consider the goldminers during the Gold Rush. There are 250 miners who simultaneously decide which of...

consider the goldminers during the Gold Rush. There are 250 miners who simultaneously decide which of the three plots to go to and mine for gold. It is known to everyone that there will be 2,500 ounces in plot A by Anchorage, 1,500 ounces in plot B by Big Lake and 1000 ounces in plot C by Cold Bay. A miner’s payoff is the number of ounces at the plot he has chosen divided by the number of miners at that plot. Find the Nash equilibrium(ia).

Expert Solution

Solution. At Nash equilibrium, no player can gain by changing his/her strategy given that all the other players' strategy remains unchanged. This means that all the players have played their best possible(giving him maximum gain possible) move in regards to the other players' moves and so any change would leave him worse off comparatively.

In our given situation the miners can go to any of the plots A, B or C. A miner from plot B (suppose) would leave to plot C or A if he gets more gold comparatively. Hence any miner would move to a new plot from an older plot if there is a prospect to higher quantities of gold. At Nash equilibrium no miner(player) changes their plot(position/strategy). Hence at Nash equilibrium, all the miners receive equal quantities of gold.

Total gold = 2500 + 1500 + 1000 = 5000
Total Miners = 250
Miners per ounce = 5000 / 250 = 200

Hence miners in plot A = 2500 / 200 = 125
Miners in plot B = 1500 / 200 = 75
Miners in plot C = 1000 / 200 = 50 Total Miners = 250

Now if any miners change his position from (say) plot B to C he would get less amount than he was getting at plot B due to overcrowding at plot C. Hence no miner would change his position and any change in their positions would leave them worse off.

Hence at Nash Equilibrium, the number of miners

Plot A = 125
Plot B = 75
Plot C = 50

Rahul Sunny answered 2 years ago

Consider a Cournot-competition under incomplete information. Two firms decide their quantity of production simultaneously. The market...

Consider a Cournot-competition under incomplete information. Two firms decide their quantity of production simultaneously. The market price P is determined by P = 100 − (q1 + q2). Assume that firm 1’s per-unit cost is commonly known at zero. On the other hand, firm 2’s per-unit cost is private information and is either at 0 or at 2. Suppose in the firm 1’s belief, the probability of c2 = 0 is 1 3 and the probability of c2 = 2...

Consider someone who is thinking about buying a new car, and trying to decide which one...

Consider someone who is thinking about buying a new car, and trying to decide which one to buy. They plan to use the car mostly for commuting. They live 35 miles from work, and will commute 190 days per year. They know that the cost of gas in the Bay Area is currently around $3.00/gallon, the cost of electricity is around $0.15/kWh. For simplicity, they decide to assume that those prices won’t change, and that inflation will be zero, for...

A car service charges customers a flat fee per ride (which is higher during rush hour...

A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolotian area during rush hour, the flat fee is $3, the cost per minute is $0.20, and the cost per mile is $1.20. Let x be the number of minutes and y the number of miles. At the end of a ride, the driver said that the passenger owed $20.60...

Consider a game in which, simultaneously, player 1 selects a number x ∈ [0, 8] and...

Consider a game in which, simultaneously, player 1 selects a number x ∈ [0, 8] and player 2 selects a number y ∈ [0, 8]. The payoffs are given by: u1(x, y) = 2xy − 8x − x 2 u2(x, y) = 4xy − y 2 (a) Calculate and graph the best responses for each player. (b) What strategies are never played? (c) Find all Nash equilibriums? (d) What is the preferred equilibrium in society? (e) How would we classify...

Consider two events which occur simultaneously in frame S. Will these events be simultaneous in all...

Consider two events which occur simultaneously in frame S. Will these events be simultaneous in all frames S'? Event A occurs before event B in frame S. Will the time ordering of these two events be the same in all frames S'?

Consider a game in which, simultaneously, player 1 selects any real number x and player 2...

Consider a game in which, simultaneously, player 1 selects any real number x and player 2 selects any real number y. The payoffs are given by: u1 (x, y) = 2x − x2 + 2xy u2 (x, y) = 10y − 2xy − y2. (a) Calculate and graph each player’s best-response function as a function of the opposing player’s pure strategy. (b) Find and report the Nash equilibria of the game. (c) Determine the rationalizable strategy profiles for this game.

A television network is attempting to decide during the summer which of the following three football...

A television network is attempting to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama vs. Auburn, Georgia vs. Georgia Tech, Miami vs. Virginia Tech. The estimated viewer ratings (millions of homes) for the games depend on the win-loss records of the six teams, as shown in the following payoff table. Determine the best game (most viewers) to televise using the following decision criteria. States of Nature - Number...

A television network is trying to decide during the summer which of the following three football...

A television network is trying to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama versus Auburn, Georgia versus Georgia Tech, or Army versus Navy. The estimated viewer ratings for the games depend on the win–loss records of the six teams, as shown in the following payoff table: Number of Viewers (1,000,000s) One Team Has Both Teams Winning Record; One Both Teams Have Winning Team Has Losing...

Eastern Engineering Company is trying to decide which of 6 projects to perform during the next...

Eastern Engineering Company is trying to decide which of 6 projects to perform during the next quarter. The net present value, the estimated cost, and the number of engineers and staff personnel required for each project are given in the following table. Project Net Present Value ($1000’s) Cost ($1000’s) Engineers Required Staff Required 1 100 35 5 2 2 145 65 8 3 3 200 95 11 2 4 250 180 4 2 5 500 250 16 7 6 695...

Consider the following game, which might model the “Split-or-Steal” game show. Two players simultaneously choose whether...

Consider the following game, which might model the “Split-or-Steal” game show. Two players simultaneously choose whether to split or steal. If they each choose to split, they each get $50. If one chooses steal and the other chooses split, then the stealer gets $100 and the splitter gets $0. If both choose steal, they each get $0. (a) Assume the players care both about their own monetary earnings and the amount of inequality between their earnings: for a pair of...

Question