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Consider the following social problem.5 A pedestrian is hit by a car and lies injured on the road. There are n people in the vicinity of the accident. The injured pedestrian requires immediate medical attention, which will be forthcoming if at least one of the n people calls for help. Simultaneously and independently, each of the n bystanders decides whether or not to call for help (by dialing 911 on a cell phone or pay phone).
Each bystander obtains v units of utility if someone (anyone) calls for help. Those who call for help pay a personal cost of c. That is, if person i calls for help, then he obtains the payoff v - c; if person i does not call but at least one other person calls, then person i gets v; finally, if none of the n people calls for help, then person i obtains zero. Assume v > c.
(a) Find the symmetric Nash equilibrium of this n-player normal-form game. (Hint: The equilibrium is in mixed strategies. In your analysis, let p be the probability that a person does not call for help.)
(b) Compute the probability that at least one person calls for help in equilibrium. (This is the probability that the injured pedestrian gets medical attention.) Note how this depends on n. Is this a perverse or intuitive result?
Player 1 has the following set of strategies {A1;A2;A3;A4}; player 2’s set of strategies are {B1;B2;B3;B4}. Use the best-response approach to find all Nash equilibria.
A supplier and a buyer, who are both risk neutral, play the following game, The buyer’s payoff is q^'-s^', and the supplier’s payoff is s^'-C(q^'), where C() is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.
Pertaining to the matrix need simple and short answers, Find (a) the strategies of the firm (b) where will the firm end up in the matrix equilibrium (c) whether the firm face the prisoner’s dilemma.
Consider the two-period repeated game in which this stage game is played twice and the repeated-game payo s are simply the sum of the payo s in each of the two periods.
Two players, Ben and Diana, can choose strategy X or Y. If both Ben and Diana choose strategy X, every earns a payoff of $1000.
The market for olive oil in new York City is controlled by 2-families, Sopranos and Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter New York City olive oil market.
Following is a payoff matrix for Intel and AMD. In each cell, 1st number refers to AMD's profit, while second is Intel's.
Determine the solution to the given advertising decision game between Coke and Pepsi, assuming the companies act independently.
Little Kona is a small coffee corporation that is planning entering a market dominated through Big Brew. Each corporation's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price.
Suppose you and your classmate are assigned a project on which you will earn one combined grade. You each wish to receive a good grade, but you also want to avoid hard work.
Consider trade relations in the United State and Mexico. Suppose that leaders of two countries believe the payoffs to alternative trade policies are as follows:
Use the given payoff matrix for a simultaneous move one shot game to answer the accompanying questions.
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