Thursday, October 12, 2023

Bankruptcies and their Infinite Individual Equilibria

I am responding to a critique of my last blog post's characterization of a point (the final landing point) on the x1-x2 plane as an equilibrium.  I still posit that is an equilibrium, and I will build out the game that is bankruptcy, restructuring, and distressed debt, and briefly introduce its game theory to show not only that this past example reached an equilibrium, but furthermore that every bankruptcy ends in an equilibrium.  After all, that's why they exist.

The players of the game are investors, employees, and other third party players.  All players fight on a multidimensional plane to maximize internal rate of return.  US Chapter 11 bankruptcy and the broader legal infrastructure function to meet two main goals of stability in the US credit markets and the turnaround of failing corporations.  They collectively are the master agenda-setter that exists to expediently "right-size" the balance sheet of the debtor and reach a stable equilibrium.  

Mr. Coppock has described an equilibrium as an outcome where no player is incentivized to change behavior.  The players in this game consider their ex-ante expected probabilities of outcomes (often regarding who gets to vote) and find a balanced solution that fits their respective risk preferences.  The rounds of strategic moves by players influence and clarify the probabilities of these outcomes.  The players play the game until an agreement is found at which point the game is played no more: there is no incentive for the players to make any more moves, and an equilibrium is found.  

Friday's "Fun" Fiasco

Last night, I came home from teaching a spin class only to find my roommates arguing about who each of them was going to bring to their sorority date function this Friday night. My friend Charlotte was particularly struggling. She had three options: bring a roommate, a set-up, or one of our guy friends. In a logical (but somewhat superficial way), I suggested she rank her potential dates based on how much fun she thought she would have with each of them. But before I suggested this, our roommates who would also be in attendance at the event cast their ranked votes on who Charlotte should bring (1 being first choice and 3 being last choice): 


                    Roommate    Set-Up    Guy Friend

Sadie                   1                2                3

Cait                     2                3                1

Annika                1                3                2

Grace                  3                1                2

Bella                   2                1                3


Based on what we've discussed in class, I suggested Charlotte use the Borda Method to determine the group's preferences (apparently, she does not care in the slightest herself the outcome...). She assigned a first place ranking 3 points, a second place ranking 2 points, and a third place ranking 1 point. If we look at everyone's totaled preferences:

Roommate: 3 + 2 + 3 + 1 + 2 = 11

Set-Up: 2 + 1 + 1 + 3 + 3 = 10

Guy Friend: 1 + 3 + 2 + 2 + 1 = 9

The Condorcet winner as determined by Borda's Method in this case would be Charlotte bringing one of our lovely roommates...needless to say I am excited to attend the date function on Friday!