dominant+strategy

Dominant Strategy:

 * __Introduction:__**

A strategy that is always better than any of the other strategies that is available to a player, regardless of what strategy any other player decides to choose. The classic example is the prisoner dilemma, were two prisoners have to decide to either keep quiet or to rat out a fellow partner in crime in order to better their position. Other examples can be found in TV games shows and even in poker. In addition, all dominant strategy equilibriums are a Nash Equilibrium.

a)** State Governments competing against other states in order to attract businesses to locate in their state. Some recent examples in the news were the Honda and Toyota automobile plants. Several Mid-Western states were offering various incentive packages to lure these companies to locate in their state.
 * Some real world examples of Dominant Strategy are:


 * b)** Unions bargining for better labor contracts with a company for their members.

do not work together the rest of the pack will catch up to them, if one decides to try to lead the entire time, he will likely end up losing since the follower will have more energy at the end due to being sheltered from the wind by the leader. Both will be forced to work together in order to keep their dominant position.
 * c)** Cycle racing where the two lead cyclists must decide when to lead and when to follow, if they


 * __External Links and references:__**

1) Managerial Economics and Business Strategy (5th Edition) – Michael R. Baye 2) [|Game Theory .net] 3) Journal of Economic Education – Spring 1999 Pages 133:140 – Gregory A. Trandel 4) [|Dominance (game theory)] 5) Nash Equilibrium:


 * __Example Multiple Choice Questions:__**

Dominant Strategy is: a) strategies that benefit a player b) strategies that benefit the other players c) strategy with the best results regardless of what other players do d) strategy with the best results only if the other players also choose it
 * QUESTION 1:**

of that the other player does.
 * Answer is c.** The dominant strategy must provide the best benefit available without any regard

There are two ice cream makers in the town of Smallville. One is Bob and Jones (BJ) and one is King of Dairy (KD). They are the only two ice cream makers in this market. Each of them is preparing for the summer ice cream season. For that preparation, they have to choose whether to advertise or to not advertise. The payoffs are below:
 * QUESTION 2:**

__ADVERTISE DECISION BJ, ADVERTISE DECISION KD, PAYOFF BJ, PAYOFF KD__ Advertise, Advertise, 200, 100 Advertise, Don't Advertise, 250, 50 Don't Advertise, Advertise, 50, 250 Don't Advertise, Don't Advertise, 100, 50

Now, do either, or both of them, have a dominant strategy?

(a.) Neither of them have a dominant strategy. (b.) BJ has a dominant strategy, but KD does not. (c.) KD has a dominant strategy, but BJ does not. (d.) They both have a dominant strategy.

advertising. No matter what BJ does, KD is better off advertising.
 * Answer is d.** They both have a dominant strategy. No matter what KD does, BJ is always better off

There is only one musical band in Smallville, called the Funky Bunch (FB). A musician is considering entering the market. His name is Marky Mark (MM). The funky bunch does not like Marky Mark very much, so they are considering whether to launch attack advertisements on television talking about how horrible Marky Mark would be for the music industry.
 * QUESTION 3:**

The payoffs are below:


 * ||  || __FB__ || __FB__ ||
 * ||  || __ATTACK__ || __DO NOT ATTACK__ ||
 * __MM__ || __ENTER__ || 100, 400 || 200, 300 ||
 * __MM__ || __DO NOT ENTER__ || 0, 400 || 0, 500 ||

Question 3A: Does FB have a dominant strategy? If so, what is it? Question 3B: Does MM have a dominant strategy? If so, what is it? Question 3C: What is the payoff for both MM and FB in this example? Question 3D (BONUS): Does this represent a Nash equilibruim?

Question 3A:** FB does not have a dominant strategy. If MM enters, then FB is better off attacking. If MM does not enter, then FB is better off not attacking. off entering the music industry. So the payoff for MM and FB are, respectively, 100, 400. payoff by unilaterally changing his or her strategy, given the other player's strategy.
 * Answers:
 * Question 3B:** MM does indeed have a dominant strategy. No matter what FB does, MM is better
 * Question 3C:** Since MM has a dominant strategy, he will enter. Therefore, FB will choose to attack him.
 * Queston 3D (BONUS):** Yes, this is a Nash equilibrium! Good job! Neither player can improve his or her