that player 1 chooses A. Since player 1 must be indi¤erent amongst choosing A and B, we obtain
2p = p + 3(1 p) , 4p = 3 , p = 3=4.