Corporate Prisoner's Dielmma

CORPORATE PRISONER’S DILEMMA This is a satire on boss-subordinate relationship in a corporate setting. So, one is expected to not take it seriously (mathematical soundness of the arguments is also open to the debate). I think the setup can be modeled as a strategic game (games people play  ). I will analyze the strategic game and argue the solution in each scenario . The whole setup also lends itself nicely to a discrete Markov Chain; I will come to it later, as I feel, I may loose the satire in too much of mathematical detail. So, back to the corporate world. For an individual in a corporate setting it boils to a two player game he is playing with the boss or his/her subordinate. I am assuming both players, the Boss and the Subordinate are rational to the core, i.e., any action they choose is at-least as good, according to their preferences, as every other available action. Each one can choose a strategy in the game that profits him the most. Available actions to each player are 1.) Dominate the other 2.) Maintain the status quo. Action Dominate other needs some explanation: when boss is in dominating position; it means he is smart and can be serious trouble for subordinate’s butt. When subordinate is in dominating position it means he has got his/her boss’s balls nicely covered. We can see that there are four possible scenarios. We will take each scenario individually and discuss the game. Some Notations: Available Actions for the both players are {Dom, MSQ}, where Dom means action dominate, and MSQ means action maintain status quo. S = strong W= week Definition of Nash Equilibrium(WIKI): If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. In other words, to be a Nash equilibrium, each player must answer negatively to the question: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?"

1.) Scenario; (S, W), Boss is Strong and Subordinate is Week

SUBORDINATE Dom.

BOSS

MSQ

Dom.

(2,-2)

(4,1)

MSQ

(1,-1)

(3,0)

ANALYSIS: Interpreting the payoffs: Payoff (2,-2) in the first cell denotes that, for the action profile [both boss and subordinate choose the action dominate], pay off of the boss is 2 and pay off of the subordinate is -2. It is clear from the payoffs in above figure that for the subordinate action Dom. is dominated by the action MSQ, i.e., it is always profitable for him to choose MSQ over Dom. Given subordinate’s preference Dom is the best strategy for the Boss. So, action profile (Dom, MSQ) is the solution action profile and also a NASH EQUILIBRIUM, i.e., boss chooses Dom, and Subordinate chooses MSQ in this game. In this scenario, if you are the subordinate you are totally screwed. [IF Subordinate can relate to it !! he is poor shod!!]

2.) Scenario; (S, S), Boss and Subordinate both are Strong

SUBORDINATE Dom.

BOSS

MSQ

Dom.

(0,0)

(2,1)

MSQ

(1, 1)

(2.5,2.5)

ANALYSIS: This is the case where both players agree to disagree. Both players respect each others professional competence and know the strategy to dominate will back fire. So, they decide on you scratch my back and I yours. Best scenario for the corporate. Nash Equilibrium is (MSQ, MSQ). [IF Subordinate can relate to it !! he is lucky dog!!]

3.) Scenario; (W, S), Boss is Week and Subordinate is Strong

SUBORDINATE Dom.

BOSS

MSQ

Dom.

(1,2)

(2,1)

MSQ

(1.5, 3)

(1,1)

ANALYSIS: Subordinate knows he has got the boss by balls. The best scenario for the subordinate. This scenario will make the Boss spiritual. Subordinate will have time of his life. Nash Equilibrium exists; though no guarantee how long it will last. Nash Equilibrium is (MSQ, Dom.). [IF Subordinate can relate to it !! he is son of a gun!!]

4.) Scenario; (W, W), Boss and Subordinate both are Week THIS SCENARIO IS NOT WORTH THE EFFORT. NEXT POST WILL RELATE IT TO MARKOV CHAIN!!!