IDC Revision

EX-6

Toolkit

  1. 1a

    The payoff matrix (Player 1 picks row, Player 2 picks column):

    Right Left
    Up (c, 1)(c,\ 1) (1, a)(1,\ a)
    Down (d, 1)(d,\ 1) (2, b)(2,\ b)

    Each cell is (P1's payoff, P2's payoff). Find conditions on a,b,c,da, b, c, d under which (Right, Down) is the unique Nash Equilibrium.
  2. 1b

    Same payoff matrix as 1a. Find conditions under which both (Right, Up) AND (Left, Down) are Nash Equilibria.
  3. 2a

    Two consumers choose between computer Model A or Model B. Consumer 1's base utility: a>0a > 0 from A, 0 from B. Consumer 2's base utility: 0 from A, b>0b > 0 from B. Both receive a network bonus c>0c > 0 if they choose the same model. Construct the payoff matrix.
  4. 2b

    For the technology-adoption game in 2a, find the condition on a,b,ca, b, c under which (A, A) is a Nash Equilibrium.
  5. 2c

    Assume a=b<ca = b < c. Find all Nash Equilibria of the technology-adoption game.
  6. 3a

    Traveller's Dilemma. Two passengers each independently report an integer value x,y∈{180,181,…,300}x, y \in \{180, 181, \ldots, 300\} NIS. Compensation is determined by the lower report, with:

    • Higher reporter → penalised 5 NIS ("greedy")
    • Lower reporter → bonus of 5 NIS ("modest")
    • Equal reports → each gets exactly what they reported

    Give the formal game description: players, strategy spaces, payoff functions.
  7. 3b

    Find all Nash Equilibria of the Traveller's Dilemma and prove uniqueness.
Toolkit used in this assignment
  1. Find pure NE in a matrix by the best-response method — underline each player's best response and look for cells underlined by both.
  2. Prove uniqueness by showing every other strategy profile has a profitable deviation for at least one player.
  3. Coordination games can have multiple NE differing only in which equilibrium is selected — symmetry/Pareto-dominance/risk-dominance helps you predict which.
  4. Iterated-dominance unravelling (Travellers Dilemma) shows that "everyone benefits from coordinating high" is not sufficient for a high outcome to be a NE.