Please enable JavaScript.

Coggle requires JavaScript to display documents.

Chapter 13: Game Theory (Concepts and definitions (Strategy (Strategy: a…

- - - - Payoffs: the benefits received by players from a game's outcome (e.g. profits for firms, utilities for individuals)
      - Game: an interaction between players (people/firms) where players behave strategically
      - Action: a move that the player makes at a specified stage in the game (e.g. out much output a firm produces in current period)
    - - Dynamic game: game in which players move either sequentially or repeatedly
      - Static game: game in which each player acts only once, and players act simultaneously, or act without knowing rivals' actions
- - - - Since firms choose strategies simultaneously, each firm selects a strategy that maximized its profit based on what it believes the other firm will do
      - Firms are playing a noncooperative game of imperfect information
    - - Prisoner's dilemma: A game in which all players have dominant strategies that result in payoffs inferior to what they could achieve with cooperative strategies.
      - Dominated strategy: strategy that produces lower payoff for every possible combination of its rival strategies than some other strategy the play can use.
      - Iterated dominance: Eliminate dominated strategies one at a time.
    - - Best Response: Strategy that maximizes player's payoff given beliefs about rivals' strategies
      - Solution concept where beliefs are consistent with how actual strategies play out
      - All player use best-response strategies to others' best response strategies
  - - - Pure Strategy: each player chooses action with certainty
      - Mixed Strategy: player chooses among possible actions according to probabilities it assigns
    - - π1 = x𝜽 + y(1-𝜽)
        π2 = w𝜽 + z(1-𝜽)
        π1 = π2
        x, y, w, z = some constant
        π1, π2 = expected payoffs for opponent
        𝜽, (1-𝜽) = probabilities of actions
        Pr(1) = 𝜽, Pr(2) = (1-𝜽)
      - Assign a probability to each action
        𝜽 and (1-𝜽)
      - Expected payoff for each strategy has to be equal
        π1 = π2
      - Payoff function is based on probabilities of opponent
- - - - signalling could involve one firm choosing a low quantity to signal to other firm that it wants to cooperate in future so that both firms use low quantities
      - threatening to punish means firms could punish rivals to ensure collusion
  - - - 1) Player 1 moves
      - 2) Player 2 observes player 1's actions, then makes a choice based on observed action
      - 3) Game ends with players receiving payoffs based on their actions
    - - Requires players to believe that their opponents will act optimally, in their own best interests
    - - In a simultaneous move game, firm 1 may not believe in firm 2's announcement of what action it will take, if the action announced is not in the best interest of firm 2.
      - Credible threat: an announced strategy is a credible threat when a rival believes the firm's announced strategy is rational and in the firm's best interest.
      - In a sequential move game, since firm 2 has already performed the action, firm 1 will act based of firm 2's action. Thus commitment makes the threat credible (e.g. burning bridges, where a general burns a bridge behind army so that army can only advance, limiting future options, making itself stronger.)
    - - 2) Determine best response for player who made next-to-last move (given previous best response)
      - 3) Repeat process back to beginning of game
      - 1) Determine best response by last player to move