Term

Definition
μ=1/n Σ[i=1,n] x_i σ=√(1/(n1) Σ[i=1,n] (x_ix_bar)^2) 


Term

Definition


Term

Definition
1) Complement(AnB) =C(A)uC(B) 2) Complement(AuB)=C(A)nC(B) 


Term

Definition
3) An(BuC)=(AnB)u(AnC) 4) Au(BnC)=(AuB)n(Auc) 


Term

Definition
1) P(A)≥0 2) P(S)=1 3) P(A1uA2u…uAn) = Σ[i=1,n] P(Ai) 


Term

Definition
# of ways of ordering n distinct objects taken r at a time: P[n,r]=n!/(nr)! 


Term

Definition
# of combos of n objects selected r at a time: C[n,r]=(n,r)=n!/(r!(nr)!) 


Term

Definition
The # of ways of partitioning n distinct objects into k distinct groups containing n1,n2,…,nk objects, respectively, where each object appears in exactly one group and Σ[i=1,k] ni=n, is N= (n, n1 n2 … nk)=n!/(n1!n2!...nk!) 


Term

Definition


Term
Multiplicative and Additive Laws 

Definition
P(AnB)=P(A)P(BA) [if A,B are independent, =P(A)P(B)] P(AuB)=P(A)+P(B)P(AnB) [if A,B are mutually exclusive, =P(A)+P(B)] 


Term

Definition
P(A)=Σ[i=1,k] P(ABi)P(Bi) 


Term

Definition
P(BjA) = P(ABj)P(Bj)/(Σ[i=1,k] P(ABi)P(Bi)) 


Term

Definition
E(Y)=μ=Σ[y] yP(y) V(Y)=σ^2=E[(Yμ)^2]=E[Y^2]μ^2 


Term

Definition
Moment: a set of numerical measures that describe or uniquely determine P(Y) under certain conditions The kth moment of the RV Y taken around the origin is E(Y^k) and is written as μ'_k 


Term

Definition
γ_1=(E(Yμ)^3)/σ^3 (γ can be positive, negative or 0/symmetric) kurtosis replaces 3 with 4 


Term

Definition
1) n identical, fixed trials 2) each trial results in 1 of 2 possible outcomes 3) probability of success is p, failure is 1p (aka q) 4) trials are independent 5) R.V. Y is the # of successes 


Term

Definition
P(Y)=(n,y)(p^y)(q^(ny)) E(Y)=np V(Y)=npq 


Term

Definition
1) F(∞)=0 2) F(∞)=1 3) F(*) is nondecreasing in y ST if y1<y2 then F(y1)≤F(y2) 


Term
Rules of noncooperative games 

Definition
1) Players ξ={1,2,…,I} where I≥2 2) Moves, feasible actions Ai=[0,∞) 3) Order of moves: sequential or simultaneous 4) Information: perfect (ie perfect recall) or imperfect 5) Payoffs: preferences over outcomes 


Term

Definition
A complete contigent play (decision rule) that specifies the player's action at every decision node s/he may encounter. Strategy profile: S={s1,s2,…,sI} 


Term

Definition
si€Si is a dominant strategy if u(si,si)>ui(si',sI') A si'€Si, si'≠si and A si€Si 


Term

Definition
si€Si is strictly dominated if E si'€Si ST ui(si',si)>ui(si,si) A si€Si 


Term

Definition
There is an NE for the strategy profile S*={s1*,s2*,…,sI*} if for all i=1,…,I ui(si*,si*)≥ui(si',si*) A si€Si 


Term
BallRomer payoff function 

Definition
u_i = w(m/p,p_i/p)zD_i FOC: W2(1,1)=0, SOC: W22(1,1)<0, W12>0 implies as income increases firms have an incentive to change prices 


Term

Definition
d(Pi*/P)/d(M/P) = W_12/W_22 = π small W12 can be the efficiency wage and large W22 is an extreme example of monopolistic competition 


Term

Definition
PC<z, PC=W(M,Pi*/P) W(M,1) 


Term
BallRomer measure of nominal rigidity 

Definition
the band where price does NOT change is (1x*,1+x*) SO Taylor Approximation is PC≈[(W_12)^2 / 2W_22]x^2 x*=√[(2zW_22)/(W_12)^2] = √(2z/πW_12) 


