# 博弈论代写 | GAME THEORY IN THE SOCIAL SCIENCES Fall 2020 Problem Set 4

这个作业是完成社会科学的游戏博弈理论

GAME THEORY IN THE SOCIAL SCIENCES

Fall 2020

Problem Set 4

1. Equilibria: Consider a two player game in which player 1 can choose

or . The game ends if he chooses while it continues to player 2 if

he chooses . Player 2 can then choose or , with the game ending

after and continuing again with player 1 after . Player 1 then can

choose or , and the game ends after each of these choices. Imagine

that the payoffs following choice by player 1 are (2 0), following

by player 2 are (3 1), following by player 1 are (0 0), and following

by player 1 are (1 2).

2. Veto Power: Two players must choose between three alternatives: ,

and . Player 1’s preferences are given by Â1 Â1 while player

2’s preferences are given by Â2 Â2 . The rules are that player 1

moves first and can veto one of the three alternatives. Then, player 2

chooses which of the remaining two alternatives will be chosen.

3. Entering an Industry: A firm (player 1) is considering entering

an established industry with one incumbent firm (player 2). Player 1

must choose whether to enter or to not enter the industry. If player 1

enters the industry then player 2 can either accommodate the entry,

or fight the entry with a price war. Player 1’s most preferred outcome

is entering with player 2 not fighting, and his least preferred outcome

is entering with player 2 fighting. Player 2’s most preferred outcome

is player 1 not entering, and his least preferred outcome is player 1

entering with player 2 fighting.

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4. Entry Deterrence: NSG is considering entry into the local phone

market in the Bay Area. The incumbent S&P, predicts that a price

war will result if NSG enters. If NSG stays out, S&P earns monopoly

profits valued at $10 million (net present value, or NPV of profits),

while NSG earns zero. If NSG enters, it must incur irreversible entry costs of $2 million. If there is a price war, each firm earns $1

million (NPV). S&P always has the option of accommodating entry

(not starting a price war). In such a case, both firms earn $4 million

(NPV). Suppose that the timing is such that NSG first has to choose

whether or not to enter the market. Then S&P decides whether to

“accommodate entry” or “engage in a price war.”

5. The Stackelberg Leader: Suppose there are two firms (the industry

is a “duopoly”) = 1 2. Each firm’s cost function is given by () =

for all (“unit cost” is constant, equal to for both firms). The

inverse demand function is linear where it is positive, given by

() = ½ − if ≤

0 if

where = 1 + 2 and 1 2. Each firm’s strategic variable

is output, as in Cournot’s model, but the firms make their decisions

sequentially, rather than simultaneously — firm 1 chooses its output,

then the firm 2 does so, knowing the output chosen by the first firm.

What is the subgame perfect equilibrium of this game?

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