HUL311 - APPLIED GAME THEORY MAJOR EXAMINATION (Nov 21, 2017), IITD SEM-I, AY 2017-18, Time Allowed: 2 Hours. (ANSWER ALL, Max marks=30) ANSWER HINTS
Q1: Short Note [5 3 = 15 marks]. You must describe the problem and highlight its solu- × tion with possible realistic implications. (a) Inefficient trade and adverse selection.
Your answer must contain (a) problem description (b) properly de- fined strategies of players (c) equilibrium solution and (d) realistic im- plications - e.g., application of ‘Lemon Market’ in international trade, insurance (with healthy and unhealthy type), second hand car market, etc.
(b) Cournot competition with cost uncertainty.
Your answer must contain (a) problem description (b) properly de- fined strategies of players (q [0, )) (c) showing the best response i ∈ ∞ function in graph with cH and cL and to show respective quantities and profits (d) realistic implications - e.g., credible cost/type revela- tion through advertersing, etc.
(c) Effort choice in study groups.
Your answer must contain (a) problem description (b) properly de- fined strategies of players (c) equilibrium solution and (d) realistic im- plications - e.g., voluntary contribution with type dependent donors - people donates beyond a cost threshold, jumping into the river to save a child - who will jump depend on cost threshold, etc.
1 Q2 [2.5 2 = 5 marks]. ∗ Consider two firms that play a Cournot competition game with demand p = 100 q; and costs 2 − for each firm given by ci(qi) = 10qi (it is known that, q = i=1 qi). Imagine that before the two firms play the Cournot game, firm 1 can invest in cost reduction.P If it invests, the costs of firm 1 will drop to c1(q1) = 5q1. The cost of investment is F > 0. Firm 2 does not have this investment opportunity. (a). Find the value F ∗ for which the unique subgame perfect equilibrium involves firm 1 in- vesting. (b). Assume that F > F ∗. Find a Nash equilibrium of the game that is not subgame perfect.
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8. Credibility and Sequential Rationality 77
Answer: If firm 1 does not invest then they are expected to play the
Cournot Nash equilibrium where both firms have costs of 10 .Each firm solves,
max (100 ( + ) 10) − − which leads to the first order condition
90 2 =0 − − yielding the best response function
90 ( )= − 2 and the unique Cournot Nash equilibrium is 1 = 2 =30with profits