Term

Definition
Symmetrical Nash Equilibria: S={s€[0,E]V_1(e,e)=0} where: e_i is an agent's action, e is an action that at the SNE where ei*(e)=e, ebar is everyone else's action, V(*) is the payoff function, E is the finite bound to an agent's action ei 


Term

Definition
Symmetric Cooperative Equilibria: S~ ={e€[0,E]V1(e,e)+V2(e,e)=0;V11(e,e)+2V12(e,e)+V22(e,e)<0} where if i) V2(ei,ebar)>0 the game exhibits positive spillovers, ii) if V2(ei,ebar)<0 the game exhibits negative spillovers, iii) if V12(ei,ebar)>0 the game exibits strtegic complementarity, iv) if V12(ei,ebar)<0 the game exhibits strategic substitutability, and v) if dΣej*/dθi>dei*/dθi>δei*/δθi the game exhibits multiplier effects, where θi is a parameter of i's payoff function that we assume to be equal for all i 


Term
strictly dominated mixed strategy 

Definition
mi is S.D. if E mi'€m(si) ST ui(mi',mi)>ui(mi,mi) A mi€Mi (to replace mixed strategies with a pure strategy, substitute mI for si) 


Term
Existence of a Nash Equilibrium 

Definition
Proposition: A NE exists if i) si is nonempty, convex and compact in R^n, ii) ui(s1,…,sI) is continuous in (s1,…,sI) and quasiconcave in si 


Term

Definition
If f(x) is a function of x and f(x*)=x*, then x* is a fixed point 


Term
Brouwer's Fixed Point Theorem 

Definition
Let S C R^n be nonempty, convex and compact and f:S>S be continuous, the there exists x*€S ST f(x*)=x* 


Term

Definition


Term
probability density function 

Definition
f(y)=dF(y)/dy=F'(y) p(a≤y≤b) = integral[a,b]f(y)dy=F(b)F(a) 


Term
E(Y), E[g(y)] (area under a curve) 

Definition
integral [∞,∞] yf(y)dy, integral [∞,∞] g(y)f(y)dy 


Term
Uniform continuous distribution function, also mean & variance 

Definition
f(y) = { 1/(θ2θ1) for θ1≤y≤θ2; 0 otherwise} E(Y)=(θ1+θ2)/2; V(Y)=σ^2=(θ2θ1)^2/12 


Term

Definition


Term

Definition
P(y1y2) = P(y1,y2)/P2(y2), provided p2(y2)>0 f(y1y2) = f(y1,y2)/f2(y2), provided f2(y2)>0 


Term
Indpendence for discrete and continuous random variables 

Definition
Discrete: P(y1,y2)=p1(y1)p2(y2) Continuous: f(y1,y2)=f1(y1)f2(y2) 


Term
COV(Y1,Y2), P(Cov. Coefficient) 

Definition
"COV(Y1,Y2)=E[(Y1μ1)(Y2μ2)]=E[Y1,Y2]μ1μ2, where E[Y1,Y2]=Σ[for all y1]Σ[for all y2] y1y2p(y1,y2), P(Cov. Coefficient) = COV(Y1,Y2)/σ1σ2 If Y1,Y2 are indpendent then COV(Y1,Y2)=0 (BUT converse is not true)" 


Term
Conditional expectation of g(Y1)Y2=y2 

Definition
For jointly continuous Y1, Y2: E(g(Y1)Y2=y2) = integral [∞,∞] g(y1)f(y1y2)dy1; For jointly discrete Y1, Y2: E(g(Y1Y2=y2)=Σ[all y1] g(y1)p(y1y2) 


Term

Definition
A function of the observable random variables in a sample and known constants 


Term

Definition
indentically and independently distributed 


Term

Definition
Central Limit Theorem: Let y1,…,yn be random samples from any distribution with a pop. mean of μ, and variance σ^2, then E(ybar)=μ, V(ybar)=σ^2/n and ybar will have approximately a normal distribution as long as the sample size is iid and sufficiently large, aka ybar~N(μ,σ^2/n) 


Term

Definition

