180914 - arcturus9/useful-link GitHub Wiki

< Prospect Theory >

  • four fold of risk

    risk-seeking over low-prob. Gain
    risk-averse over high-prob. Gain
    risk-averse over low-prob. Loss
    risk-seeking over high-prob. Loss

  • U ftn vs V ftn

< Game Theory >

n player
n-tuple of pure strategies -> prob. distribution
pay-off function : expectation of the players (polylinear form in prob.)

  • rational behavior

    A set A of actions from which the decision-maker makes a choice.
    A set C of possible consequences of these actions.
    A consequence function g:A -> C that associates a consequence with each action.
    A preference relation (a complete transitive reflexive binary relation) > on the set C.
    Utility ftn : U : C -> R(real space)

  • strategic game

    Definition 11.1 A strategic game consists of a finite set N (the set of players)
    for each player i of N a nonempty set A_i (the set of actions available to player i)
    for each player i of N a preference relation > i on A = A_j (the preference relation of player i).
    If the set Ai of actions of every player i is finite then the game is finite.

< Survival Game Theory >

  • survival ftn
    S(t) = 1- F(t)

  • Kaplan-Meier estimator
    S(t) = Pi (1 - p_i/n_i)

< 조건 >

  • utility function
    u_p(i) = [0, 1,2,…8,9]
    u_n(i) = [0, -1,-2,…-8,-9] u(i) = u_p(i) + u_n(i)

  • value function
    v_p(i) = u_p(i) v_n(i) = u_n(i) * L v(i) = v_p(i) + v_n(i)

  • realized utility function r(i) = r_p(i) + r_n(i) r_p1(i) = [0,0,0,0, 1,1,1,1, … 9,9,9,9]
    r_p2(i) = [0,0,0,0, 0,0,2,2, … 0,0,18,18]
    r_p3(i) = [0,0,0,0, 0,0,0,4, … 0,0,0,36]

< Result >

  • Effect of Uncertainty

    • uncertainty가 없으면, risk neutral이 optimal 이고,
    • uncertainty가 있으면, loss aversion 이 optimal 이 됨.

  • Comparison of Gain/Loss uncertainty

    • Loss uncertainty는 loss aversion이 optimal이고,
    • Gain uncertainty는 risk-seeking이 optimal이 됨!

  • Effect of Metabolism

    • Metabolism 상황이 좋아지면, optimal risk-preference가 loss aversion 쪽으로 이동

  • Effect of death point

    • d.point이 커지면 risk-seeking이 risk-aversion으로 바뀌기도 한다 (13d)

  • 요약
    (1) No uncertainty --> risk neutural / Both side Uncertainty --> risk averse
    (1) Gain uncertainty --> risk seeking / Loss uncertainty --> risk averse
    (3) Environment Effect (Metabolism)

다음주 할일
< Paper관련 >

  • 관련 선행연구(Game theory, risk preference, agent model) 리스트 작성 및 내용 요약
  • 결과 세부 정리 (강조할 부분 결정, 시각화, 추가 결과 확인)

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