Question

Produce an example from your life or career of a situation where you faced a strategic decision along the lines of a game theoretic environment. If you are not comfortable doing that then please construct a reasonable example situation. You must have 2 players in the game you and another entity. The actions of neither player are known with certainty and there is no way to put a probability statement on either strategy. Limit your example to 2 players and 2 strategies. Fully describe the payoffs as you describe your game present your game in a matrix or tabular format such as found in the textbook something like Table 10.2. You might use as your 2 players you and some “group” of people, firms, or society. It is very helpful if the payoffs can be expressed as numbers of some form, but don’t let that stop you. Do not use games of chance with known probabilities or then it isn’t really a game we are talking about. So please don’t write about “One night at the Horseshoe casino….” I am not asking to delve into the details of your life to any degree further than you are willing to share with your classmates. Your example must be different from examples used in class and the payoffs must not be symmetric, i.e. the numbers in the diagonal elements of the matrix should not be equal.

a. Present your game in “tabular” or “matrix” format showing the players, their strategies, and the outcomes.

b. Identify if your game leads to a prisoners’ dilemma type outcome. It may, or it may not.

c. Outline the outcome of the game and the strategies that each player pursued. You don’t have to say whether you “won” or “lost” the game.

d. Was this outcome the “best” for you and the other player combined or was there an outcome where, in some sense, you both collectively would have benefitted more? Fully explain.

Answer 1

Economics as a subject interests me the most because whatever I learn during my course doesn’t just get limited to credits and assignments, but is very much present in my daily activities. One such situation happened to me a few years back involving a fun competition organized in my neighbourhood by students of a management programme as a part of their coursework.

Girls and boys aged 18 to 21 were asked to first write about a consumer good of their choice and how if they became the director a company selling that consumer good, would change the course of business operation to bring in more profits. Ten students were selected. Then among those ten students, an hour long quiz session was conducted testing our general knowledge and aptitude. Even though my GK is not very strong, I managed to scrap through into the finals by just 1 point. My opponent was a year elder to me. Now comes the part which I could relate to step by step as I began to know more about game theory.

My opponent and I were given a challenge to sell 150 units each of a particular product to 150 of our neighbours within a day. There was no rule that we had to sell all 150 of them, but the challenge was to earn higher revenue. But the main problem was that both of us were selling the same product- maybe slightly differentiated versions of it in the same locality. This meant that most likely only one of us would make a sale to each customer because they wouldn’t buy the same thing twice. If I could strategically choose the time and technique of my sale well, they’d rather buy the product from me than from him. This also meant that, whatever decision I took to price my product and whether I’d dare to try out different techniques to make a sale, would directly affect both our sales and vice-versa. The outcome and strategies have been explained in part c) of the question.

The game matrix has been represented in the table below where my payoffs have been bolded in black and his revenues have been italicized and underlined.

a) The matrix is not symmetric because the diagonal elements are different.

	PLAY	DON’T PLAY
PLAY	-20                                        -20	40                             0
DON’T PLAY	0                             70	0                                              0

b) In general, a Prisoner’s Dilemma shows outcomes where players might not cooperate even though cooperation lies in the best interest of both the players. By cooperation here I mean that since both of us earn negative payoffs if we play, it would be best for the both of us to not play the game and earn nothing rather than losing $20. However, asymmetry in games increases the chances of non-cooperation. Here, since I had a chance of earning more revenue than he did, I was more tempted to try and make a sale. Given all his efforts, he’d earn a maximum of $40 but I’d earn $70. I had a higher incentive to move away from cooperation and play. Thus, a situation similar to Prisoner’s Dilemma did arise.

c) We could either enter and “play” the selling-game at the same time, approaching the same houses and applying the same techniques and lose about $20 each. By lose, I mean that my costs of selling would be more than the revenue I would earn by selling and vice-versa. If both of us chose to stay out and “don’t play” to make no sale at all, we’d earn $0. However, if he came into my territory before I could make a sale, he’d earn $40 and I’d earn $0. If I went into selling before he could grab the customers, I’d earn $70 and he’d earn $0. (I’d earn more because I was confident of making better sales than he could, with all his effort). Since I’d earn higher revenues and most likely, I would, because I knew that my opponent was lazy and didn’t like working too hard and would easily give up, it was wise for me to play the game. That meant I would be risking $20, but that risk was low. I was quite sure that since my opponent wouldn’t even more than $40, and was risk-averse, he’d rather stay at home and earn $0 than lose $20. Thus, it was more likely that he’d choose “don’t play”. However, there still was a possibility that he would get all charged up for this game and “play” not to earn $40 but to prevent me from earning $70.

d) This outcome was not the “best” per se. Number wise speaking, it would’ve been wise for us to cooperate and not play the game at all. Then, if either party would've defected and played, the maximum loss to the other was a certain $0 and not more. However, beyond what is visible from the game, since I know I’m the smarter one, with better business acumen, I’d ask him to stay out and would give him $15 from my share of revenues. This way, the risk averse and lazy person that he was, he’d be more than happy to sit at home and relax. I’d make a great sale and earn better revenues. He’d be better off because let alone losing $20, he’d instead earn $15 doing nothing. This was an outcome that we could’ve collectively arrived at and benefitted more. However, this outcome was hypothetical because I'm analyzing the payoffs associated directly with my game that are visible from the matrix. I completely neglected the aspect of prizes to the winner. If he'd be tempted for the bigger picture to win the prize, I doubt if my proposal would work then.