In class we have spoken about game theory and as an example, Prisoner’s Dilemma. I found an article online that relates to Prisoner’s Dilemma called “The Leaders Dilemma: How to Generate Cooperation at Home or Work”. The article deals with a dilemma which involves companies’ strategies and whether to lead or follow. It can be difficult to go first and be the leader knowing that others competing will just criticize you, correct your flaws, and come up with a similar or better product. Due to this, companies are left to decide whether to come up with a product that is average and has little flaws, or a high-margin one that can backfire. This is what the author calls “The Leader’s Dilemma”.

 The main problem with this game is that the play is sequential, the leader sets his/her output first and then followers choose their best response output based on the leader’s output. It deals with something we haven’t covered in class called the Stackelberg Model. The leaders first choose to make a low-margin or high-margin product and the followers then decide whether they want to match the product or imitate (modify) it. The high-margin product has a payoff two times as large as the low-margin product, and if the follower decides to match the product, the two companies split the profit. If the follower company imitates a high-margin product then it gets all the profit, and if a follower store imitates a low-margin product then the imitation will be of such low quality that it will not profit. So the dominant strategies are for the leader to create a low-margin product and for the follower to match it. This gives them equal payoffs, but payoffs are smaller if the leader made a high-margin product and the follower matched it. Exactly what happens in “Prisoner’s Dilemma.” 

 This chart depicts that scenario:

But if the problem is the fact that the game is played sequentially, the author proposes making the game to be played simultaneously. Simultaneous two-player game theory is exactly what has been covered in class. Now the companies make decisions unaware of the other firm’s actions. There is no pure Nash Equilibrium in this case and both companies are forced to mix strategies since they want to be random and unpredictable. Here is a chart depicting this new scenario:

There must be an equilibrium with mixed strategies and in this game it turns out that at equilibrium player 1 will pick low-margin with probability 2/3 (and high-margin with probability 1/3) and player 2 will pick imitate with probability 1/3 (and match with probability 2/3). Their playoff increases by 33% and so since in the original example their payoff was 1, their new payoffs are 1.33.  

It is very interesting that switching to simultaneous play, being ignorant and not having anything to base your decision on, can improve your payoff. I would have thought that knowing as much as possible of other players would benefit you, but go figure. Companies should in fact not worry or be concerned of what other companies are doing in order to maximize both their payoff and social welfare.    

Resource Link: 

http://mindyourdecisions.com/blog/2008/04/22/the-leaders-dilemma-how-to-generate-cooperation-at-home-or-work/